Acta Mechanica Solida Sinica

, Volume 23, Issue 4, pp 312–323

# Approximate Solutions for Transient Response of Constrained Damping Laminated Cantilever Plate

Article

## Abstract

Theseries composed by beam mode function is used to approximate the displacement function of constrained damping of laminated cantilever plates, and the transverse deformation of the plate on which a concentrated force is acted is calculated using the principle of virtual work. By solving Lagrange’s equation, the frequencies and model loss factors of free vibration of the plate are obtained, then the transient response of constrained damping of laminated cantilever plate is obtained, when the concentrated force is withdrawn suddenly. The theoretical calculations are compared with the experimental data, the results show: both the frequencies and the response time of theoretical calculation and its variational law with the parameters of the damping layer are identical with experimental results. Also, the response time of steel cantilever plate, unconstrained damping cantilever plate and constrained damping cantilever plate are brought into comparison, which shows that the constrained damping structure can effectively suppress the vibration.

## Key words

constrained damping cantilever plate damping laminated plate transient response beam mode function combination

## References

1. [1]
Johnson, C.D. and Kienholz, D.A., Finite element prediction of damping in structures with constrained layers. AIAA J, 1982, 20(9): 1284–1290.
2. [2]
Cupial, P. and Niziol, J., Vibration and damping analysis of a three-layered composite plate with a viscoelastic mid-layer. Journal of Sound and Vibration, 1995, 183(1): 99–114.
3. [3]
Qian, Z.D., Cheng, G.P. and Zhu, D.M., Vibration analysis of plate attached to constrained damping laye. Journal of Nanjing University of Aeronautics & Astronautics, 1997, 29(5): 517–522 (in Chinese).Google Scholar
4. [4]
Gui, H.B., Vibration and Damping Analysis of Stiffened Plate with Viscoelastic Damping Treatment. Dalian: Dalian University of Technology, 2001 (in Chinese).Google Scholar
5. [5]
Wang, H.C. and Zhao, D.Y., Dynamic analysis and experiment of viscoelastic damped sandwich plate. Journal of Ship Mechanics, 2005, 9(4): 109–118 (in Chinese).Google Scholar
6. [6]
Hu, M.Y. and Wang, A.W., Free vibration and transverse stresses of viscoelastic laminated plates. Applied Mathematics and Mechanics, 2009, 30(1): 101–108 (in Chinese).
7. [7]
Tang, G.J., Li, E.Q. and Li, D.K. et al., Semi-analytical dynamics solution of constrained layer damping plate. Chinese Journal of Solid Mechanics, 2008, 29(2): 149–156 (in Chinese).Google Scholar
8. [8]
Liu, T.X., Hua, H.X. and Shi, Y.M. et al., Analysis of dynamic behavior of sandwich plate with constrained layer damping structure. Engineering Mechanics, 2002, 19(6): 98–103 (in Chinese).
9. [9]
Wang, J.S. and Wu, Y.S., Vib-acoustic analysis of viscoelastic composite sandwich plates with transversely deformable core. Journal of Vibration and Shock, 2006, 25(5): 6–9 (in Chinese).Google Scholar
10. [10]
Cao, Z.Y., Vibration Theory of Plates and Shells. Beijing: The Railway Publishing House, 1989: 445–452 (in Chinese).Google Scholar
11. [11]
Rao, D.K., Frequency and loss factor of sandwich beams under various boundary conditions. Journal of Mechanical Engineering Science, 1978, 20: 271–282.
12. [12]
Mao, L.W., Dynamic Characteristics Analysis of Viscoelastic Laminated Plate. Wuhan: Naval University of Engineering, 2009 (in Chinese).Google Scholar