Vibration analysis of a generalized thermoelastic microbeam based on a Pasternak foundation with dual phase-lag model

Abstract This research opens new horizons by studying the vibration characteristics of a generalized thermoelastic microbeam supported by a Pasternak foundation using a dual phase lag (DPL) model that uniquely incorporates the effects of thermal relaxation in this complex system. The governing equations were solved analytically using the Laplace transform method, allowing accurate calculations of the temperature, moment, displacement, and deflection. The graphical results demonstrate the significant influence of the slope time coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> , Pasternak foundation parameters, and various thermoelastic models on the dynamic behavior of the microbeam. The DPL model shows clear differences from conventional thermoelasticity, emphasizing the need to consider thermal relaxation in the microstructures. The strong correlation between the derived beam response and dynamic deflection in previous studies, which used simpler thermoelastic beam theories and Bernoulli-Euler theories, confirms the accuracy and relevance of the proposed model. This study presents a comprehensive and advanced analytical framework for understanding the thermomechanical behavior of microbeams in complex settings, providing valuable insights for the design and optimization of micro/nanoelectromechanical systems (MEMS/NEMS), where thermal effects are critical.