Nonlinear Superharmonic Resonance of Damped Circular Sandwich Plates with Initial Deflection

Abstract:

The nonlinear superharmonic resonance phenomenon of damped circular sandwich plates under uniform load is investigated. From the movement equation of circular sandwich plate showed in displacement components, got the relevant nonlinear vibration equation by Galerkin method. Under the clamped BC. Using multi-scale method, the periodical solutions were obtained which was of nonlinear the third-order superharmonic resonance. The FRF equation of the superharmonic resonance is obtained, and the necessary and sufficient condition on stability of the vibration are obtained synchronously.The infection to the amplitude while the correlative physical and geometric parameters changing were discussed, Drew the trajectories in moving phase planes during the stabilization process, and the stabilities and singularities of the solutions are analyzed.

• Periodical: Advanced Materials Research (Volumes 199-200)
• Pages: 1080-1083
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.199-200.1080
• Online since: February 2011
• Authors: Guo Jun Du, Xiao Man Liu, Yu Da Hu, Chao Yu
• Keywords: Circular Sandwich Plate, FRF, Multi-Scale Method, Nonlinear Vibration, Superharmonic Resonance

References

[1] Liu Renhuai, Li Dong, Yuan Hong: Journal of Vibration Engineering, Vol. 18 (2005), p.395(in chinese).

[2] Chen Chunsheng: Applied Acoustics, Vol. 63(2002), pp.939-956.

[3] Abde Rahman: Shock and Vibration, Vol. 10(2003), pp.301-312.

[4] Chung J: J. of Sound and Vibration, Vol. 231(2000), pp.375-391.

[5] Naidu N.V., Sinha P. K: Composite Structures, Vol. 77(2007), pp.475-483.

[6] Li Yinshan, Zhang Haimei, Yang Guitong: Appl. Math. & Mech, Vol. 24(2003), pp.1017-1026(in chinese).

[7] Huang Xiaolin, Shen Huishen: International Journal of Solids and Structures, Vol. 41(2004), pp.2403-2427.

[8] Sundarajan N., Prakash T., Ganapathi M: Finite Elements in Analysis and Design, Vol. 42(2005), pp.152-168.

[9] Liu Renhuai: China Engineering Science, Vol. 2(2000), pp.60-67.

[10] Liu Renhuai: Applied Mathematics and mechanics, Vol. 2(1980), pp.173-190.

[11] Du Guojun, Li Huijian: Appl. Math. & Mech., Vol. 21(2000), pp.192-200.

[12] Du Guojun, Ma Jianqing: Applied Mathematics and mechanics, Vol. 28(2007), pp.1081-1092.