Buckling and vibrations of polar orthotropic circular plates of linearly varying thickness resting on an elastic foundation

Gupta, Utkarsh; Lal, Roshan; Jain, S. K.

doi:10.1016/0022-460x(91)90491-2

Cited by 12 publications

(1 citation statement)

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“…2 Gupta and Jain studied the buckling behavior and vibration of polar orthotropic circular plates with linearly varying thickness resting on an elastic foundation. 3 Liu and Chen used the finite element method to analyze the geometrically nonlinear free vibrations of polar orthotropic circular plates. 4 Gupta and Ansari studied the assymmetric vibrations and elastic stability of polar orthotropic circular plates of linearly varying thickness subjected to hydrostatic in-plane force based on the classical plate theory.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of Polar-Orthotropic Circular Plates

Akour

Nayfeh

2006

Int. J. Str. Stab. Dyn.

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The dynamics of nonlinear polar orthotropic circular plates with simply supported boundary condition are investigated. Kirchhoff strain displacement relations for thin plates plus next higher-order nonlinear terms (von Karman type geometric nonlinearity) are considered. Lagrangian density function and Hamilton's principle are utilized to derive Lagrange's equations, from which the equations of motion and associated boundary conditions are derived. Analytical solution is obtained by the perturbation techniques and numerical solution by the Runge-Kutta method. Phase diagrams, discrete Fast Fourier Transform (FFT diagrams) and time history responses are presented for studying the forced vibration behavior. The sub-harmonic and primary resonances are studied as well as the effect of adding damping foil layers. The quadratic term in the governing equation plays a softening role on the overall behavior of the plate due to its relatively large coefficient. The increase of damping tends to smooth out the unstable region (i.e. jump phenomenon) in the system.

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Section: Introductionmentioning

confidence: 99%