Nonlinear impact and damping investigations of viscoporoelastic functionally graded plates with in-plane diffusion and partial supports

Abstract

Fluid seepage and viscoelasticity play important roles in the dissipation of the undesired vibration and impact energies of the poroelastic structures. In the present article, the impact behavior of viscoporoelastic functionally graded plates with bending-induced fluid-flow is analyzed, for the first time. Moreover, the effects of partial support are investigated. Biot’s poroelasticity and Zener’s viscoelasticity models are combined, for the first time and then, the governing equations of the impact of the plate are derived based on the non-linear Hertz law. The nonlinear finite element form of the governing integrodifferential equations of the solid skeleton and the fluid pressure is obtained based on Galerkin’s method and solved using a special accumulation-based time-marching procedure. Treating the adopted quadratic through-thickness distribution of the fluid pressure is another superiority of the present research. The second-order Runge-Kutta numerical time-integration, trapezoidal discretization, and Picard’s iterative updating techniques are employed to deal with the time-dependency of the resulting equations. The effects of the poroelastic, viscoelastic, and support parameters on the time variations of the contact force, indentation, lateral deflection, and pore pressure moment are investigated. Results reveal that the viscoporoelastic plates may exhibit some behaviors that are in contradiction to those of the traditional plates.