Dynamic response of wave propagation in functionally graded beams with defects: effects of porosity and cracks

Abstract

The analysis of the dynamic response to wave propagation in the FG pinned–pinned beams with various defects, such as cracks and varying porosity distributions, is what this paper has to offer. The bidirectional distribution, which is primarily represented in the density, Poisson coefficient, and Young's modulus, is taken into consideration while developing higher-order shear deformation beam theory for wave propagation in defective FG structure beams. A power law index is used to assess the thickness and width of the porous FG beam's material properties. Using Hamilton's principle, the governing equations of wave propagation in the multi-crack porous 2D-FG beam are derived. An eigenvalue problem is solved to determine the bidirectional porous FG beam's analytic dispersion relation. Three models of porosity that approximate distributions were examined. There was a high degree of consistency between the results obtained for bidirectional FG cracked beams and those documented in the literature. The influence of different parameters, the number of waves propagating, the volume fraction distributions, and the porosity models on the dynamic of wave propagation modes in imperfect functionally graded beams are covered in detail, and to look into how significant parameters affect the damaged structure's dynamic behavior. This study innovates by combining the simultaneous analysis of the effects of bidirectional porosity and multiple cracks, thus providing a more complete understanding of the complex interactions influencing wave propagation. In addition, it proposes new porosity models adapted to composite materials, which had not been fully explored in previous research.