Non-Linear Forced Vibration of Fully Clamped FGM Skew Plates using Homogenization Technique

Abstract

The present work concerns the geometrically non-linear forced vibration of fully clamped functionally graded skew plates (FGSP). The theoretical model based on Hamilton’s principle and spectral analysis previously applied to obtain the non-linear mode shapes of thin straight structures is used. A homogenization technique is developed to reduce the FGSP problem under consideration to that of an equivalent isotropic homogeneous skew plate. Results are given for the linear and non-linear fundamental frequency of fully clamped FGSP, considering different parameters, such as the skew angle, the excitation force level. The results show a non linearity of the hardening type with a shift to the right of the bent non linear frequency response function, in the neighbourhood of the fundamental mode.

Keywords

• linear vibrations
• FGM skew plate
• Homogenization technique
• Forced vibration.