Abstract
This paper deals with the large-amplitude axisymmetric free vibrations of cylindrically orthotropic thin circular plates of varying thicknesses with edge elastically restrained against rotation and in-plane displacement. Geometric nonlinearity due to moderately large deflections is included. Linear, parabolic and cubic variations of thickness are considered. Harmonic vibrations are assumed and time is eliminated from the von Kármán-type governing equations by the Kantorovich averaging method. The orthogonal point collocation method is used for spatial discretisation. Results are presented for the linear frequency of first axisymmetric mode and for the amplitude-period response. The effect of taper ratio, orthotropic parameter and rotational and in-plane stiffness of the support on the nonlinear vibration behaviour is investigated.
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