论文标题
从新运动描述中衍生弹性波方程
Derivation of Elastic Wave Equation from New Motion Description
论文作者
论文摘要
在经典力学中，用牛顿的三个运动定律描述了一个物体的运动，这意味着可以用粒子模型来描述组成连续体的材料元素的运动。但是，这种观点不是客观的，因为基于粒子模型的弹性理论无法预测横波的存在。在本文中，弹性体的材料元素被视为刚体，并且基于它得出了传统的弹性波方程。在派生中，构成关系和应变置换关系被相应地修改。该研究表明，弹性体中的纵向和横向波分别对应于材料元素的翻译和旋转运动。此外，在连续力学中，剪切应力和剪切应变的互惠不再需要，局部刚性体旋转会造成压力。
In classical mechanics, the motion of an object is described with Newton's three laws of motion, which means that the motion of the material elements composing a continuum can be described with the particle model. However, this viewpoint is not objective, since the existence of transverse wave cannot be predicted by the theory of elasticity based on the particle model. In this paper, the material element of an elastomer is regarded as a rigid body, and the traditional elastic wave equation is derived based on it. In the derivation, the constitutive relations and strain-displacement relations are correspondingly modified. The study reveals that the longitudinal and transverse waves in elastomer correspond to the translational and rotational motion of the material element, respectively. Besides, the reciprocity of shear stress and shear strain is no longer requisite in continuum mechanics, and the local rigid body rotation contributes stress.
