Wave Propagation in Beams with Functionally Graded Porosity Distribution under Highly Transient Axial and Transverse Impacts

Recent advances in the manufacturing process provide a possibility of fabricating a new generation of porous materials denoted by functionally graded porous materials (FGPM). This paper aims to present a time domain analysis of wave propagation through the porous structures with functionally graded porosity distribution, which has not been completely studied before. For this purpose, the beams with different functionally graded porosity distributions subjected to both axial and transverse tip impact loads with a high-frequency content are investigated. The shear deformable cantilevered functionally graded porous beams with various porosity distributions through the beam thickness are studied. The governing differential equations are derived using the Hamiltonian principle based on the Timoshenko beam theory. A locking-free first-order shear deformable beam element is used to derive the finite element formulation of the equations. The Newmark time integration method is used to perform a time domain analysis of the equations of motion and to investigate the transient response of the beams. The axial and transverse wave propagation characteristics through functionally graded (FG) porous beams are found using time domain analysis of the results. Deflection and velocity time histories of the tip and each point of the beam, reflection time, and variation of support reactions are obtained. The influences of the porosity magnitude and porosity distribution on the wave propagation characteristics and overall time responses are investigated. The results reveal that porosity distribution has a significant effect on the wave amplitude, wave speed, and reflection from the boundary. Also, this study can help in a better understanding of porous structures' behavior subjected to high-transient impact loads in different engineering applications.