ABSTRACT

This paper aims to inspect the nonlocal Erigen’s elasticity model for free vibrations of thermoelastic diffusive sphere in the reference of dual-phase-lag (DPL) model of generalized thermoelasticity. The effect of non-locality and different models of generalized thermoelasticity, i.e. dual-phase-lag (DPL), Lord–Shulman (LS) models and coupled thermoelasticity (CTE) in the presence and absence of diffusion, has been taken under investigation. Due to time harmonic vibrations, the constitutive relations and governing equations are transformed into ordinary differential equations. By applying the stress free thermal boundary conditions, the frequency equation has been taken under investigation for the possible modes of vibrations in compact form. To discover free vibration analysis from frequency equations, the numerical functional iteration technique has been applied for generating numerical data with the assistance of MATLAB software tools. The obtained analytical results have been presented graphically from numerical computations and simulations. The effect of elastic nonlocality on the frequency shift and thermoelastic damping is represented graphically in some cases of interest and analyzed the obtained numerical results.

摘要

本文旨在参考广义热弹性的双相滞后（DPL）模型检验热弹性扩散球自由振动的非局域Erigen弹性模型。在存在和不存在扩散的情况下，非定域性和不同广义热弹性模型的影响，即双相滞后（DPL）、Lord-Shulman（LS）模型和耦合热弹性（CTE），已经在研究中。由于时间谐波振动，本构关系和控制方程转化为常微分方程。通过应用无应力热边界条件，频率方程已被用于研究紧凑形式的可能振动模式。从频率方程中发现自由振动分析，数值函数迭代技术已应用于在 MATLAB 软件工具的帮助下生成数值数据。所获得的分析结果已通过数值计算和模拟以图形方式呈现。在一些感兴趣的情况下，弹性非定域性对频移和热弹性阻尼的影响以图形方式表示，并分析了获得的数值结果。