基于层合理论的被动约束层阻尼板有限元建模及动力学分析

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (23) : 148-153.

论文

黄志诚1，王兴国1,吴南星1，褚福磊2，罗经3

作者信息 +

Finite element modeling and dynamic analysis of passive constrained layer damping plate based on laminated theory

HUANG Zhicheng1, WANG Xingguo1, WU Nanxing1, CHU Fulei2， LUO Jing3

Author information +

文章历史 +

摘要

基于层合理论建立了被动约束阻尼板的有限元动力学模型。构造了一种4节点,每个节点5自由度三层板单元用于模拟基板、黏弹性阻尼层和约束层的相互作用。黏弹性材料频率依赖特性用Biot模型描述。借助辅助坐标将其引入到被动约束阻尼板的有限元方程中，并将其转化成常规二阶微分方程形式以简化求解过程。通过算例和实验结果作比较验证了本文方法的有效性。结果表明，与传统的有限元建模理论比较,采用层合理论,减少了结构自由度,并且具有良好的计算精度。

Abstract

The finite element dynamic model of a passive constrained layer damping (PCLD) plate was established based on the laminated theory.A 3-layer plate element with four-node and 5-DOF per node was constructed to simulate interaction among base plate, viscoelastic damping layer and constraint layer.The frequency-dependent properties of viscoelastic material were described with Biot model, and they were introduced into the finite element dynamic equation of a PCLD plate by means of auxiliary coordinates, and then the latter was converted into the ordinary second-order differential equation form to simplify the solving process.The effectiveness of the proposed method was verified with the comparison between numerical examples and test results.Results showed that compared with the traditional finite element modeling theory, using the laminated theory can reduce the structure’s DOF and have good calculation accuracy.

导出引用

黄志诚1，王兴国1,吴南星1，褚福磊2，罗经3. 基于层合理论的被动约束层阻尼板有限元建模及动力学分析[J]. 振动与冲击, 2020, 39(23): 148-153

HUANG Zhicheng1, WANG Xingguo1, WU Nanxing1, CHU Fulei2， LUO Jing3. Finite element modeling and dynamic analysis of passive constrained layer damping plate based on laminated theory[J]. Journal of Vibration and Shock, 2020, 39(23): 148-153

参考文献

[1] Bilasse M, Daya E M, Azrar L. Linear and nonlinear vibrations analysis of viscoelastic sandwich beams. Journal of Sound and Vibration, 2010, 329(23): 4950-4969.
[2]Johnson C D, Kienholz D A. Finite element prediction of damping in structures with constrained viscoelastic layers. AIAA Journal, 1982, 20(9): 1284-1290.
[3]Plouin A S, Balmes E. Pseudo-modal representations of large models with viscoelastic behavior: Proceedings of the society of photo-optical instrumentation engineers   (SPIE), 1998: 3243, 1440-1446.
[4]Soni M L. Finite element analysis of viscoelastically damped sandwich structures. Shock and Vibration Information Center　The Shock and Vibration Bull, 1981, 1: 97-109.
[5]Reddy, J.N. On Refined Computational Models of Composite Laminates. International Journal of Numerical Methods in Engineering, 1989，27,：361-382.
[6]Reddy, J.N. On the Generalization of Displacement-Based Laminate Theories. Applied Mechanics Reviews, 1989，42（11）： 213-222.
[7]Robbins, D. H. and Reddy, J. N. Analysis of Piezoelectrically Actuated Beams Using a Layer—Wise Displacement Theory. Computers & Structures, 1991, 41 (2):265–279.
[8]Park C H, Baz A. Comparison between finite element formulations of active constrained layer damping using classical and layer-wise laminate theory. Finite Elements in Analysis and Design, 2001, 37(1): 35-56.
[9]Moreira R, Rodrigues J D. A layerwise model for thin soft core sandwich plates. Computers & Structures, 2006, 84(19): 1256-1263.
[10] Il-Kwon Oh. Dynamic characteristics of cylindrical hybrid panels containing　viscoelastic layer based on layerwise mechanics. Composites Part B: Engineering，2007，38（2）：159-171
[11] Cetkovic M, Vuksanovic Dj. Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model. Composite Structures, 2009, 88(2): 219-227.
[12] Chien H. Thai, A.J.M. Ferreira, E. Carrera, H. Nguyen-Xuan. Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory. Composite Structures, 2013, 104(10): 196-214.
[13]邓年春, 邹振祝, 杜华军, 等. 约束阻尼板的有限元动力分析. 振动工程学报, 2003,16 (04): 101-104.
       Deng Nianchun, Zou Zhenzhu, Du Hua Jun, Huang Wenhu. A finite element dynamic analysis of constrained plates. Journal of Vibration Engineering, 2003, 16 (04): 101-104.
[14]邓年春，邹振祝，黄文虎. 约束阻尼板的主被动一体化振动控制.机械工程学报，2004，40（3）：128-132.
        Deng Nianchun, Zou Zhenzhu, Huang Wenhu.Research on hybrid control for constrained plates, Journal of Mechanical Engineering, 2004，40（3）：128-132.
[15] Huang Zhi Cheng, Qin Zhao Ye, Chu Fu Lei. Vibration and damping characteristics of sandwich plates with viscoelastic core [J]. Journal of Vibration and Control, 2016, 22(7):1876–1888.
[16] Khalfi B, Ross A. Transient response of a plate with partial constrained viscoelastic layer damping. International Journal of Mechanical Sciences, 2013, 68: 304-312.
[17] 黄志诚，秦朝烨，褚福磊. 基于剪切耗能假设的黏弹性夹芯梁的振动和阻尼特性[J]. 振动与冲击，2015，34（7）：183-191.
         Huang Zhicheng, Qin Zhaoye, Chu Fulei. Vibration and damping characteristics analysis of viscoelastic sandwich beams based on the shear dissipating energy assumption. Journal of Vibration and shock, 2015，34（7）：183-191.
[18] Biot M A. Variational principles in irreversible thermodynamics with application to viscoelasticity. Physical Review, 1955, 97(6): 1463-1469.
[19] Trindade M A, Benjeddou A, Ohayon R. Modeling of frequency-dependent viscoelastic materials for active-passive vibration damping. Journal of Vibration and Acoustics, 2000, 122(2): 169-174.
[20] Bilasse M, Azrar L, Daya E M. Complex modes based numerical analysis of viscoelastic sandwich plates vibrations. Computers & Structures, 2011, 89(23-24): 539-555.
[21]　黄志诚，吴南星，王兴国，褚福磊. Biot本构模型黏弹夹芯梁振动特性分析及其实验研究.振动工程学报，2019，32（2）：199-205.
Huang Zhicheng, Wu Nanxing, Wang Xingguo. Vibration characteristic analysis and experimental study of Biot constitutive model viscoelastic sandwich beam. Journal of vibration engineering, 2019，32（2）：199-205.