Theoretical analysis and experimental verification on the mechanism of vibration acoustic modulation based on a nonlinear spring model
LIU Xuejun1，YANG Xiaohua1，MA Guangting2，ZHANG Ding1
1.Department of Aviation Mechanism , Qingdao Branch, Naval Aeronautical and Astronautical University, Qingdao 266041, China；
2.The 91899 th of Unit of PLA, Huludao 125001
On line Fatigue Crack Monitoring is an important initiative to ensure the safety of aircrafts. Aiming at the deficiency of the conventional non destructive test method that cannot be achieved online and in situ,the vibroacoustic modulation(VAM) provides an effective method for crack monitoring based on the ultrasonic nonlinearity caused by cracks. A nonlinear spring model was used to simulate the crack and a 1D harmonic wave propagation model in structures with cracks interfaces was established. Approximate expressions of fundamental waves, modulation sideband harmonics and higher harmonics were obtained, and the corresponding relationship between the amplitude of harmonic components and the excitation signal parameters was analyzed. The relationship between the stiffness coefficent and the ratio R of the amplitude of harmonic components to the multiplication of two fundamental waves amplitudes was derived. Through the VAM test on a plate,the relationship between the harmonic components amplitudes and the low frequency vibration amplitudes was analyzed, and the change of index R along with the change of external force was discussed. The experimental results are in good agreement with the results derived from the model. The theoretical guidance was provided for the crack detection using the method of VAM.
刘学君 1，杨晓华 1，马广婷 2，张玎 1. 基于非线性弹簧模型的振动声调制机理研究[J]. 振动与冲击, 2018, 37(10): 233-240.
LIU Xuejun1，YANG Xiaohua1，MA Guangting2，ZHANG Ding1. Theoretical analysis and experimental verification on the mechanism of vibration acoustic modulation based on a nonlinear spring model. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(10): 233-240.
[1] 袁慎芳.结构健康监控[M].北京：国防工业出版社，2007.
YUAN S F. Structural health monitoring and damage control[M]. Beijing: National Defence Industry Press,2007:206-212（in Chinese）
[2] 陈军, 李志浩, 林莉,等. 铝板中Lamb波检测的实验研究[J]. 应用声学, 2011, 30(2):98-104.
CHEN J, LI Z H, LIN L, et al. Experiment investigations of Lamb waves in an aluminum plate [M]. Applied Acoustics, 2011, 30(2):98-104
[3] 孙虎, 周丽. 基于谱元法的裂Lamb纹梁波传播特性研究[J]. 工程力学, 2012, 29(9):50-55.
SUN H, ZHOU LI. Lamb wave propagation in a cracked beam using spectral finite element method [M]. Engineering mechanics, 2012, 29(9):50-55.
[4] 张正罡, 刘丹, 他得安. 多通道超声兰姆波检测板状结构中的裂纹[J]. 应用声学, 2015,34(3):189-194.
ZHANG Z G, LIU D, TA D A. detection of crack in plate structural using multi-channel ultrasonic Lamb waves [M]. Applied Acoustics, 2015,34(3):189-194.
[5] Su Z Q, Zhou L M, Ye L, et al. Lamb Wave Based Monitoring of Fatigue Crack Growth Using Principal Component Analysis[J]. Key Engineering Materials, 2013, 558:260-267.
[6] Yun D S, Choi S H, Kim C S, et al. Imaging of Harmonic Wave Generated by Contact Acoustic Nonlinearity in Obliquely Incident Ultrasonic Wave[J]. Journal of the Korean Society for Nondestructive Testing, 2012, 32(4):362-368.
[7] Kee S H, Zhu J. Surface Wave Transmission across a Partially Closed Surface-Breaking Crack in Concrete[J]. Aci Materials Journal, 2014, 111(1):35-46.
[8] 郑阳, 周进节. 兰姆波在裂纹处的模态转换及散射特性研究[J]. 工程力学, 2014,31(6):21-29.
ZHENG Y, ZHOU J J. Mode conversion and scattering properties of Lamb waves near localized cracking [J]. Engineering mechanics, 2014,31(6):21-29.
[9] Wan X, Tse P W, Xu G, et al. FEM Simulation of Nonlinear Lamb Waves for Detecting a Micro-Crack in a Metallic Plate[M]// Engineering Asset Management - Systems, Professional Practices and Certification. Springer International Publishing, 2015:1561-1569.
[10] Roh Y, Kim B, Lee S, et al. The reflection and transmission of Lamb waves across a rectangular crack as a function of the crack geometry[C]// Ultrasonics Symposium, 2008. Ius. IEEE, 2008:1912 - 1915.
[11] Mishra S, Kumar A, Mishra R K, et al. Structural health monitoring and Propagation of Lamb waves to identification of crack[J]. Fordham Envtl.l.rep, 2015, 126(4):873–875.
[12] Broda D, Staszewski W J, Martowicz A, et al. Modelling of nonlinear crack–wave interactions for damage detection based on ultrasound—A review[J]. Journal of Sound & Vibration, 2014, 333(4):1097-1118.
[13] Pieczonka L, Klepka A, Staszewski W J. Nonlinear vibroacoustic wave modulations for structural damage detection: an overview[J]. Optical Engineering, 2015, 55(1).
[14] Chen B Y, Tay T E. Recent Developments in Modelling of Progressive Damage in Fibre-Reinforced Composites[J]. Applied Mechanics & Materials, 2015, 784:274-283.
[15] Kim S, Adams D E, Sohn H, et al. Crack detection technique for operating wind turbine blades using Vibro-Acoustic Modulation[J]. Structural Health Monitoring, 2014, 13(6):660-670.
[16] 焦敬品, 何存富, 吴斌. 接触缺陷的振动调制超声导波检测技术研究[J]. 声学学报: 中文版, 2009, 34(3):242-248.
JIAO J P, HE C F, WU B. Vibro-modulation and guided wave techniques for contact defect detection in plate[J]. Acta acustica, 2009, 34(3):242-248.
安志武, 王小民, 毛捷,等. 粘接界面的非线性弹簧模型及实验验证[J]. 声学学报, 2010, 35(5):481-487.
AN Z W, WANG X M, MAO J. theoretical and experimental research on nonlinear spring models of a bonding interface[J]. ACTA ACUSTICA, 2010, 35(5):481-487.
[17] Sohn H, Lim H J, Desimio M P, et al. Nonlinear ultrasonic wave modulation for online fatigue crack detection[J]. Journal of Sound & Vibration, 2014, 333(5):1473-1484.
[18] Klepka A, Staszewski W J, Jenal R B, et al. Nonlinear acoustics for fatigue crack detection – experimental investigations of vibro-acoustic wave modulations[J]. Structural Health Monitoring, 2012, 11(2):197-211.
[19] Donskoy D, Sutin A, Ekimov A. Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing[J]. Ndt & E International, 2QR001, 34(4):231-238.
[17]
[18] AN Z W, WANG X M, MAO J. theoretical and experimental research on nonlinear spring models of a bonding interface[J]. ACTA ACUSTICA, 2010, 35(5):481-487.
[19][20] 胡海峰. 板状金属结构健康监测的非线性超声理论与关键技术研究[D]. 国防科学技术大学, 2011:45-50.
HU H F. Research on Theory and Key Technologies of Nonlinear Ultrasonics for Health Monitoring of Plate-like Metallic Structures[D]. National University of Defense Technology,2011:45-50.
[20][21] Pieczonka Ł, Klepka A, Staszewski W J, et al. Analysis of Vibro-Acoustic Modulations in Nonlinear Acoustics Used for Impact Damage Detection - Numerical and Experimental Study[J]. Key Engineering Materials, 2013, 558(558):341-348.
[21] Biwa S, Ishii Y. Second-harmonic generation in an infinite layered structure with nonlinear spring-type interfaces[J]. Wave Motion, 2016, 63:55-67
[22]
[23] Korshak, B.A., Solodov, I. Y., Ballad,E.M. DC effects, sub-harmonics, stochasticity and “memory” for contact acoustic non-lineartiy[J]. Ultrasonics,2002,40(1-8):707-713. SHI Yan, SHU Ge-qun, BI Feng-rong. Acoustic characteristics simulation of engine exhaust muffler based on CFD [J]. Journal of vibration engineering, 2011, 24(2): 205-209.
[24] Nakajima S. On the Acoustic Nonlinearity of Solid-Solid Contact With Pressure-Dependent Interface Stiffness[J]. Journal of Applied Mechanics, 2004, 71(4):págs. 508-515.
[25] 杨晓华, 刘学君, 张玎, 辛志东, . 基于振动声调制的板类结构裂纹定位成像[J/OL]. 北京航空航天大学学报, http://www.cnki.net/kcms/detail/11.2625.V.20161017.0955.007.html
YANG X H, LIU X J, ZHANG D. Localization and imaging of crack damage in plate-like structures based on vibro-acousic modulation [J/OL]. Journal of Beijing University of Aeronautics and Astronautics, http://www.cnki.net/kcms/detail/11.2625.V.20161017.0955.007.html
