Fractional thermoviscoelastic damping response in a non-simple micro-beam via DPL and KG nonlocality effect

This study introduces a novel framework for investigating thermoelastic damping (TED) in viscoelastic micro-scale rectangular beams using the Euler-Bernoulli beam theory (EBBT). A two-temperature thermoviscoelastic model is developed, uniquely integrating non-Fourier effects and fractional-order parameters through a generalized thermoelasticity approach with an internal heat source and the dual-phase-lag (DPL) thermal conduction model. This innovative approach addresses the limitations of classical models by incorporating size-dependent effects and spatially varying thermal properties, providing new insights into thermal-mechanical coupling in micro-scale systems. Explicit formulas are derived for the inverse quality factor and frequency shifts, with the study comprehensively analyzing the influence of parameters such as beam thickness, aspect ratios, end constraints, relaxation constants, and fractional-order parameters. Novel findings reveal critical thickness ranges and phase-lag effects that govern energy dissipation and system dynamics. The results highlight the divergence from existing models, emphasizing the importance of nonlocal and fractional-order frameworks for accurately predicting damping and frequency behavior. Practical applications of the study include the optimization of micro-electromechanical systems (MEMS), nano-scale resonators, sensors, and energy-harvesting devices. By bridging theoretical advancements with tangible engineering solutions, this research provides a robust foundation for future exploration in thermal management and micro-scale system design, marking a significant contribution to the field. Graphical representations illustrate the effects of temperature discrepancy factors on damping and frequency shifts in non-simple micro-beams, offering a comprehensive understanding of the interaction between thermal and mechanical responses.