Resumen de Analytical solution for thermoelastic oscillations of nonlocal strain gradient nanobeams with dual-phase-lag heat conduction
Dandan Liu, Shahab Esmaeili, Hongxiao Wang, Tie Geng
In order to examine the impact of structural and thermal scale parameters on thermoelastic vibrations of Euler-Bernoulli nanobeams, this article intends to provide a size-dependent generalized thermoelasticity model with the help of nonlocal strain gradient theory (NSGT) in conjunction with dual-phase-lag (DPL) heat conduction model. To highlight the role of each scale parameter in size-dependent motion and heat conduction equations, normalized forms of these nonclassical coupled thermoelastic equations are extracted by introducing and exploiting some dimensionless parameters. By exploiting power series expansion as a general solution for arbitrary boundary conditions, system of partial differential equations reduces to system of ordinary differential equations in time domain. The Laplace transform is then utilized to attain the analytical solution of this set of differential equations. By conducting a case study on a hinged-hinged nanobeam, with the aim of illustrating the impact of nonclassical structural and thermal parameters on thermoelastic vibrations, size-dependent numerical results are compared with those estimated by classical elasticity theory and heat conduction model. Meaningful disparity between classical and nonclassical results reveals the pivotal role of scale parameters in realistic assessment of thermoelastic behavior of nanobeams. Outcomes also indicate that corresponding to the relationship between the magnitudes of two scale parameters of NSGT, the nonclassical model of nanobeam can exhibit either softening or hardening behavior compared to the classical one. This affirms the ability of NSGT to justify both stiffness softening and stiffness hardening phenomenon in nanostructures.
