This paper considers dynamic behavior of non-classical thermoelastic solid continua. The mathematical model consists of the conservation and balance laws of non-classical continuum mechanics that incorporates additional physics of internal rotations arising due to deformation gradient tensor. We consider plane stress behavior with small deformation, small strain physics only. Galerkin Method with Weak Form (GM/WF) in space is considered to construct a space–time decoupled finite element formulation giving rise to ordinary differential equations (ODEs) in time containing mass matrix, stiffness matrix due to classical as well as non-classical physics and acceleration and displacement associated with nodal degrees of freedom. This formulation is utilized to: (1) study natural undamped modes of vibration (2) study transient dynamic response by time integrating the ODEs in time (3) study the transient dynamic response by transforming the ODEs in time to modal basis using eigenvectors of the undamped natural modes. The ODEs in modal basis are used to construct transient dynamic response by time integrating them as well as by considering their analytical solutions. The solutions of the model problem obtained using the mathematical model based on non-classical continuum mechanics with internal rotations are presented and are compared with those obtained using the mathematical model based on classical continuum mechanics to demonstrate the influence of new physics due to internal rotations on the dynamic response of solid continua.

中文翻译：

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使用基于具有内旋转的非经典连续介质力学导出的数学模型的热弹性固体连续介质的动力学行为

本文考虑了非经典热弹性固体连续体的动力学行为。数学模型由非经典连续介质力学的守恒定律和平衡定律组成，该定律结合了由变形梯度张量引起的内部旋转的附加物理原理。我们仅考虑具有小变形、小应变物理的平面应力行为。空间弱形式的伽辽金方法 (GM/WF) 被认为是构建一个时空解耦的有限元公式，在时间上产生常微分方程 (ODE)，包含质量矩阵，由于经典和非经典的刚度矩阵物理以及与节点自由度相关的加速度和位移。该配方用于：(1) 研究振动的自然无阻尼模式 (2) 通过对 ODE 进行时间积分来研究瞬态动态响应 (3) 通过使用无阻尼自然模式的特征向量将 ODE 的时间转换为模态基来研究瞬态动态响应。模态基中的 ODE 用于通过对它们进行时间积分以及考虑它们的解析解来构造瞬态动态响应。给出了使用基于具有内旋转的非经典连续介质力学的数学模型得到的模型问题的解，并与使用基于经典连续介质力学的数学模型得到的解进行比较，以证明由于内旋转而产生的新物理对模型问题的影响。固体连续体的动态响应。