基于能量辐射传递法的功能梯度板高频振动响应分析

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (22) : 40-48.

论文

许爱林1,2，代成浩1,2，陈海波1,2

作者信息 +

Analysis on the high-frequency vibration response of a functionally graded plate based on the radiative energy transfer method

XU Ailin1,2，DAI Chenghao1,2，CHEN Haibo1,2

Author information +

文章历史 +

摘要

本文研究的目的是将能量辐射传递法(RETM)推广到功能梯度板模型中，以预测结构的高频振动响应。基于一阶剪切变形理论推导了功能梯度板的振动控制方程，获得了波传播特性参数。在该方法中，结构内部的能量响应由激励产生的直接场与边界虚源产生的反射场叠加得到。在临界频率以下，能量响应由一种传播波控制；而在临界频率以上，由三种传播波控制。数值算例结果与模态叠加法和功率流分析(PFA)进行了对比，验证了RETM在计算不同物理参数下功能梯度板高频振动响应的准确性。研究了不同厚度下剪切变形和转动惯量对能量响应的影响，讨论了材料梯度因子、结构阻尼和激励频率对高频振动能量的影响。结果表明材料梯度因子的变化会导致结构波传播特性和能量分布特征的变化，越大能量的衰减速度越快，衰减幅度越大。

Abstract

The purpose of this study is to generalize the radiative energy transfer method (RETM) to the functionally graded plate model to predict the high-frequency vibration response of structures. Based on the first-order shear deformation theory, the vibration governing equation of functionally graded plate is derived and the wave propagation characteristics are obtained. In this method, the energy inside the structure can be obtained by the superposition of the direct field generated by the real source and the reflection field generated by the boundary virtual sources. Below the critical frequency, the energy response is controlled by a propagating wave; while above the critical frequency, the energy response is controlled by three propagating waves. Numerical results are compared with those calculated by the modal superposition method and power flow analysis (PFA) to verify the accuracy of RETM in calculating the high-frequency vibration response of functionally graded plate under different physical parameters. The influence of shear deformation and rotational inertia on the energy response under different thickness is studied. The effects of material graded factor, structural damping and excitation frequency on high frequency vibration energy are discussed. The study shows that the change of material graded factor will lead to the change of mechanical properties of the plate, and the higher the is, the faster the energy attenuation rate and the greater the attenuation range will be.

导出引用

许爱林1,2，代成浩1,2，陈海波1,2. 基于能量辐射传递法的功能梯度板高频振动响应分析[J]. 振动与冲击, 2023, 42(22): 40-48

XU Ailin1,2，DAI Chenghao1,2，CHEN Haibo1,2. Analysis on the high-frequency vibration response of a functionally graded plate based on the radiative energy transfer method[J]. Journal of Vibration and Shock, 2023, 42(22): 40-48

参考文献

[1] 王用岩. 高频声振耦合分析与疲劳寿命预报方法研究 [D]; 中国科学技术大学, 2016.
[2] KOIZUMI M. FGM activities in Japan [J]. Composites Part B: Engineering, 1997, 28(1): 1-4.
[3] GUPTA A, TALHA M. Recent development in modeling and analysis of functionally graded materials and structures [J]. Progress in Aerospace Sciences, 2015, 79: 1-14.
[4] NIKBAKHT S, KAMARIAN S, SHAKERI M. A review on optimization of composite structures Part II: Functionally graded materials [J]. Composite Structures, 2019, 214: 83-102.
[5] 游进, 孟光, 李鸿光. 声振系统中高频能量流分析法研究进展 [J]. 振动与冲击, 2012, 31(11): 62-69.
YOU J,MENG G,LI H. Review of mid-to-high frequency energy flow analysis method for vibro-acoustic systems [J]. Journal of Vibration and Shock, 2012, 31(11): 62-69.
[6] 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.
[7] 林天然, 李震. 统计能量分析方法及应用综述 [J]. 振动与冲击, 2021, 40(13): 222-238.
LIN T, LI Z. Overview of statistical energy analysis and its applications[J]. Journal of Vibration and Shock, 2021, 40(13): 222-238.
[8] NEFSKE D J, SUNG S H. Power Flow Finite Element Analysis of Dynamic Systems: Basic Theory and Application to Beams [J]. Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1989, 111(1): 94-100.
[9] PARK D H, HONG S Y, KIL H G. Power flow model of flexural waves in finite orthotropic plates [J]. Journal of Sound and Vibration, 2003, 264(1): 203-224.
[10] 王迪, 朱翔, 李天匀, 等. 基于能量有限元法的功能梯度梁振动分析 [J]. 振动与冲击, 2018, 37(03): 119-124.
WANG D, ZHU X, LI T, et al. Vibration analysis of a FGM beam based on energy finite element method. Journal of Vibration and Shock, 2018, 37(3): 119-124.
[11] LE BOT A. Energy Transfer for High Frequencies in Built-up Structures [J]. Journal of Sound and Vibration, 2002, 250(2): 247-275.
[12] LE BOT A. A Vibroacoustic Model For High Frequency Analysis [J]. Journal of Sound and Vibration, 1998, 211(4): 537-554.
[13] LE BOT A. Comparison of vibrational conductivity and radiative energy transfer methods [J]. Journal of Sound and Vibration, 2005, 283(1-2): 135-151.
[14] 周红卫. 高频声振耦合能量有限元若干问题研究 [D]; 中国科学技术大学, 2015.
[15] 钟强. 结构高频声振统计特性及能量辐射传递模型研究 [D]; 中国科学技术大学, 2021.
[16] ZHONG Q, CHEN H, LE BOT A. Radiative energy transfer model for finite anisotropic plates [J]. Journal of Sound and Vibration, 2021, 497: 115947.
[17] TIELIANG Y, WEIGUANG Z, QIBAI H, et al. Sound radiation of functionally graded materials plates in thermal environment [J]. Composite Structures, 2016.
[18] CHEN Y-X, LI F-L, HAO Y-X. Analysis of vibration and sound insulation characteristics of functionally graded sandwich plates [J]. Composite Structures, 2020, 249: 112515.
[19] LOJA M A R, BARBOSA J I. In-plane functionally graded plates: A study on the free vibration and dynamic instability behaviours [J]. Composite Structures, 2020, 237: 111905.
[20] PAPKOV S O, BANERJEE J R. Dynamic stiffness formulation and free vibration analysis of specially orthotropic Mindlin plates with arbitrary boundary conditions [J]. Journal of Sound and Vibration, 2019, 458: 522-543.
[21] 张玲, 朱翔, 李天匀, 等. 功能梯度板的振动功率流特性分析 [J]. 振动与冲击, 2016, 35(16): 187-191.
ZHANG L, ZHU X, LI T, et al. Vibration power flow analysis of functionally graded rectangular plates[J]. Journal of Vibration and Shock, 2016, 35(16): 187-191.
[22] LIU Z, NIU J. Vibrational energy flow model for functionally graded beams [J]. Composite Structures, 2018, 186: 17-28.
[23] JHA D K, KANT T, SINGH R K. A critical review of recent research on functionally graded plates [J]. Composite Structures, 2013, 96: 833-849.
[24] ABRATE S. Functionally graded plates behave like homogeneous plates [J]. Composites Part B: Engineering, 2008, 39(1): 151-158.
[25] NELSON H M. High frequency flexural vibration of thick rectangular bars and plates [J]. Journal of Sound and Vibration, 1978, 60(1): 101-118.
[26] JUNGER M C, FEIT D. Sound, structures, and their interaction [M]. MIT Press, 1972.
[27] PARK Y-H, HONG S-Y. Vibrational power flow models for transversely vibrating finite Mindlin plate [J]. Journal of Sound and Vibration, 2008, 317(3-5): 800-840.