Free and forced vibration analysis of functionally graded porous frames

Purpose The purpose of this study is to analyze the free and forced vibration behavior of frames constructed from functionally graded porous materials (FGPMs). By utilizing Timoshenko beam theory, this research aims to provide a comprehensive understanding of how varying porosity affects the dynamic response of the frame, contributing valuable insights into the design and optimization of FGPM structures in engineering applications. Design/methodology/approach This research employs Timoshenko beam theory to calculate the kinetic and potential energies of frame members with different porosity types. A specific finite element approach is used to derive mass and stiffness matrices and the force vector. The assembled global matrices facilitate the formulation of equations that account for continuity at joints. The Newmark method is applied to determine the time response of the system, allowing for a detailed analysis of the vibration characteristics influenced by various parameters. Findings The study demonstrates that the vibration characteristics of FGPM frames are significantly influenced by porosity and applied forces. The results reveal a strong correlation with previous studies for simpler configurations, validating the model’s accuracy. Additionally, the analysis highlights how varying material properties and loading conditions affect the dynamic behavior of the structure, providing crucial data for engineering applications in vibration control and structural optimization. Originality/value This paper offers a novel contribution to the field of structural dynamics by focusing on FGPMs, which have been less explored in vibration analysis. The integration of Timoshenko beam theory with detailed finite element methods enhances the understanding of FGPM behavior under dynamic loading. The findings provide valuable guidelines for engineers and researchers seeking to design advanced materials with tailored vibration properties, thereby expanding the practical applications of FGPMs in modern engineering challenges.