Biot model parametric determination of viscoelastic material and its application in viscoelastic damping structure
HUANG Zhicheng1, WU Nanxing1, WANG Xingguo1, CHU Fulei2
1. College of Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333000, China;
2. Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
Abstract：The viscoelastic materials are widely used to reduce vibration and noise in Engineering. The study of its constitutive model has important significance for the dynamic analysis of viscoelastic composite structure. The Biot constitutive model can describe the frequency dependent dynamic behavior of the viscoelastic materials. A method for determining its parameters and combining into the finite element dynamic equation of viscoelastic damping structure is presented. In the method, the multi - parameter nonlinear curve fitting of the viscoelastic material storage modulus and loss factor data in the frequency domain is carried out. It can be transformed into a nonlinear optimization problem with constraints in the complex frequency domain, which can greatly simplify the nonlinear multi-parameter determination problem. The Biot model of viscoelastic material is introduced into the finite element dynamic equation of viscoelastic damping structure by means of auxiliary dissipative coordinates, and then converted into a conventional second-order linear differential equation, which simplifies the solution. Finally, the method is validated by experimental research. The results show that the method proposed here is correct, simple and effective.
黄志诚1，吴南星1，王兴国1,褚福磊2. 黏弹性材料Biot模型参数确定及其在黏弹阻尼结构中的应用[J]. 振动与冲击, 2020, 39(17): 70-75.
HUANG Zhicheng1, WU Nanxing1, WANG Xingguo1, CHU Fulei2. Biot model parametric determination of viscoelastic material and its application in viscoelastic damping structure. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(17): 70-75.
[1] 李军强 ,刘宏昭 , 王忠民. 线性粘弹性本构方程及其动力学应用研究综述[J].振动与冲击 , 2005,24(2):116－121.
Li Junqiang, Liu Hongzhao, Wang Zhongmin. Review on the liner constitutive equation and its dynamics applications to viscoelastic materials [J]. Journal of vibration and shock, 2005, 24(2): 116－121.
[2] 周光泉，刘孝敏.粘弹性理论[M].合肥:中国科技大学出版社，1996
Zhou Guangquan, Liu Xiaoming. Viscoelastic theory [M]. Hefei: University of Science and Technology of China press, 1996
[3] Shen I.Y. Hybrid damping through intelligent constrained layer treatments [J]. J. Vibration and Acoustics, 1994, 116(3):341-349
[4] A.M.Baz. Optimization of energy dissipation characteristics of active constrained layer Damping [J].J of Smart Material and Structures, 1997, 6(3): 360- 368
[5] 杨挺青.粘弹性力学[M].武汉:华中理工大学出版社,1990
Yang Tingqing. Viscoelasticity [M]. Wuhan: Central China Polytechnic University Press, 1990
[6] Ronald L Bagley. Fractional Calculs - A Different Approach to the Analysis of Viscoelastically Damped Structures [J]. AIAA Journal, 1983, 21(5): 741- 748
[7] Ronald L Bagly, Peter J Torvik. Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures [J]. AIAA Journal, 1985, 23(6): 918-925
[8] Ronlad L Bagley, Calico R A. Fractional Order State Equations for the Control of Viscoelatically Damped Structures [J]. Journal of Guidance Control & Dynamics, 1991, 14(2): 304-311.
[9] Golla, D. F. and Hughes P.C. Dynamics of viscoelastic structure- a time-domain, finite element formulation [J]. ASME Journal of Applied Mechanics, 1985, 52 (4): 897-906.
[10] McTavish DJ, Hughes PC. Finite element modeling of linear viscoelastic structures: the GHM method[C]. 33rd structures, structural dynamics and materials conference, Dallas, TX, U.S.A. p. 1753–63.
[11] McTavish D.J., Hughes P.C. Modeling of linear viscoelastic space structures[J]. ASME Journal of Vibration and Acoustics, 1993, 115 (1): 103-110.
[12] Jianlian Cheng, Xudong Qian. Temperature-dependent viscoelastic model for asphalt concrete using discrete rheological representation [J]. Construction and Building Materials, 2015, 93:157-165.
[13]Park S W. Analytical modeling of viscoelastic dampers for structure and vibration control [J]. International Journal of Solids and Structures, 2001, 38(44-45):8065-8092
[14] Bagley R L, Torvik P J. Fractional calculus-a different approach to the analysis of viscoelastically damped structures [J].AIAA J, 1983, 21 (5):741-748
[15] 张亮, 杜海平, 石银明, 史习智. ZN-1型粘弹性材料的GHM模型参数确定(英文) [J]. 稀有金属材料与工程, 2002, 31(2): 92-95.
Zhang Liang, Du Haiping, Shi Yinming, Shi Xizhi. Parametric Determination for GHM of ZN-1 Viscoelastic Material [J]. Rare metal materials and engineering, 2002, 31(2): 92-95.
[16] M.A.Biot. Variational principles in irreversible thermodynamics with application to viscoelasticity [J]. Physical Review, 1955, 97(6): 1463-1469.
[17] GUO Xu, JIANG Jun. Passive vibration control of truss-cored sandwich plate with planar Kagome truss as one face plane.2011, 54(5):1113-1120.
[18] J. Zhang, G. T. Zheng. The Biot model and its application in viscoelastic composite structures [J]. Journal of Vibration and Acoustics, 2007, 129(5): 533-540.
[19]Drozdov A D. Mechanics of viscoelastic solids [M]. Chichester: John Wiley Sons, 1998.
[20] 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 Zhi-cheng，QIN Zhao-ye，CHU Fu-lei. Vibration and damping characteristics analysis of viscoelastic sandwich beams based on the shear dissipating energy assumption [J]. Journal of vibration and shock, 2015，34（7）：183-191.
