ABSTRACT

The present work is concerned with a novel generalized thermoelasticity theory introduced by Yu et al. [A modified Green-Lindsay thermoelasticity with strain rate to eliminate the discontinuity. Meccanica. 2018;53:2543–2554] which considers the strain-rate along with temperature-rate term in the constitutive equations. This theory is an attempt to modify the Green-Lindsay (GL) thermoelasticity theory. For an unbounded isotropic homogeneous elastic medium, the present work analyzes the propagation of plane harmonic waves in the context of this new theory. In order to investigate the effects of strain-rate term, the unified governing equations related to three thermoelastic models namely, classical coupled thermoelastic model, GL model and new model have been considered. The dispersion relation for the propagation of longitudinal plane waves in the contexts of all three models has been derived in a unified way, which is further solved by the computational tool for a particular material. The behavior of different wave components for longitudinal waves is examined through graphical representation and the effects of temperature-rate and strain-rate terms on the plane wave propagation are investigated. Significant differences in predictions by this new model as compared to other models are highlighted.

摘要

目前的工作与 Yu 等人介绍的一种新的广义热弹性理论有关。[修正的格林-林赛热弹性与应变率，以消除不连续性。麦卡尼卡。2018;53:2543–2554]，其中考虑了本构方程中的应变率和温度率项。该理论是对格林-林赛 (GL) 热弹性理论的一种尝试。对于无界各向同性均匀弹性介质，本工作在这一新理论的背景下分析了平面谐波的传播。为了研究应变率项的影响，考虑了与三种热弹性模型相关的统一控制方程，即经典耦合热弹性模型、GL 模型和新模型。在所有三个模型的背景下，纵向平面波传播的色散关系已经以统一的方式推导出来，并通过特定材料的计算工具进一步解决。通过图形表示来检查纵波的不同波分量的行为，并研究温度-速率和应变-速率项对平面波传播的影响。突出显示了该新模型与其他模型相比在预测方面的显着差异。通过图形表示来检查纵波的不同波分量的行为，并研究温度-速率和应变-速率项对平面波传播的影响。突出显示了该新模型与其他模型相比在预测方面的显着差异。通过图形表示来检查纵波的不同波分量的行为，并研究温度-速率和应变-速率项对平面波传播的影响。突出显示了该新模型与其他模型相比在预测方面的显着差异。