Fractional dual phase-lag Model for Vibration analysis of a generalized nonlocal thermoelastic microbeam based on a Pasternak foundation

Micromechanical systems have wide-ranging applications in various industrial sectors including biomedical engineering and aerospace. Therefore, many studies have focused on analyzing microstructural vibrations, such as microbeams and microplates. Consequently, this study analyzed the vibration behavior of a generalized thermoelastic microbeam supported by the Pasternak rule with two parameters under the fractional dual-phase-lag model to explain the thermal relaxation effects. The governing equations were solved using the Laplace transform method, and the distributions of the temperature, moment, and displacement deflection were calculated and presented graphically. By interpreting the numerical results in graphic form, a detailed analysis and discussion of the effects of the fractional-order parameter, Pasternak parameters, and different thermoelastic models are presented within the observed domains. The study found remarkable agreement between the resulting beam response and dynamic deflection compared to previous research, which applied thermoelastic beam theories and the Bernoulli-Euler theory. This demonstrates the importance of practical research in mechanical engineering and materials science, and its potential for development in this field.