Modal characteristics of functionally graded porous Timoshenko beams with variable cross-sections

The study focuses on the free vibration analysis of beams composed of functionally graded porous materials and characterized by a variable cross-section along their length. A broad range of beams is examined encompassing various tapered configurations, porosity profiles, and porosity content. The equations of motion are derived using Hamilton's principle within the framework of Timoshenko beam theory. These equations are solved semianalytically using the differential transform method, which has been adapted to incorporate various boundary conditions such as clamped-clamped, clamped-free, clamped-pinned, and pinned-pinned constraints within a general formulation of the beam eigenvalue problem. To validate the proposed solution technique, computed natural frequencies are compared with existing literature results for tapered inhomogeneous beams and uniform porous beams. Notably, new results are obtained for tapered porous beams. In this regard, a comprehensive parametric study explores the influence of various factors on the natural frequencies and mode shapes of functionally graded porous beams with variable cross -sections. These factors include the type of porosity profiles, a range of porosity parameters, cross-section taper ratios, and specific boundary conditions. The findings deepen our understanding of the modal characteristics of functionally graded porous beams, providing valuable guidance for engineering design and structural optimization in relevant applications. Additionally, they may serve as benchmarks for other researchers.