On the vibrations of the non-polynomial viscoelastic composite open-type shell under residual stresses

Abstract

This paper presents the first attempt to investigate the mechanical behaviors of the three-dimensional theory of poroelasticity for functionally graded graphene platelets reinforced composite (FG-GPLRC) open-shell resting on a non-polynomial viscoelastic substrate involving friction force and under residual stresses. For this purpose, three parameters viscoelastic foundation is developed by taking into account the torsional interaction and horizontal friction force. The open-type shell comprises multilayers with uniformly dispersed graphene platelets (GPLs) in each fictitious layer of facing sheets. Still, its weight fraction changes layer-by-layer along the thickness direction. For solving the governing equations, the state-space based differential quadrature method is presented to determine the frequency response of the sandwich open-type shell. The influences of several parameters, such as various types of horizontal friction force, initial circumferential stress, linear and torsional gradient elastic foundation, and damping parameter, are investigated on the amplitude and frequency of the FG-GPLRC open-shell resting on a non-polynomial viscoelastic substrate. Results reveal that the poroelasticity theory has an overestimation of the frequency in comparison with 3D- elasticity. The fundamental and golden results of this paper are that by considering initial compressive stress, the system's stability increases, and the energy absorption of the structure improves.