Symmetry Effects on Broadband Dynamic Response and Sensitivity of Thermally Loaded Functionally Graded Porous Timoshenko Beams Using GDQM

Functionally graded porous (FGP) metal-foam beams offer advantages for lightweight structures, but thermal loading can alter their vibration response and stability. This study develops a framework based on the Generalized Differential Quadrature Method (GDQM) to investigate the effects of through-thickness porosity symmetry and asymmetry on the broadband dynamic response, thermal stability, and parameter sensitivity of FGP Timoshenko beams. The formulation incorporates temperature-dependent material properties, thermally induced compressive axial force, symmetric and asymmetric porosity distributions, three temperature profiles, and different boundary conditions. The governing equations are derived using Timoshenko beam theory and solved using GDQM. Validation against analytical and published benchmark solutions precedes parametric and normalized sensitivity analyses. Under the investigated thermal loading conditions, increasing temperature shifts the resonance characteristics toward lower frequencies and reduces the thermal stability margins. Uniform temperature distributions produce the strongest thermo-mechanical effects, whereas linear and nonlinear profiles yield similar broadband responses. Asymmetric porosity produces greater sensitivity and lower stability margins than symmetric porosity, demonstrating the influence of material symmetry on the thermoelastic dynamic behavior. Stronger boundary constraints enhance stability. Sensitivity analyses identify elastic modulus, temperature rise, and porosity coefficient as key parameters controlling the broadband response. Increasing structural damping suppresses resonance amplitudes and normalized temperature-rise sensitivity without significantly changing the resonance frequencies. The proposed framework supports stability-aware assessment and design of lightweight porous beams operating in thermal environments.