On asymptotic analysis for large amplitude nonlinear free vibration of simply supported laminated plates

Siu Kai Lai, C. W. Lim, Y. Xiang, W. Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)

Abstract

An analytical approximation is developed for solving large amplitude nonlinear free vibration of simply supported laminated cross-ply composite thin plates. Applying Kirchhoff's hypothesis and the nonlinear von Kármán plate theory, a one-dimensional nonlinear second-order ordinary differential equation with quadratic and cubic nonlinearities isformulated with the aid of an energy function. By imposing Newton's method and harmonic balancing to the linearized governing equation, we establish the higher-order analytical approximations for solving the nonlinear differential equation with odd nonlinearity. Based on the nonlinear differential equation with odd and even nonlinearities, two new nonlinear differential equations with odd nonlinearity are introduced for constructing the analytical approximations to the nonlinear differential equation with general nonlinearity. The analytical approximations are mathematically formulated by combining piecewise approximate solutions from such two new nonlinear systems. The thirdorder analytical approximation with better accuracy is proposed here and compared with other numerical and approximate methods with respect to the exact solutions. In addition, the method presented herein is applicable to small as well as large amplitude vibrations of laminated plates. Several examples including large amplitude nonlinear free vibration of simply supported laminated cross-ply rectangular thin plates are illustrated and compared with other published results to demonstrate the applicability and effectiveness of the approach.
Original language English 0510101-0510108 Journal of Vibration and Acoustics, Transactions of the ASME 131 5 https://doi.org/10.1115/1.3142881 Published - 1 Oct 2009 Yes

Keywords

• Asymptotic analysis
• Laminated plate
• Nonlinear system
• Simply supported

ASJC Scopus subject areas

• Mechanics of Materials
• Acoustics and Ultrasonics
• Mechanical Engineering