Nonlinear Dynamics of Polar-orthotropic Circular Plates

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.