基于一阶剪切变形理论和哈密顿原理建立了三层粘弹性夹芯梁结构的有限元模型并对其振动和阻尼特性进行了研究。建模时认为粘弹材料层不可压缩，振动能量是依靠粘弹性层的剪切变形来耗散的。为验证本模型的正确性，将其与解析解作了对比。同时，为了证明本方法的优越性，将其与常用的“实特征模态”、“近似复特征模态”、“钻石法”和“近似法”四种数值方法做了比较。结果表明本方法的精度在这几种数值方法中是最好的。最后，讨论了粘弹性夹芯梁结构参数变化对系统固有频率和损耗因子的影响，得到了一些有工程实际意义的结论。
Abstract
The finite element model for the three-layer viscoelastic sandwich beam is developed based on the first-order shear deformation theory and the Hamilton principle. The vibration and damping characteristics of the viscoelastic sandwich beam are studied. The viscoelastic core of the sandwich beam is considered incompressible, and the vibration energy is dissipated only by the shear deformation of the viscoelastic core. The accuracy and efficiency of the finite element model presented in this paper are verified by comparing with the analytical solutions. The numerical solutions of the presented method, the real eigenmodes (RM) method, the approached complex eigenmodes (ACM) method, the diamante approach (DA) and the asymptotic numerical method (ANM) are compared with the analytical solution. The results show that the presented method has better accuracy and efficiency than those commonly used numerical methods. Finally, the effects of the parameter variation of the viscoelastic sandwich beam on its natural frequencies and loss factors are discussed. Some meaningful conclusions are obtained.
关键词
振动和阻尼特性； /
黏弹夹芯梁；剪切耗能；有限元
{{custom_keyword}} /
Key words
Vibration and damping characteristics /
Viscoelastic sandwich beam /
shear dissipating energy /
Finite element method
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Grootenhuis P. The control of vibrations with viscoelastic materials [J]. Journal of Sound and Vibration, 1970，11(4): 421-433
[2] Marcelo A T. Hybrid Active-Passive Damping Treatments Using Viscoelastic and Piezoelectric Materials: Review and Assessment [J]. Journal of Vibration and Control, 2002, 8:699–745.
[3] Marcelo A T. Experimental analysis of active–passive vibration control using viscoelastic materials and extension and shear piezoelectric actuators. Journal of Vibration and Control, 2010, 17(6) 917–929
[4] Nakra B C. Vibration control in machines and structures using viscoelastic damping [J]. Journal of Sound and Vibration, 1998, 211(3):449-465
[5] Kerwin E M. Damping of Flexural Waves by a Constrained Viscoelastic Layer [J]. Journal of the Acoustical Society of America, 1959, 31(7):952~962
[6] Ditaranto, R.A. Theory of Vibratory Bending for Elastic and Viscoelastic Layered Finite Length Beams [J]. J. Applied Mechanics 1965, 87:881~886
[7] Mead, D.J.and Markus.S. The Forced Vibration of a Three-Layer Damping Sandwich Beam with Arbitrary Boundary Conditions [J]. J. Sound and Vibration 1969, 10(2):163~175
[8] Rao D K. Frequency and loss factors of sandwich beams under various boundary conditions [J]. Mechanical Engineering Science, 1978, 20: 271–282
[9] 李恩奇, 唐国金, 李道奎等. 局部覆盖约束层阻尼梁动力学问题的解析解[J]. 振动与冲击，2007，26（5）：85-89
Li E Q, Tang G J, LI D K, et al. Analytical solution for a beam with partially covered constrained layer dampling [J]. Journal of vibration and shock, 2007，26（5）：85-89
[10]Johnson C D, Kienholz D A. Finite element prediction of damping in structures with constrained layers[J].AIAA J, 1982,120(9):1284-129
[11] Galucio A C, Deu J F, Ohayon R. Finite element formulation of viscoelastic sandwich beams using fractional derivative operators [J]. Computational Mechanics, 2004, 33: 282–291
[12] Kumar N, Singh S P. Vibration and damping characteristics of beams with active constrained layer treatments under parametric variations [J]. Materials and Design, 2009, 30:
4162–417
[13]石银明, 华宏星, 傅志方. 约束层阻尼梁的有限元分析[J]. 上海交通大学学报, 2000, 34(9):1289-1290
Shi Y M, Hua H X, Fu Z F. Finite element analysis of constrained layer damping beams [J]. Journal of shanghai jiaotong university, 2000, 34(9):1289-1290
[14]高淑华,赵阳,李淑娟，等.粘弹性结构动力学分析的等效粘性阻尼算法[J]. 振动与冲击，2005，24（1）：18－27
Gao S H, Zhao Y, Li S J, et al. Equivalent visco-damping method for the dynamic response analysis of visco-elastic structure [J]. Journal of vibration and shock, 2005, 24 (1): 18 – 27
[15] Baber T T, Maddox B A, Orazco C E. A finite element model for harmonically excited viscoelastic sandwich beams [J]. Computers &structures, 1998, 66(1): 105-113
[16]Daya E M, Potier-Ferry M. A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures [J]. Computer Structure, 200179(5):533–41.
[17] Kumar S, Kumar R, Sehgal R. Enhanced ACLD treatment using stand-off-layer: FEM based design and experimental vibration analysis [J]. Applied Acoustics, 2011, 72: 856–872
[18] Bilasse M, Daya E M, Azrar L. Linear and nonlinear vibrations analysis of viscoelastic sandwich beams [J]. Journal of sound and vibration, 2010, 329: 4950-4969
[19] Bilasse M, Charpentier I, Daya E M, Koutsawa Y, A generic approach for the solution of nonlinear residual equations. Part II: homotopy and complex nonlinear eigenvalue method [J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198: 3999–4004.
[20] Abdoun F, Azrar L, Daya E M，Ferry P. Forced harmonic response of viscoelastic structures by an asymptotic numerical method [J]. Computers and Structures, 2009, 87:91–100
[21] Soni M L. Finite element analysis of viscoelastically damped sandwich structures, Shock Vibrat. Bull. 1981, 55 (1):97–109.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(1573 KB)
