Large amplitude free vibration of simply supported antisymmetric cross-ply plates

AIAA Journal ◽  
1991 ◽  
Vol 29 (5) ◽  
pp. 784-790 ◽  
Author(s):  
Gajbir Singh ◽  
G. Venkateswara Rao ◽  
N. G. R. lyengar
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Simply Supported

Free Vibration of a Large-Amplitude Deflected Plate—Reexamination by the Dynamical Systems Theory

1986 ◽  
Vol 53 (3) ◽  
pp. 633-640 ◽  
Author(s):  
J. Lee
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Invariant Tori ◽  
Plate Thickness ◽  
Standard Technique ◽  
Simply Supported ◽  
Nonlinear Plate ◽  
Power Spectral ◽  
Mode Truncation ◽  
Energy Components

For a simply supported large-amplitude deflected plate, Fourier expansion of displacement reduces the nonlinear plate equation to a system of infinitely coupled modal equations. To close off this system, we have suppressed all but the four lowest-order symmetric modes. In the absence of damping and forcing, the four-mode truncation can be recasted into a Hamiltonian of 4 DOF. Hence, the free vibration of nonlinear plate can be investigated by the standard technique of Hamiltonian systems. It has been found that subsystems of 2 DOF are practically stable in that the invariant tori remain on a smooth surface up to total energy of 1000, at which modal displacements can be 40 times the plate thickness. On the other hand, the trajectory of 4 DOF system develops chaos at a much lower energy value of 76, corresponding to modal displacements twice the plate thickness. This has been evidenced by many spikes in the power spectral density of displacement time-series and an erratic pattern that modal energy components cut through an energy sphere.

On Asymptotic Analysis for Large Amplitude Nonlinear Free Vibration of Simply Supported Laminated Plates

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
S. K. Lai ◽  
C. W. Lim ◽  
Y. Xiang ◽  
W. Zhang
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Nonlinear Differential Equation ◽  
Large Amplitude ◽  
Analytical Approximation ◽  
Laminated Plates ◽  
Thin Plates ◽  
Nonlinear Free Vibration ◽  
Simply Supported ◽  
Analytical Approximations

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 is formulated 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 third-order 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.

Free vibration of simply supported and clamped elliptical plates

1992 ◽  
Vol 158 (2) ◽  
pp. 383-386 ◽  
Author(s):  
K.L. Prasad ◽  
A. Venkateshwar Rao ◽  
B. Nageswara Rao
Keyword(s):  
Free Vibration ◽  
Simply Supported
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