15 May 2021, Volume 40 Issue 9
    

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  • HU Jiahui1, WU Hao1, FANG Qin2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 1-11.
    Abstract ( 438 ) Download PDF ( 200 )   Knowledge map   Save
    Under action of explosion load, masonry infilled wall widely used in civil structures can generate fragments to seriously threaten safety of people and equipment inside buildings, especially, under near zone explosion, wall body can cause more serious local damage, and debris can fly faster, but the existing research work is still less.Here, based on near-field explosion tests of ordinary clay fired brick infilled wall, the numerical simulation of damage and dynamic response of masonry infilled wall under near-field explosion was performed.The applicability of the Load Blast method, the arbitrary Lagrange-Eulerian (ALE) method and the impulse method to simulate near-field explosion load and predict wall damage and dynamic response were verified contrastively.The impulse method was used to further discuss effects of explosion distance, bond strength of mortar interface and building block material model under the same proportional distance.The results showed that in near zone explosion, under the same proportional distance, wall body damage usually increases with increase in explosion distance, and develops from local failure to the overall collapse failure mode; the anti-blast performance of wall body is strengthened with increase in bond strength of block mortar, and it is mainly controlled by shear failure stress; the prediction effect of MAT_BRITTLE_DAMAGE model or MAT_WINFRITH_CONCRETE model is better than that of MAT_SOIL_AND_FOAM model.
  • XIONG Chunbao, WANG Meng, YU Lina
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 12-18.
    Abstract ( 498 ) Download PDF ( 102 )   Knowledge map   Save
    In bridge GNSS-RTK deformation monitoring, monitoring signals can be affected by multi-path noise errors.Here, aiming at this problem, a method to combine adaptive EMD (CEEMDAN) and wavelet transform (WT) was proposed to denoise the bridge GNSS-RTK monitoring data.CEEMDAN was used to decompose the bridge’s vibration response, and obtain its intrinsic mode functions (IMFs).Effective IMFs were identified using correlation coefficient.Meanwhile, different wavelet bases in WT were used to perform threshold denoising for remaining IMFs with coexisting noise and signal.Finally, the signal was re-constructed.Through processing simulation test data and the actually measured data of Haihe River cable-stayed bridge based on GNSS-RTK, the results showed that compared with EEMD, CEEMDAN can effectively solve the problem of modal aliasing, the proposed CEEMDAN-WT method has a good noise reduction effect on bridge monitoring data, and can successfully extract bridge real displacement information.
  • LI Wenwu1, QIU Wenliang2, TIAN Tian1, ZHANG Zhe2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 19-29.
    Abstract ( 231 ) Download PDF ( 63 )   Knowledge map   Save
    In order to investigate the seismic behavior of bridge columns reinforced by a partially-embedded core steel tube(BCRPCT), eight circular column specimens with an aspect ratio of 3.0 were designed and tested under cyclic loading conditions.The test variables were core steel tube embedment length and specification, axial load ratio and stirrup ratio.Based on the test observations, the failure mechanism of BCRPCT is revealed.Besides, the effects of the test variables on the lateral load capacity, deformability and strength attenuation of BCRPCT are also evaluated.Test results demonstrate that affected by the core steel tube embedment length or specification, BCRPCT showed three different failure pattrens, namely shear failure or flexural failure at the column mid-height and flexural failure at the column base.With the increase of core steel tube embedment length, the lateral load capacity of BCRPCT was progressively enhanced; however, the deformability exhibited a tend of first increase and then decrease.It is also found that the deformability and the stability of strength attenuation can be improved by increasing the stirrup ratio or decreasing the axial load ratio.At last, on the basis of analysis of the mechanical properties, the practical method for lateral load capacity predition of BCRPCT is suggested through construct the intermediate variable of equivalent aspect ratio.
  • ZHANG Shan1, ZHOU Ding1, HAN Huixuan2, ZHANG Jiandong1, HU Chaobin1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 30-36.
    Abstract ( 433 ) Download PDF ( 72 )   Knowledge map   Save
    Based on the 2-D elasticity theory, natural vibration characteristics of T-beams with a crack were studied using Chebyshev-Ritz method.Firstly, according to the principle of the same strain and the unchanged total internal force, the beam was equivalent to a rectangular cross-section beam composed of two material layers with different characteristics using the transfer section method.Then, the equivalent beam was divided into 4 sub-domains along the crack and layer interface.The natural vibration characteristic equation of each sub-domain was deduced using Rayleigh-Ritz method, and the natural vibration characteristic equation of the whole cracked T-beam was derived with displacement continuity conditions on interfaces of sub-domains.Chebyshev polynomials were applied to construct displacement trial functions of various sub-domains, and the fast convergence solutions were obtained using the orthogonality and completeness of Chebyshev polynomials.The correctness of the proposed method was verified by comparing its solving results with those using the finite element analysis for actual T-beams.Finally, a cracked T-beam fixed at both ends was taken as an example, effects of crack position and its depth on this beam’s natural vibration characteristics were analyzed.
  • AN Huang, ZHAO Rongzhen
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 37-42.
    Abstract ( 190 ) Download PDF ( )   Knowledge map   Save
    Aiming at the problem of the traditional data dimension reduction methods being difficult to consider both the local manifold structure learning and multi-manifold discriminant structure learning, a new algorithm for dimension reduction of a rotor fault data set was proposed based on the correlation-entropy kernel locality preserving multi-manifold discriminant projection (CKLPMDP).The remarkable feature of this algorithm was the correlation entropy measure being used to supervise construction of neighbor graphs.Firstly, the data set was mapped to a high-dimensional kernel space, and then the data set’s local manifold structure and multi-manifold discrimination structure information was comprehensively considered in the kernel space to extract low-dimensional sensitive feature vectors of the optimal characterizing fault data set.The low-dimensional classification effect was visually displayed by using 3-D graphs.Low-dimensional sensitive feature vectors were input into a K-nearest neighbor (KNN) classifier, the class spacing and within class distance in KNN classifier’s recognition rate and clustering analysis were taken as the indexes to measure the effect of dimension reduction.The vibration signal data set of a double-span rotor test platform was used to verify the proposed algorithm.Compared with other typical feature extraction methods, it was shown that the proposed algorithm can extract local manifold and multi-manifold discriminant information more effectively, and have better classification performance in rotor fault recognition.
  • LI Jiawei1, 2, SHEN Yongjun1, 2, YANG Shaopu1, 2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 43-47.
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    The gradient descent method is a classical convex optimization algorithm.Here, combined with the theory of fractional-order advanced calculus, the fractional-order gradient descent method was investigated.It was shown that compared with the conventional gradient descent method, the fractional-order gradient descent method with the order larger than 1 has faster convergence speed and lower convergence accuracy, while it with the order less than 1 has higher convergence accuracy and slower convergence speed.In order to combine advantages of different fractional-order gradient descent methods and solve the contradiction between convergence speed and convergence accuracy, 3 improved variable fractional-order gradient descent methods were proposed based on the published study results to obtain better optimization algorithm performances.Typical examples were taken to verify relevant conclusions.
  • ZHOU Wei, FENG Zhongren, WANG Xiongjiang
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 48-54.
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    In recent years, the status of operational modal analysis in structural parameter identification is gradually rising.Here, aiming at low signal-to-noise ratio (SNR) of structural vibration response under environmental excitation, the auto-regressive (AR) power spectrum was introduced to improve the empirical Fourier decomposition, and a structural operational modal analysis method based on improved empirical Fourier decomposition (EFD) was proposed.In order to verify the feasibility and effectiveness of the proposed method, operational modal parameters of a 4-story simulated frame and a pedestrian cable-stayed bridge were recognized using this method, and the results were compared with those identified using the stochastic subspace identification (SSI).The results showed that modal parameters identified using the proposed method agree well with those identified using SSI; in case of dense modes, this method has certain advantages, so improving empirical Fourier decomposition can provide a reference for future structural modal identification.
  • GAO Chao1, HUANG Chunyue1, LIANG Ying2, FU Yuxiang1, KUANG Bing1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 55-62.
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    The 3-D finite element model for micro-scale chip scale package (CSP) solder joint was established.The model’s stress and strain simulation analyses were performed under bending-vibration composite loading to analyze effects of solder joint material, diameter and height as well as pad diameter on micro-scale CSP solder joint bending-vibration coupled stress and strain.Taking solder joint diameter and height as well as pad diameter as design variables, 17 sets of solder joint models with combinations of different levels were designed, and the maximum bending-vibration coupled stress of the corresponding solder joint was obtained through calculation.Regression equations for solder joint’s bending-vibration coupled stress and structural parameters were established using the response surface method, and solder joint’s structural parameters were optimized using the particle swarm optimization (PSO) method.The results showed that if solder joint material is SAC387, its bending-vibration coupled stress is the maximum; its maximum bending-vibration coupled stress and strain decrease with increase in solder joint height and pad diameter, and increase with increase in solder joint diameter; the optimal level combination of solder joint structural parameters is composed of solder joint diameter 0.18 mm, solder joint height 0.16 mm, and pad diameter 0.15 mm; after optimization, the maximum bending-vibration coupled stress of CSP solder joint drops by 8.49%.
  • ZHANG Haijun, SU He, WU Pei, ZONG Zheying, ZHANG Yong’an, XUE Jing
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 63-70.
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    Numerical computation was performed for airflow regeneration noise in exhaust muffler with split-flow gas hedging, and the correctness of the computation method was verified with tests.Taking the total sound pressure level of airflow regeneration noise as the response value, the test for airflow regeneration noise was designed using the software Design-Expert.According to regression analysis, a mathematical model of total sound pressure level with test factors including diameter of internal cavity, shape and center distance of hedging hole, cone angle of internal cavity split-flow unit as well as airflow speed was established using Box-Behnken test design scheme, and the model’s significance was tested.Influence laws of second-order interaction of different factors on airflow regeneration noise were deeply analyzed.The results showed that with increase in airflow speed, airflow regeneration noise increases significantly, and its gradient is more than 1; shape and center distance of hedging hole have a significant impact on airflow regeneration noise, and when shape of hedging hole is rectangular and center distance of hedging hole is average value, airflow regeneration noise is smaller; cone angle of inner cavity split-flow unit and diameter of inner cavity have smaller influence on airflow regeneration noise; the optimal test conditions are obtained by taking airflow regeneration noise as the optimization index.
  • LU Jinhua, CHEN Xingchong, DING Mingbo, MA Huajun, ZHANG Xiyin
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 71-76.
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    Here, aiming at situations of only one main crack being formed at the bottom of a railway gravity bridge pier with low reinforcement, concrete at the bottom of the pier being not obviously crushed without plastic hinge area formed, and existing obvious rocking phenomenon under dynamic action, a simplified aseismic calculation model for this kind of bridge pier was proposed.It was shown that this model is a 4-spring one of the 2-spring model of a free swing bridge pier added 2 springs for a longitudinal steel bar only under tension.According to the model pier test results, stiffness values of springs only under tension were determined.The calculation results of the 4-spring model under static and dynamic actions were compared with the test ones.It was verified that the 4-spring aseismic analysis model can be used for simplified aseismic calculation of railway gravity bridge pier.
  • YANG Xiongjun, HUANG Jinshan, ZHANG Jianguo, LEI Ying
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 77-83.
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    Here, effective simulation of stochastic fluctuating wind field of transmission tower-line system was investigated.For the transmission tower, only downwind and crosswind fluctuating winds were considered and simplified as two independent 1-D wind fields.For transmission lines, fluctuating winds in cross and vertical directions were considered and simulated as correlated 2-D fluctuating wind fields.Hermite interpolation was used to fit the objective function, and reduce computation amount of Cholesky decomposition of power spectral matrix in the traditional harmonic superposition method.Fast Fourier transform (FFT) technique was also adopted to accelerate the superposition of triangular series.In addition, the spectral representation method of orthogonal random variables was used to express a random function as an orthogonal function with 2 elementary random variables in form of polynomials.Compared with other existing approaches, the number of representative time histories of generated random processes needed after dimension reduction of random variables could be less.Finally, numerical examples verified the high efficiency of the proposed simulation method.
  • ZHANG Ailin1,2,3, ZHU Lina2, ZHANG Yanxia1,2, WEN Wen2, LIN Haipeng2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 84-91.
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    In order to solve problems of insufficient circumferential stiffness and uneven arrangement of notochord grid in traditional cable dome structure, a star shaped tetrahedral cable dome was proposed.The notochord of the cable dome was continuously arranged in the circumferential direction to increase the anti-uneven load ability of the structure.The horizontal projection of the notochord grid was a star shaped monomer with the same projection area to ensure the uniformity of the upper chordal grid and improve the overall stability of the structure.Aiming at the problem of force- finding of the cable dome structure, in order to conveniently acquire distribution law of prestress of each cable pole, the node balance method and the displacement method were used to derive the calculation formula for initial prestress of the structure in the ideal state, calculate initial prestresses of cable struts under different rise-span ratios, deduce the appropriate rise-span ratio and strut height for the structure, and provide a basis for the further study and mechanical performance analysis of the structure.At the same time, the static performance analysis of the structure under the full span uniform vertical load was performed.The results showed that with increase in rise-span ratio and strut height, the internal force of each cable rod gradually decreases, the rise-span ratio of the structure should be 1/10-1/8.5, and the corresponding strut height should be in the range of Δtan 15° to Δtan 20°, thus the structure has stronger load-bearing capacity and good mechanical performance.
  • CHENG Tiedong, YI Qiwen, WU Yiwen, DAI Congcong, CAI Gaipin, YANG Lirong, YIN Baoyong
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 92-101.
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    Here, aiming at the problem of mine micro-seismic and blast vibration signals being difficult to automatically identify, a signal feature extraction method based on improved EWT_MPE (experience wavelet transform _multi-scale permutation entropy)  was proposed, and applied in mine micro-seismic signal feature extraction.Firstly, a new improved method was proposed for the over-segmentation problem of EWT in previous processing complex signal spectra, and the feasibility and correctness of the improved algorithm were verified using simulated signals.Secondly, the actual collected micro-seismic and blast signals were decomposed using the improved EWT, and by means of correlation analysis, the optimal components IMF1-IMF5 were selected from the decomposed IMF (intrinsic mode function) components.The selected IMF components were used to reconstruct a signal, and calculate its MPE value.Finally, the GK fuzzy clustering algorithm was used to classify and identify micro-seismic and blast vibration signals of rock mass.The results showed that micro-seismic signal’s MPE value is smaller than blast signal’s; when the embedding dimension m=5, the scale factor s=12, and the time delay =1, the difference of the two signals’ MPE values is the largest; the classification recognition correctness rate based on the improved EWT_MPE_GK fuzzy clustering algorithm reaches 93.5%, and the average fuzzy entropy (E) is closer to 0, and the classification coefficient (C) is closer to 1; compared with the traditional EWT_MPE_GK fuzzy clustering and EMD_MPE_GK fuzzy clustering, the improved EWT_MPE_GK fuzzy clustering algorithm’s effect is better and its recognition correctness rate rises by 3% and 5.5%, respectively.
  • TANG Qizhi1, XIN Jingzhou1, ZHOU Jianting1, FU Lei2, ZHOU Binfeng3
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 102-109.
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    Aiming at the problem of traditional methods for damage identification being difficult to distinguish multi-damage states and the reliability of prediction results, a method for damage identification was proposed based on autoregressive (AR) model and Gaussian process (GP).It was shown that this method uses AR model to fit acceleration response data of a structure, and for the first time, parameters L1 and L2 are  introduced to characterize the information about damage location and damage level; based on residual and coefficient of AR model, damage sensitivity features for locating damage position and identifying damage degree are established, respectively; GP’s classification algorithm is combined with its regression algorithm to realize multi-damage location and probability output of damage degree.The effectiveness of the proposed method was verified with a numerical simulation example of a reinforced concrete model arch, and the identification results based on AR model’s residual and coefficient were analyzed contrastively.The results showed that the proposed method can identify multi-damage states and output prediction results with probabilistic significance, which is helpful to judge the reliability of the results and realize damage early warning; the identification accuracy and reliability of damage sensitivity feature based on residual are higher with better anti-noise performance; in the case of 10% noise pollution, the relative error mean and discrete coefficient mean of the identification results are only 6.52% and 0.19, respectively.
  • CHEN Xiaoyu1,3, ZHANG Xuhui1,2, ZUO Meng1, FAN Hongwei1,2, WANG Lin1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 110-119.
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    In order to analyze vibration characteristics of an arc-thready nonlinear magnetic coupled piezoelectric energy harvester, the magnetic force model was established by using the magnetizing current method, the energy harvester’s nonlinear recovering force model was obtained using the test data fitting method, and the system’s dynamic equations were established using the generalized Hamilton variation principle.The harmonic balance method was used to solve the system’s dynamic equations, and reveal effects of excitation conditions and magnetic distance on the harvester’s vibration characteristics.The correctness of the theoretical analysis was verified with tests.The results showed that the large-amplitude response bandwidth and response amplitude of the energy harvester increase with increase in excitation intensity; decrease in magnetic distance can increase large-amplitude  response bandwidth, and decrease response amplitude; compared with the energy harvester with a straight beam structure, the harvester with arch-thready structure can increase its output voltage and improve its energy-capturing performance; the study provides a theoretical guidance for designing arch-thready piezoelectric energy harvester, and a new idea for improving its performance.
  • ZHU Yueyue1, HUANG Zhiwei3, XIE Xiling1, ZHANG Zhiyi1,2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 120-124.
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    Here, in order to reduce transmission of lateral vibration of a propulsion shafting system under excitation of propeller, a control method to use active supports was proposed.Active supports were arranged at the position of stern bearing in vertical and horizontal directions to connect stern bearing and hull.Electromagnetic actuator was installed in active supports, and the direct velocity feedback control strategy was adopted.Propeller’s lateral excitation transmitted to hull through stern bearing support was suppressed to reduce hull surface vibration and sound radiation induced by lateral pulse force of propeller.The propeller shafting-active support-hull coupled dynamic model and the hull sound radiation computation model were established.The simulation results showed that active supports have obvious suppression effect on sound power of hull surface under excitation of propeller.The theoretical analysis results were verified with tests.The test results showed that orthogonal active supports can attenuate vibration velocity on hull surface in normal direction caused by shaft end excitation.
  • MIN Wei, YANG Ke, LI Cheng, WANG Hongyu, DUAN Pei
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 125-132.
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    Based on deflection phenomenon of force-displacement curve and phase lag phenomenon of time history curve of a double-outbar pore type viscous damper, the mathematical model for velocity-load characteristics of the viscous damper was established considering shear thinning characteristics and compressibility of dimethyl silicone oil.The mechanical characteristics of the viscous damper under sinusoidal displacement excitation signal were simulated using the software MATLAB Simulink.The results showed that the output damping force of the viscous damper is directly determined by the shear thinning characteristics of dimethyl silicone oil; the compressibility is the main reason for deflection of force-displacement curve of the viscous damper; the test results verifies the correctness of  the above conclusions.
  • ZHU Benrui1, SUN Chao2, HUANG Yan1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 133-141.
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    Aiming at the problem of ice-induced frequency lock-in (FLI) vibration of offshore wind turbine (OWT) in ice area, the ice-induced vibration response analysis was performed, and the wind turbine vibration control method in ice area was proposed based on 3-D pendulum tuned mass damper (3D-PTMD).Based on the self-excited vibration theory of Mttnen-Blenkarn, ANSYS parametric design language (APDL) was used to develop the wind turbine self-excited vibration analysis program in ice area.Based on the blade element momentum theory, considering Prandtl blade-tip loss correction and Grauert correction, the aerodynamic load of wind turbine blade was calculated by using the program developed with MATLAB.The national renewable energy laboratory (NREL) 5 MW offshore monopile wind turbine was taken as an example.Considering the once-in-a-year ice situation in Bohai Sea of our country, the vibration response analyses of the wind turbine structure under different directions of ice-wind combination conditions were performed.The ice speed range for FLI event happening was deduced, and vibration responses of the wind turbine tower with and without 3D-PTMD were compared.The results showed that the ice speed corresponding to FLI happening of the monopile OWT is within the range of 0.01 m/s-0.06 m/s; when ice and wind acting on the turbine structure in the same direction, the ice speed range corresponding to FLI happening of the monopile OWT is the maximum and the vibration response of the tower structure is the maximum; 3D-PTMD can significantly suppress in-plane and out-plane vibration responses of the tower under combined action of ice-wind loads to greatly improve its service safety; the study results can provide a technical support for safe operation of OWTs serving in ice area.
  • YU Zhongyang1,2, ZHANG Hongru1,2, QIU Yanjia1,2, ZHANG Ran1,2, LI Hao1,2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 142-151.
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    With development of underground rail transit in recent years, cross subway stations are widely applied in practical engineering.It is of great significance to understand and improve aseismic performance of such subway stations.Here, for the first time, the shaking table test method was used to study such a subway station structure to reveal propagation characteristics of ground motion in the station area, seismic response characteristics of the station structure, especially, the effects of the station’s cross transfer linkage segment on aseismic performance of the station’s overall structure.Test results showed that propagation of seismic wave is obviously affected by the site’s characteristics, especially, seismic wave’s part with frequencies close to the predominant frequency of the site, the site response spectrum is obviously amplified; with ground motion enhancing, the amplification effect of the site can be weakened, but the distribution of the acceleration response amplification spectrum of the site is more abundant, the spectrum range of the site response is widened and the seismic risk of the station rises; at the same time, under different working conditions, the influence of the interchange segment of the station structure model on the station overall structure is basically within 1.5 times of the structure width; when the distance exceeds this range, the structure model is no longer affected by the interchange segment of the station; compared to the station with a single body, the bottom structure of the cross type station is more unfavorable to earthquake resistance; the above conclusions can provide a strong support for understanding and improving seismic response characteristics of such subway stations and the subsequent aseismic designs.
  • TU Wenbing, LIANG Jie, LUO Ya, ZHOU Jianmin, ZHOU Shengtong
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 152-159.
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    The dynamic effect of moving parts of rolling bearing plays an important role in load distribution and performance of rolling bearing, especially, under variable speed conditions.Here, taking a deep groove ball bearing as the study object, its dynamic model was established considering clearance, centrifugal force and gravity of rolling element, dynamic effect of rolling element and inner race.The operation process of the rolling bearing under acceleration condition was dynamically simulated to analyze dynamic load distribution characteristics of rolling element and their mechanism under the action of radial loads, and effects of clearance, inner race mass and angular acceleration on dynamic load of rolling element were revealed.The study results showed that under acceleration condition, the load distribution curve of rolling element is no longer symmetric along the load action line and has fluctuates with different degrees, especially, in the late stage of acceleration process; the maximum contact load of rolling element basically keeps unchanged in the early stage of acceleration process, but fluctuates and rises in the later stage, and the unstable motion of inner race in acceleration process causes the change of contact load of rolling element; the change degree of dynamic load in acceleration process increases with increase in radial clearance and inner race mass, and increase in angular acceleration makes the change of dynamic load more severe in the later stage of acceleration process; the study results can provide a theoretical basis for load calculation and design of rolling bearing.
  • ZHANG Lei1,2, GAO Peng1,2, YAN Ming1, DU Zhipeng1,2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 160-165.
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    In order to improve the protective capability of isolator of inertial navigation equipment, based on the concept of Stewart platform, an 8-bar isolator was proposed to be able to greatly unload impact load in any direction.The isolator could significantly improve the protection ability of inertial navigation equipment.Firstly, stiffness characteristics of the structure were analyzed, and it was found that its static stiffness is consistent with the theoretical design value.Based on vibration tests, it was concluded that the natural frequency of the structure meets design requirements, and its vibration isolation effect is better.At the same time, based on large number of shock tests and simulation, through analyzing equipment response peaks and isolation rate, it was proved that the structure has better shock isolation performance, and its horizontal direction is more prominent.The simulation and test data were used to draw the structure’s shock response spectrum, it was concluded that the shock isolation ability of the structure in frequency domain is also significant.In summary, it was shown that in time domain and frequency domain, the 8-bar isolator has stronger shock isolation ability; the analysis of structure and shock isolation characteristics of the isolator can provide a reference for optimal design of the isolator.
  • ZHU Limeng, GAO Xiaofei, ZHANG Chunwei
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 166-174.
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    In order to study out of plane anti-impact performance of unwielded steel plate-concrete-steel plate composite shear wall with all bolted joints, its finite element (FE) model was established based on the software ABAQUS and the model effectiveness was verified with the existing test data.Then, effects of impact mass, impact energy, axial compression ratio and cross section form on the wall anti-impact ability were analyzed to acquire its failure mode.The results showed that when the impact energy is the same, the energy dissipated by the wall increases with increase in impact mass; when the impact mass is the same, the change of impact energy can affect the energy absorption ratio of each part of the wall; the smaller axial compression ratio is beneficial to the wall anti-impact ability, the axial compression ratio may not be considered in design and the result is safer; the wall anti-impact performance when the wall end U-steel opening inward is better than that when it opening outward; the anti-impact performance of the wall with split bolt is better than that of the wall with staggered stud; combined with the results of FE analysis, based on the calculation method of beam plastic displacement under impact, the calculation formula of plastic displacement of this wall under out of plane impact load is derived, and its calculation results agree better with the results of FE analysis.
  • LIN Tengjiao, CHEN Menghan, YANG Jin
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 175-183.
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    In order to accurately calculate the meshing stiffness of a herringbone gear pair considering tooth profile modification and load deformation, the tooth surface equation of herringbone gear with tooth crest and tooth root modification was derived.Based on the potential energy method and numerical integration formula, an accurate calculation method for herringbone gear meshing stiffness considering tooth profile modification parameters and undercut width was proposed, and the correctness of the algorithm was verified by finite element simulation analysis.Effects of undercut width, modification parameters and input torque on the coincidence degree and meshing stiffness of herringbone gear pair were analyzed.The results showed that the meshing stiffness of herringbone gear pair increases with increase in width of undercut while the tooth width of single helical gear remains unchanged; with increase in modification amount and length, the coincidence degree and meshing stiffness decrease, while with increase in the order of modification curve, the coincidence degree and meshing stiffness increase, but when the order of modification curve is higher than the 4-order, the meshing stiffness changes little; when the input torque increases, the coincidence degree and meshing stiffness firstly increase and then keep unchanged.
  • LIU Chuncheng, SUN Hongyun
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 184-194.
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    Effects of 3 terrain factors (mountain length, mountain slope and mountain spacing) on wind speed and wind deflection response characteristics of transmission lines in canyon and mountain pass were studied.Horizontal and vertical average wind speeds at each point of transmission lines in canyon and mountain pass were obtained using CFD numerical simulation, and effects of mountain length, mountain slope and mountain spacing on the average wind speed at each point of transmission lines were analyzed.The finite element model of 3-span transmission line across canyon and mountain pass was established.Displacements of each point of the line were calculated by using numerical simulation wind speed and ground wind speed, respectively to obtain the percentage of wind deflection angle increasing.Quadratic regression equations of 3 terrain factors and the percentage of wind deflection angle increasing were established by using the response surface method to analyze effects of terrain factors on wind deflection angle.The results showed that the acceleration effect of canyon and mountain pass on transverse wind is obvious, the wind speed at entrance of mountain is the largest, and the acceleration effect on vertical wind speed is not significant; the longer the mountain and the larger the spacing between mountains, the smaller the percentage of wind deflection angle increasing; with decrease in mountain slope, the percentage firstly increases and then decreases; the sensitivities of 3 terrain factors on the percentage of wind deflection angle increasing, from large to small, are mountain length, spacing and slope; the study results can provide a valuable reference for the anti-wind deflection design of transmission lines under terrain conditions of canyon and mountain pass.
  • YANG Qun1,2,3, WU Qianyun3, JIANG Huimin3, TAO Tao3, LIU Xiaobing1,2,3
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 195-205.
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    In order to study aerodynamic characteristics of tandem multi-square columns, wind pressure coefficient, lift and drag coefficients, and Strouhal number of tandem 2 square columns and tandem 3 square columns with different spacing ratios were studied by using the rigid model pressure measurement wind tunnel test method when Reynolds number was 3.2×104 and the spacing ratio was in the range of 1.2-8.The results showed that the critical spacing ratio of tandem 2 square columns is 3-3.5, and tandem 3 square columns has two critical spacing ratios of 2.5-3 and 3.5-4.Through comparing tandem 2 square columns and tandem 3 square column, it was shown that adding a square column downstream of tandem 2 square columns can significantly affect the aerodynamic characteristics of the original tandem 2 square columns, the absolute values of its average drag coefficient, pulsating lift coefficient and Strouhal number all decrease when the spacing ratio L/D≤3.5, but this reduction effect weakens when the spacing ratio L/D≥4, the distribution of wind pressure is similar to that of the original tandem 2 square columns, but their values are different, their difference is the most obvious when the spacing ratio is 3.5; the aerodynamic force and wind pressure coefficient of the added square column increase suddenly when the spacing ratio is 2.5-3, and vice versa when the spacing ratio is 3.5-4.
  • YAN Banshan1, WANG Xiaopeng1, XI Yanhui1, YE Qin2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 206-211.
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    The vibration of transformer core seriously affects its production quality and service life.Here, aiming at the core vibration problem, a method to add elastic damping interlayer between adjacent transition layers of core was proposed.The finite element method was used to do modal analysis and harmonic response analysis of the core before and after adding damping interlayer, respectively.Vibrations of the core under excitation forces with different frequencies before and after adding damping interlayer were simulated numerically and verified with tests adding damping interlayer.Simulation and test results showed that adding damping interlayer can effectively reduce bending vibration of iron core caused by magnetostriction of silicon steel sheets; increasing thickness and layer number of damping interlayer can make the core vibration reduction effect more obvious; the study results provide a reference for guiding enterprises to produce iron cores with lower vibration.
  • LIU Jianwen1, SHI Chenghua1, LEI Mingfeng1,2, PENG Limin1, LI Xiang1, CAO Chengyong1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 212-220.
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    The differential deformation after construction caused by foundation settlement and adjacent construction disturbance widely exists in the existing metro shield tunnels in China, it has adverse effects on tunnel structural performance during tunnel service period.Based on Hertz non-linear elastic contact theory to simulate wheel-rail contact relationship, considering spatial structure characteristics and mutual contact relationship of vehicle, track, tunnel and surrounding rock, an integrated calculation model of vehicle-rail-tunnel-surrounding rock was established, and the structural dynamic response caused by train operation after shield tunnel heave deformation caused by foundation pit excavation was calculated.The results showed that the tunnel heave deformation aggravates dynamic responses of track structure and tunnel structure; dynamic stress of lining ring joint concrete at edge and center of foundation pit changes sharply; shear force of longitudinal joint bolt at top and bottom of lining arch is greatly affected, while internal force of circumferential bolt at arch waist changes significantly.
  • CAO Yinhang1, LIU Gongmin1, ZHANG Long2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 221-227.
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    Here, the general procedure of the transfer matrix method for pipeline dynamic calculation and the establishment process of the point transfer matrix for the absorption transfer matrix method of arbitrary pipeline branch element were derived firstly, solving dynamic problems of branched pipeline systems was realized, and their correctness was verified by comparing the theoretical calculation results with test ones.Then, based on the selected basic model of branched pipeline design, the uniform design principle was used to select calculation samples, and the transfer matrix method was used to do the sample model calculation.Finally, the second-order polynomial response surface function was used to approximate a regression model, and the genetic algorithm was used to optimize the branched pipeline design.It was shown that adopting the transfer matrix method, the uniform design principle and the mathematical modeling optimization method, calculation cost and resources can be better saved; the study results have a certain guiding significance for branched pipeline design process.
  • DAI Feng
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 228-231.
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    With the development of high integration and high density of electronic equipment, the spacing of bonding wires inside chips becomes smaller and smaller.In harsh vibration environment, bonding wires may have cross, touch short circuit and other reliability problems.Here, aiming at the short circuit problem of a certain chip bonding wire in practical engineering, the natural frequency of the chip’s bonding wire was obtained with theoretical analysis.Establishing the finite element model was used to study the contact problem caused by  bonding wire deformation in random vibration, and the threshold value of the power spectral density of bonding wire contact acceleration was obtained.Finally, the high-speed camera technique was used to do test verification.The results showed that the theoretical and numerical analysis method can accurately obtain the impact contact threshold of bonding wire to provide a reliability criterion for application of bonding wires in vibration environment.
  • YAN Bingsheng1, NIE Shijie1, TANG Baoping2, LIU Ziran1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 232-236.
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    The mechanical properties of 0Cr17Ni4Cu4Nb stainless steel are quite different under the treatment of different aging temperatures.Here, aiming at this problem, a non-linear ultrasonic detection technique was proposed to detect specimens of this stainless steel under treatment of different aging temperatures.By measuring the ultrasonic non-linear coefficient β of the specimens with different aging temperatures, it was shown that β increases with increase in aging temperature.Further, the microscopic observation showed that this steel’s microstructure changes after aging treatment are mainly separating out and growth of precipitated phase; the precipitation amount of precipitated phase also increases with increase in aging temperature.The analysis told that the precipitation amount of precipitated phase of this steel after aging treatment is the main reason for the variation of ultrasonic nonlinear coefficient; the nonlinear ultrasonic detection technique can be used to detect the variation of precipitated phase separated out inside this stainless steel.
  • ZHANG Long1, CAI Binghuan1, XIONG Guoliang1, HU Junfeng2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 237-245.
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    Cycle impact caused by rolling bearing local fault transmitted from bearing to sensor is affected by transmission path, environmental noise and accidental impact interference, which makes fault feature extraction difficult and diagnosis effect poor.Here, a composite fault diagnosis method of rolling bearing based on the maximum correlation kurtosis deconvolution and adjustable quality factor wavelet transform was proposed.The former was used to weaken the influence of transfer path, while the latter was used to suppress noise components with filtering, and their parameter optimizations consistently took the correlated kurtosis, which could consider characteristics of rolling bearing fault impact cycle, as the optimization index to ensure the overall effect of feature extraction.Meanwhile, this index could not be affected by accidental impact interference.Simulated and test signals were analyzed using the proposed method, and the results were compared to those using the common methods, such as, fast spectral kurtosis to verify the effectiveness and superiority of the proposed method in rolling bearing fault diagnosis.
  • SHEN Chao1,2, BO Jingshan1,2, ZHANG Xuedong3, ZHANG Jianyi2, LIANG Jianhui3, QI Wenhao1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 246-253.
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    Under suitable conditions, strong earthquake can cause surface rupture and damage to projects.Avoiding a surface rupture zone caused by seismogenic fault is one of important contents of project site selection.Here, based on the geotechnical centrifugal simulation technology, the process of reverse fault dislocation was successfully simulated in 100g centrifugal field, and surface deformation evolution characteristics of 40 m thick dry sand and wet sand sites during bedrock having different dislocations were obtained.According to test results, the surface deformation process was divided into 4 stages including whole uplift stage, uplift deformation one, scarp translation one and deformation mitigation lag one.Finally, the recommended value of ground surface rupture avoidance distance for strong earthquakes was given.It was shown that the test study and related results here have important theoretical and practical significance for understanding and studying the deformation of soil body caused by dislocation of hidden reverse fault and determining the avoidance distance of surface rupture of seismogenic fault.
  • LI Xiaoqin, ZHANG Tian
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 254-263.
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    Here, in order to establish a calculation method of compressive stiffness recovery factor wc for describing  cracking-closing behavior of concrete under cyclic loading in the concrete damaged plasticity (CDP) model, firstly, the relationship between exponential softening stress and cracking displacement was established based on the cracking fracture energy of concrete, and then the existing calculation models for concrete tensile and compressive damage parameters were evaluated contrastively to choose their calculation models suitable for structural analysis of reinforced concrete (RC) structure, and the calculation model for wc was established based on θ-th power of the ratio of tensile residual fracture energy density to cracking fracture energy density.In this model, effects of element characteristic length and concrete tensile damage parameter on wc were considered, and the value range of the stiffness recovery correction parameter θ was discussed.However, wc could be only defined as a certain constant in CDP model.To overcome this limitation, the severely damaged RC joint member under cyclic loading was taken as the study object, based on the statistical relation between the existing concrete crack features and tensile damage levels, a model simplification handling method was proposed.The RC joint member was divided into two parts of slight damage and damage-failure zones.Several groups of RC joint members under cyclic loading were simulated numerically and their results were compared with test data to verify the correctness of the proposed method and the feasibility of the model simplification handling method.
  • HOU Xingmin, SUN Meng, ZHANG Yilin
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 264-269.
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    P-wave velocity of rock block is an important parameter reflecting rock block’s physical properties, development of internal fissures and cracks, and completeness of rock mass.Accurate measurement of P-wave velocity of rock block is an urgent work in field of rock mechanics.The rock mass wave velocity testing methods mentioned in relevant code have seismic exploration technique, ultrasonic method and so on, while only the ultrasonic method is used in rock block wave velocity testing.Due to different frequencies of vibration wave and ultrasonic one, there is a certain difference between wave velocity values measured with the two methods.Therefore, when the vibration method is used to measure longitudinal wave velocity of rock block, the ultrasonic method is also used to do so, and the obtained rock mass integrity coefficient can’t accurately reflect the completeness of rock mass.Based on the above analysis, here, the vibration method was used to accurately measure longitudinal wave velocity of rock block.Vibration was excited at one end of a rock block, and vibration signals were collected using sensors arranged at both ends of the rock block to obtain its longitudinal wave velocity.The comparison between the measured value of rock block’s longitudinal wave velocity using the vibration method and that using the ultrasonic method showed that the maximum relative error between them is -7.87%.
  • CHEN Xin1, MA Wenting1, HAO Yaodong2, LIANG Hongyu1, HUANG Xiaodi2, MA Fangwu1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 270-277.
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    Gradient porosity structure has a great influence on sound absorption performance of porous materials, and it can broaden sound absorption frequency band of porous materials.Here, elastic porous material with gradient porosity was taken as the study object, and based on Biot theory and the transfer matrix method, effects of common gradient structure and gradient difference on its sound absorption coefficient were studied.The multi-island genetic algorithm (MIGA) was used to search the optimal thickness distribution of its gradient structure.The study showed that through reasonably designing porosity and layer thickness, the sound absorption performance of the expected frequency band can be improved; the gradient structure of porosity from high to low and then from low to high can obviously improve the broad frequency band sound absorption coefficient; the study results have important guiding significance for designing elastic porous materials and their application in acoustic package.
  • ZHANG Weizheng1, ZHAO Pengbo1, ZHANG Zuoli1, LIU Fangmin2
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 278-284.
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    Aiming at complex situation of stress, deformation and vibration of valve plate and valve stem of DN 1500 triple eccentric metal hard seal butterfly valve under multi-physical field coupling, the valve’s fluid-structure interaction characteristics and resonance characteristics under different opening degrees were analyzed by combining ANSYS numerical simulation technique with the traditional empirical formula.The results showed that when the valve is at different opening degrees, flow condition inside the valve is different; the smaller the opening degree, the more disorder the flow condition; with increase in opening degree, the flow condition is relatively stable; when the valve is at 30% opening and 50% opening, valve plate and valve stem are easy to have resonance; when the valve is at 75% opening, stress and deformation of valve plate and valve stem are the maximum; the study results play an important role in operation and safety of large diameter triple eccentric metal hard seal butterfly valve, and also have a certain guiding significance for subsequent structure optimization and avoiding resonance.
  • XU Jianle1,2, CUI Hongyu1, HONG Ming1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 285-291.
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    Because of its good impact resistance, large specific strength and high specific stiffness, grid sandwich panel is widely used in practical engineering.Although the grid sandwich panel structure has excellent sound insulation performance in high frequency band, its sound insulation performance is not ideal in medium and low frequency bands due to the limitation of the mass law.As a kind of periodic structure, phononic crystal has excellent noise suppression performance because of its special band gap characteristics to make elastic wave with specific frequency unable to propagate in a structure.Here, phononic crystal structure was combined with sandwich plate structure to design a kind of phononic crystal sandwich plate structure with excellent sound insulation performance in setting frequency range.Numerical simulation and structural model tests were performed to do verification.It was shown that the designed phononic crystal sandwich plate structure has excellent sound insulation performance.
  • JIANG Wei1,3, WU Ronghua1,2, YUAN Fang1
    JOURNAL OF VIBRATION AND SHOCK. 2021, 40(9): 292-297.
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    Sliding mode control based on improved exponential approach law has characteristics of fast response, strong robustness and strong adaptability, and a wide application prospect in H-bridge inverter control.However, the sliding mode control is a kind of nonlinear control mode, and inevitably exhibits abundant nonlinear dynamic behavior.The stability of the system is closely related to the selection of circuit and control parameters.Here, H-bridge inverter with sliding mode control based on improved exponential approach law was taken as the study object.Firstly, the working process of the system was analyzed, and the discretized model of the system was derived by using the stroboscopic mapping theory.Secondly, the bifurcation diagram was used to observe the evolution process of the system nonlinear dynamic behavior under the action of different control parameters, and the folding chart was used to do verifications one by one.Thirdly, the fast-varying stability theorem was used to analyze the stability of the system, and the study conclusion is completely consistent with that drawn by bifurcation diagram and folding chart analyses.Finally, the study showed that changes of external circuit parameters, such as, input voltage, load resistance and inductance have important effects on the system nonlinear dynamic behavior; the study results can provide a reliable theoretical basis for development, manufacturing and adjusting of H-bridge inverter with sliding mode control based on improved exponential approach law, and have certain theoretical significance and practical engineering value.