Modal density calculation of finite length waveguide structure based on 2.5D finite element method

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (5) : 90-98.

ZHANG Shumin1, SHENG Xiaozhen2, YANG Shijun3

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Abstract

Modal density is one of the main parameters of the statistical energy analysis subsystem, which reflects the energy storage capacity of a vibration system. The accuracy of the modal density can directly influence the prediction accuracy of a subsystem. Group velocity is the speed of the energy of propagation wave, which is an important parameter to study the wave characteristics. In this paper, the dispersion curve of the waveguide structure is firstly calculated based on the two-and-half dimensional finite element method. Different waves are categorized by the concept of wave assurance matrix, and expression of the group velocity of different waves is given. Formulations of the total modal density and different characteristic waves are derived. The wave characteristics and modal density are analyzed and calculated for a single panel and an extruded aluminum panel. Results show that with the increase of frequency, the modal density calculated by the method proposed in this paper agrees well with other methods. At cut-on frequencies, the group velocity is zero and the modal density tends to infinite, but the average modal density in the frequency band is a finite value. The group velocity and modal density may become negative near some cut-on frequencies, which means the propagation direction of the waves and the energy of waves are opposite. The modal density of different waves can be obtained after categorized. Some results can provide reference basis for dividing the subsystems of the statistical energy analysis.

Key words

modal density / group velocity / dispersion curve / waveguide / 2.5D finite element method

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ZHANG Shumin1, SHENG Xiaozhen2, YANG Shijun3. Modal density calculation of finite length waveguide structure based on 2.5D finite element method[J]. Journal of Vibration and Shock, 2022, 41(5): 90-98

References

[1] Lyon R H, Dejong R G. Theory and application of statistical energy analysis [M], Butterworth-Heinemann (1995), London.
[2] 姚德源, 王其政. 统计能量分析原理及其应用 [M]. 北京: 北京理工大学出版社, 1995.
YAO Deyuan, WANG Qizheng. Principle and application of statistical energy analysis [M]. Beijing University of Technology Press (1995), Beijing.
[3] Jean-Loup Christen, Mohamed Ichchou, Bernard Troclet, Olivier Bareille, Morvan Ouisse. Global sensitivity analysis and uncertainties in SEA models of vibroacoustic systems[J]. Mechanical Systems and Signal Processing, 2017, 90.
[4] Xie G, Thompson D J, Jones C J C. Mode count and modal density of structural systems: relationships with boundary conditions[J]. Journal of Sound and Vibration, 2004, 274(3-5):621-651.
[5] Langley R S. The Modal Density and Mode Count of Thin Cylinders and Curved Panels[J]. Journal of Sound and Vibration, 1994, 169(1):43-53.
[6] Erickson L L. Modal densities of sandwich panels: theory and experiment[J]. The Shock and Vibration Bulletin, 1969, 39(3): 1-16.
[7] Clarkson B L, Ranky M F. Modal density of honeycomb plates[J]. Journal of Sound and Vibration, 1983, 91(1):103-118.
[8] Renji K, Nair P S, Narayanan S. Modal density of composite honeycomb sandwich panels [J]. Journal of Sound and Vibration, 1996, 195(5):687-699.
[9] Clarkson B L. The derivation of modal densities from point impedances[J]. Journal of Sound and Vibration, 1981, 77(4):583-584.
[10] Clarkson B L, Pope R J. Experimental determination of modal densities and loss factors of flat plates and cylinders[J]. Journal of Sound and Vibration, 1981, 77(4):535-549.
[11] Zhang J, Xiao X, Sheng X, et al. SEA and contribution analysis for interior noise of a high speed train[J]. Applied Acoustics, 2016, 112:158-170.
[12] 伍先俊, 程广利, 朱石坚. 低阻尼板结构模态密度测试方法[J]. 振动与冲击, 2006(03): 159-161+168+214.
WU Xianjun, CHENG Guangli, ZHU Shijian. A test method of the modal density of lightly damped plate structure [J]. Journal of Vibration and Shock, 2006(03): 159-161+168+214.
[13] 宋继强, 王登峰, 马天飞, 卢炳武, 轧浩. 汽车车身复杂子结构模态密度确定方法[J]. 吉林大学学报(工学版), 2009, 39(S2):269-273.
Song Jiqiang, WANG Dengfeng, MA Tianfei, et al. Calculation method of auto body complex sub-structure modal density [J]. Journal of Jilin University (Engineering and Technology Edition), 2009, 39(S2): 269-273.
[14] Keswick P R, Norton M P. A comparison of modal density measurement techniques[J]. Applied Acoustics, 1987, 20(2):137-153.
[15] Langley R S. On the Modal Density and Energy Flow Characteristics of Periodic Structures[J]. Journal of Sound and Vibration, 1994, 172(4):491-511.
[16] Cotoni V, Langley R S, Shorter P J. A statistical energy analysis subsystem formulation using finite element and periodic structure theory[J]. Journal of Sound and Vibration, 2008, 318(4-5):1077-1108.
[17] Aalami, B. Waves in Prismatic Guides of Arbitrary Cross Section[J]. Journal of Applied Mechanics, 1973, 40(4):72-72.
[18] Gavri L. Computation of propagative waves in free rail using a finite element technique[J]. Journal of Sound and Vibration, 1995, 185(3):531-543.
[19] Kishori, Lal, Verma. Wave propagation in laminated composite plates[J]. International Journal of Advanced Structural Engineering, 2013.
[20] Kim H, Ryue J, Thompson D J, et al. Application of a wavenumber domain numerical method to the prediction of the radiation efficiency and sound transmission of complex extruded panels[J]. Journal of Sound and Vibration, 2019.
[21] Renno J M, Mace B R. On the forced response of waveguides using the wave and finite element method[J]. Journal of Sound and Vibration, 2010, 329(26): 5474-5488.
[22] Renno J M, Mace B R. Calculating the forced response of two-dimensional homogeneous media using the wave and finite element method[J]. Journal of sound and vibration, 2011, 330(24): 5913-5927.
[23] Finnveden S. Evaluation of modal density and group velocity by a finite element method[J]. Journal of Sound and Vibration, 2004, 273(1-2):51-75.
[24] Sheng X, Jones C J C, Thompson D J. Modelling ground vibration from railways using wavenumber finite- and boundary-element methods[J]. Proceedings of the Royal Society A, 461 (2005) 2043-2070.
[25] Wolf, J. Investigation of Lamb waves having a negative group velocity[J]. Journal of the Acoustical Society of America, 1988, 83(1):122-126.
[26] Yu C. Negative group velocity for waves in a plate[J]. Tsinghua Ence and Technology, 1996, 1(3): p. 250-252.
[27] Mace B R, Manconi E. Wave motion and dispersion phenomena: Veering, locking and strong coupling effects[J]. Journal of the Acoustical Society of America, 2012, 131(2):1015-1028.
[28] Zhang S, Sheng X, Yang S, et al. Improving the double-exponential windowing method to identify modal frequencies and damping ratios of dynamically large structures[J]. Journal of Sound and Vibration, 2020, 476:115314.