FGP Beam Using Higher Order Shear Deformation Theory - Numerical Vibrational Analysis

Functionally Graded Materials, which are heterogeneous and advanced materials, are composed of continuously varying distributions of two or more constituent phases. Their volume or weight proportion, direction, and shape can all affect the phase distribution differently. A significant portion of functionally graded materials are affected by pores. By gradually spreading the dispersion of pores from the surface to the interior, it is possible to incorporate numerous features. This study employs a third-order shear deformation theory to describe the free vibration behaviour of two functionally graded porous beams subjected to various boundary conditions. These are simply supported (SS), clamped-clamped (CC), and clamped-free (CF). The material properties of the beam reveal exponentially shifting patterns in both directions. Utilizing Hamilton's approach allowed for the analysis of the free vibration response. These equations of motion are derived to achieve this objective. Cross section axial, transverse, and rotational deflections are expressed using polynomial expressions. These forms also contain auxiliary functions that are employed to satisfy the boundary conditions. Verification and convergence investigations are conducted utilising the calculated findings from a previous research. Findings of these investigations are presented to facilitate an understanding of the implications of varying gradient indices, aspect ratios, and boundary conditions on the free vibration responses of two-directional functionally graded porous beams are found to be in agreeable.