The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin isotropic skew plates

The present work concerns the nonlinear dynamic behavior of skew plates at large vibration amplitudes with fully clamped edges. The large amplitude free vibration problem is modelled by a set of nonlinear algebraic equations using Hamilton's principle and spectral analysis. The natural frequencies and modes of vibration have been obtained for fully clamped edges for various values of the skew angle. The relationship between the amplitude and frequencies is studied for isotropic skew plates. It was found that the frequencies of non linear vibration increase with increasing amplitude. Numerical details are presented and results are given, corresponding to the linear case and to the nonlinear case for various values of theta and various amplitudes of vibration. The results, compared to the previous ones available in the literature, show a reasonably good agreement.