The dual phase lag model for thermoelastic microbeams embedded in an elastic foundation incorporating fractional Kelvin–Voigt viscoelasticity

This research presents the dual-phase lag model (DPL) for thermoelastic microbeams. The model, supported by Winkler foundations, incorporates fractional Kelvin–Voigt viscoelasticity. The model addresses the complexities of heat transfer and mechanical behavior in micro-scale structures by accounting for phase lags in both temperature and heat flux, which are crucial for accurate predictions at small scales. By integrating fractional Kelvin–Voigt viscoelasticity, the study improves the comprehension of time-dependent material responses, capturing the unique behaviors of viscoelastic materials at the micro-level. The governing equations combine the dual-phase lag mechanism with Winkler foundation assumptions for a comprehensive analysis of thermoelastic behavior. Advanced mathematical techniques, including the Laplace transform, are applied to derive expressions for key parameters such as temperature distribution, deflection, and stress profiles. Numerical simulations provide graphical representations that evaluate the effects of factors like fractional order, foundation stiffness, and viscoelastic properties on microbeam behavior. This model is a valuable tool for engineers and researchers designing advanced materials and structures for dynamic thermal and mechanical conditions, promoting innovation in nanotechnology, materials science, and structural engineering.