Nonlinear dynamics of axially functionally graded, porous sandwich panel subjected to periodic non-uniform in-plane excitation

Abstract

The dynamic response of axially functionally graded (AFG) porous core sandwich panels under periodic non-uniform in-plane axial loads is investigated. The panel is a circular cylindrical shell with a rectangular base with simply supported, in-plane movable edges. The material properties of the face sheet are obtained using the rule of mixture, and porosity in the core is assumed to be randomly distributed. The core is modelled for compressibility with fourth and fifth-order expansions by neglecting the tangential displacement due to large rotations. Non-uniform in-plane stresses are obtained using the Airy stress function. The equations of motion are derived by using variational principles and multi-term Galerkin's approach. The region of dynamic instability is obtained using Bolotin's method; the novelty is that a proportional damping model of the panel is retained in this study. The Newmark-Beta technique is applied to calculate time-histories and phase-plane responses. Results show that damping plays a significant role in dynamic responses. Different from most of the semi-analytical solutions published in the literature, the present study satisfies both natural and essential boundary conditions. The functional gradation of material shows that by increasing the power law constant (k), the material properties present a softening character. Non-uniform in-plane loads are studied, which is another significant novelty for the problem under investigation. Porosity can play an important role in structural performance; it can be due to manufacturing defects or desired for the development of lightweight structures. Therefore, the influence of porosity is studied in detail by considering a random void distribution for both open and closed-type cellular structures.