Free and forced vibration analysis of FG-porous beams on variable elastic foundations: a comprehensive study using higher-order beam theory and meshless collocation method

This study presents a comprehensive free and forced vibration analysis of functionally graded porous beams resting on variable elastic foundations. The governing equations are formulated and solved to investigate the dynamic behavior of the beams under different boundary conditions utilizing higher-order beam theory and the meshless collocation method. Various porosity distributions and foundation types, including Winkler and Pasternak models with linear, parabolic, sinusoidal, cosine, and exponential stiffness variations, are considered. The effect of porosity patterns and foundation stiffness on the natural frequencies and forced response is analyzed in detail. The results indicate that porosity distribution significantly influences the vibrational characteristics, with specific configurations enhancing stiffness and stability. The effectiveness of the proposed meshless method is validated through comparisons with available benchmark results, demonstrating its accuracy and computational efficiency. The findings contribute to the optimal design and analysis of functionally graded porous beams in engineering applications where dynamic performance is critical.