Effect of Peripheral Loading on Vibration of Elastically Supported Bi-Directional FGM Mindlin Circular Plates with Non-Linear Thickness Variation

摘要

In the present study, the effect of non-linear thickness variation and Winkler's foundation has been analysed on axisymmetric vibrations of bi-directional functionally graded circular plates subjected to uniform in-plane peripheral loading employing first order shear deformation theory. The mechanical properties of the plate material are assumed to vary in radial and transverse directions while the thickness of the plate is varying quadratically along radial direction. The coupled differential equations governing the motion of such a plate model have been derived using Hamilton's energy principle. The approximate solution of these equations for simply supported edge condition has been obtained by Harmonic differential quadrature method. The effect of different parameters has been studied on the vibration characteristics for the first three modes of vibration. The critical buckling loads in compression have been calculated by putting the frequencies to zero. The validity of the present technique is confirmed by comparing the results with the results of other authors.