Wave propagation in bidirectional functionally graded tapered beams incorporating porosity effect

This study addresses wave propagation in beams made of bidirectional functionally graded materials (BDFG) and having nonuniform cross section by using a quasi-3D analytical solution. For the first time, this aspect will be studied. The mechanical characteristics of the beams are supposed to be variable in both axial and transvers direction according to a specific law depending on the porosity. The mathematical formulation used is based on a displacement field containing indeterminate terms and requiring a few variables to be determined. The thickness and width of the beams are assumed to be linearly variable in the longitudinal direction. The equations governing the simply supported beams are obtained by applying the principle of virtual work and are then analytically solved to obtain the phase velocities and wave frequencies. In addition, the validation results reveal excellent concordance of the proposed theory with those given in the literature. Then, a detailed parametric study is carried out to investigate the influence of the several geometrical and material parameters on the wave propagation in BDFG tapered beams. It is observed that these parameters have significant impact on the wave propagation in BDFG tapered porous beams. These results can be used as benchmark solutions for future studies.