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

¹ Université Mohammed V Ecole Mohammadia D’ingénieurs, Avenue Ibn Sina, B.P.765, Agdal, Rabat, Morocco
² Université Mohammed V Ecole Mohammadia D’ingénieurs, Avenue Ibn Sina, B.P.765, Agdal, Rabat, Morocco

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.