Vibration transmission bandgap analysis of porous functionally graded periodic beams in thermal environment using the wave-based approach

Porous functionally graded materials (FGMs) have attracted considerable attention in advanced engineering structures due to their lightweight characteristics and tunable mechanical properties. In this study, the vibration characteristics of porous functionally graded periodic beam structures under thermal environments are investigated using the wave-based analytical framework. Based on the Timoshenko beam theory, the displacement field is expressed in the form of wave functions, and the displacement and force parameter matrices for beam elements are derived. By imposing the continuity conditions between adjacent elements, the global formulation for periodic beam structures is established, enabling efficient calculation of the frequency response functions. The accuracy of the proposed model is validated through comparisons with finite element results, showing excellent agreement. On this basis, the vibration transmission characteristics of porous functionally graded periodic beams are systematically analyzed. Parametric studies are conducted to examine the effects of temperature variation, porosity coefficient, gradient index, and geometric parameters on the frequency response and vibration transmission bandgaps. Unlike previous studies that primarily focus on either homogeneous periodic structures or non-periodic porous functionally graded beams under isothermal conditions, the present work establishes a unified wave-based framework for analyzing vibration transmission in porous functionally graded periodic beams with temperature-dependent material properties. The combined effects of periodicity, material gradation, porosity, and thermal loading on bandgap characteristics are systematically revealed, providing new insights for the design of lightweight structures with enhanced vibration attenuation performance.