Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections

2006 ◽  
Vol 291 (3-5) ◽  
pp. 539-565 ◽  
Author(s):  
M. Amabili
Keyword(s):  
Large Amplitude ◽  
Rectangular Plates ◽  
Geometric Imperfections ◽  
Large Amplitude Vibrations ◽  
Theory And Experiments

Effects of Geometric Imperfections on Large-Amplitude Vibrations of Rectangular Plates With Hysteresis Damping

1984 ◽  
Vol 51 (1) ◽  
pp. 216-220 ◽  
Author(s):  
David Hui
Keyword(s):  
Large Amplitude ◽  
Plate Thickness ◽  
Rectangular Plates ◽  
Structural Damping ◽  
Geometric Imperfections ◽  
Geometric Imperfection ◽  
Forcing Function ◽  
Initial Geometric Imperfections ◽  
Spatial Shape ◽  
Large Amplitude Vibrations

The present paper deals with the effects of initial geometric imperfections on large-amplitude vibrations of simply supported rectangular plates. The vibration mode, the geometric imperfection, and the forcing function are taken to be of the same spatial shape. It is found that geometric imperfections of the order of a fraction of the plate thickness may significantly raise the free linear vibration frequencies. Furthermore, contrary to the commonly accepted theory that large-amplitude vibrations of plates are of the hardening type, the presence of small geometric imperfections may cause the plate to exhibit a soft-spring behavior. The effects of hysteresis (structural) damping on the vibration amplitude are also examined.

Large Amplitude Vibrations of Completely Free Rectangular Plates

2012 ◽  
Author(s):  
F. Alijani ◽  
M. Amabili
Keyword(s):  
Shear Deformation Theory ◽  
Energy Functional ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Geometric Imperfections ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Collocation Scheme ◽  
Large Amplitude Vibrations

Nonlinear forced vibrations of completely free rectangular plates are studied using multi-modal Lagrangian approach. Nonlinear higher-order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is investigated. Geometric imperfections are taken into account. The analysis is carried out in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is conducted to obtain the natural frequencies and mode shapes. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained. A pseudo arc-length continuation and collocation scheme is employed to carry out a bifurcation analysis. The effect of number of modes retained in the approximation, thickness ratio and geometric imperfections on the trend of nonlinearity is discussed.

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