Response of nonlocal thermoelastic nanobeams supported by Pasternak foundations to the effect of generalized fractional theory with three-phase lags.

This work explores the fractional-order three-phase lag (TPL) thermoelasticity model to examine how thermal relaxation parameters affect the vibrational behavior of generalized nonlocal thermoelastic nanobeams supported by Pasternak foundations. This research broadens the understanding of nonlocal thermoelastic vibrations in nanoplates and nanobeams. Numerical analysis was used to calculate and visually present the temperature, torque, and displacement distributions. The Laplace transform method facilitated the resolution of the governing equations. A thorough analysis and discussion of the numerical data, supported by graphical representations, detail the effects of the fractional order factor, Pasternak parameters, and various thermoelastic models on the observed fields. The researchers found notable consistency when comparing the resultant beam response and dynamic deflection with earlier studies that applied the Bernoulli-Euler and nonlocal thermoelastic nanobeam theories. This underscores the importance of applied research in uncovering the unique properties of nanotechnology systems during the production of nanoscale materials and structures, which are especially beneficial in multiple industrial fields, particularly in mechanical engineering and materials science.