On the Propagation of Bulk Waves in Functionally Graded Beams with Consideration for Imperfection

Wave propagation analysis can be employed in various fields, such as nondestructive testing and structural health monitoring, which makes it so interesting and attractive. In the present investigation, an analytical method based on an exponential function was used to solve the wave propagation problem in functionally graded (FG) beams with consideration for imperfection via refined higher-order shear deformation theory. The recently developed porosity-dependent homogenization model was used to analyze the influence of imperfection on the wave dispersion behavior of porous beams. Material properties of FG beams were assumed to change across the thickness. The conventional porosity model illustrates a linear relationship between the porosity coefficient and material properties. However, the influence of porosity is actually characterized by a nonlinear relationship. This statement rose from some experimental investigations. To examine the interchange between the porous beam and foundation, Winkler–Pasternak two-parameter models were used as the elastic foundation. Uniform temperature change is taken into account to study the thermal environment effect. The principle of Hamilton is implemented to derive equations of motion for imperfect FG beams. The obtained governing equations were analytically solved. The influence of the wave number, porosity coefficient, temperature change, gradient index, length-to-thickness ratio, Winkler and Pasternak coefficients on the wave propagation in porous FG beams was studied.