Thermal-porosity-dependent damped vibration of visco-Pasternak-supported beams under localized heat exposure

In this paper, a theoretical framework is developed and validated for the damped vibration analysis of visco-Pasternak-supported porous beams under localized heat exposure. The formulation incorporates porosity-dependent material gradation, thermal fields with different longitudinal distributions, and foundation damping effects, thereby capturing the multi-physics interactions that govern dynamic behavior. Benchmark comparisons against established solutions confirm the accuracy and reliability of the present approach. Extensive parametric investigations are then performed to reveal the influence of key variables, including temperature rise and heated length ratio, porosity coefficient, slenderness, and foundation stiffness and damping parameters, on the damped frequencies, real parts of the eigenvalues, and relative damping ratios. Results highlight the competing roles of stiffness degradation, mass reduction, and porosity-modified thermal stresses, leading to non-monotonic or stabilizing trends not observed in simpler models. The proposed framework provides new insights into the coupled thermomechanical behavior of porous nanostructured beams and offers a versatile tool for the design and assessment of advanced lightweight structural elements in thermally varying environments.