Abstract

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.

摘要

为了研究结构和热尺度参数对欧拉-伯努利纳米梁热弹性振动的影响，本文打算借助非局域应变梯度理论（NSGT）结合双相提供一个依赖于尺寸的广义热弹性模型-lag (DPL) 热传导模型。为了突出每个尺度参数在尺寸相关运动和热传导方程中的作用，通过引入和利用一些无量纲参数来提取这些非经典耦合热弹性方程的归一化形式。通过利用幂级数展开作为任意边界条件的通解，偏微分方程组可简化为时域常微分方程组。然后利用拉普拉斯变换来获得这组微分方程的解析解。通过对铰接纳米梁进行案例研究，旨在说明非经典结构和热参数对热弹性振动的影响，将尺寸相关的数值结果与经典弹性理论和热传导模型估计的结果进行比较。经典和非经典结果之间的显着差异揭示了尺度参数在纳米梁热弹性行为的实际评估中的关键作用。结果还表明，与 NSGT 两个尺度参数大小之间的关系相对应，纳米束的非经典模型与经典模型相比可以表现出软化或硬化行为。