A Semi-Analytical Framework for Nonlinear Vibration Analysis of Variable Stiffness Plates

Focus of this paper is the development of a fast semi-analytical framework to address the nonlinear vibration response of plates with Variable Stiffness (VS) configuration. A formulation is developed based on a mixed variational theorem. A Ritz-like approach is employed for handling the spatial dependence, whilst several techniques are developed and compared for the temporal dependence: the method of averaging, a perturbation approach, an iterative procedure based on the Harmonic Balance Method (HBM) and a direct integration method. The proposed framework allows fast parametric studies to be performed for assessing the nonlinear vibration response of VS plates. The comparison against reference results demonstrates the validity of the proposed formulations in capturing the nonlinear free and forced responses with relative computational ease. This aspect is further exploited by presenting parametric studies, where the role of fiber path and boundary conditions is assessed. These studies aim at providing further understanding into the underlying mechanical response and illustrate the potential of the proposed semi-analytical approaches as a valuable mean to assist the design of VS plates.