Low-velocity impact analysis of the hierarchical viscoelastic FGM plates, using an explicit shear-bending decomposition theory and the new DQ method

Effects of the hierarchical viscoelastic nature of the materials on the low-velocity impact responses of the structures have not been taken into account so far. In the present research, low-velocity impact of the general (hierarchical) viscoelastic functionally graded material plates is investigated. In contrast to the available impact researches, not only modulus of the impacted layer, but also stiffness and viscoelasticity of the underneath layers are taken into account to define the apparent stiffness of the contact region and modify Hertz contact law. In this regard, the Mori–Tanaka micromechanical-based material model is also employed. The plate is modeled based on a theory with explicit bending-shear decomposition. The resulting integro-differential governing equations are solved by the new version of the differential quadrature method (DQM) in conjunction with a novel time integration scheme. A comprehensive sensitivity analysis is performed to investigate influences of various geometric, kinematic, and material parameters on time histories of the lateral deflection, indentation, and contact force. Results reveal that stiffness of the plate increases due to the viscoelastic nature of the materials and the relaxation effects are noticeable only after a remarkable number of oscillations following the impact.