《弹性力学》（双语版） 第十一章 弹性波

Elasticity CHAPTER 11 ELASTIC WAVE

1 Elasticity

弹单性生力学 第十一丝波

Chapter 1l Elastic Wave D Summarize D 1-1 Movement differential equations of elastic objects [ D 8 11-2 Without rotating wave and equal volume wave D811-3 Transverse wave and vertical wave D§11-4 Spherical wave

3 Summarize §1-1 Movement differential equations of elastic objects §11-2 Without rotating wave and equal volume wave §11-3 Transverse wave and vertical wave §11-4 Spherical wave Chapter 11 Elastic Wave

第十一章弹性波 E概述 D§1-1弹性体的运动微分方程 §11-2无旋波与等容波 D]§11-3横波与纵波 D§11-4球面波

4 概述 §1-1 弹性体的运动微分方程 §11-2 无旋波与等容波 §11-3 横波与纵波 §11-4 球面波 第十一章 弹性波

Clastics wave Summarize When elastic object bears loads in static force equilibrium conditions, not all the parts of object has displacement, distortion and streSs At the beginning of the loads, the parts which are more far from the loads have no impacts. After then, the displacement, distortion and stress caused by loads transmit to other places in a finite speed of wave This wave is called elastic wave his chapter will first give movement differential equations of elastic objects, then introduce some conceptions of elastic wave and simplify the equations according to different elastic waves, at last give the speed transmitting formulas of wave in infinite elastic objects

5 Summarize: When elastic object bears loads in static force equilibrium conditions, not all the parts of object has displacement, distortion and stress. At the beginning of the loads, the parts which are more far from the loads have no impacts . After then ,the displacement , distortion and stress caused by loads transmit to other places in a finite speed of wave. This wave is called elastic wave. This chapter will first give movement differential equations of elastic objects, then introduce some conceptions of elastic wave and simplify the equations according to different elastic waves, at last give the speed transmitting formulas of wave in infinite elastic objects

弹篮波 概述 当静力平衡状态下的弹性体受到荷载作用时,并不是在 弹性体的所有各部分都立即引起位移、形变和应力。在作用 开始时,距荷载作用处较远的部分仍保持不受干扰。在作用 开始后,荷载所引起的位移、形变和应力,就以波动的形式 用有限大的速度向别处传播。这种波动就称为弹性波。 本章将首先给出描述弹性体运动的基本微分方程,然后 介绍弹性波的几个概念,针对不同的弹性波,对运动微分方 程进行简化,最后给出波在无限大弹性体中传播速度公式

6 概述 当静力平衡状态下的弹性体受到荷载作用时，并不是在 弹性体的所有各部分都立即引起位移、形变和应力。在作用 开始时，距荷载作用处较远的部分仍保持不受干扰。在作用 开始后，荷载所引起的位移、形变和应力，就以波动的形式 用有限大的速度向别处传播。这种波动就称为弹性波。 本章将首先给出描述弹性体运动的基本微分方程，然后 介绍弹性波的几个概念，针对不同的弹性波，对运动微分方 程进行简化，最后给出波在无限大弹性体中传播速度公式

Plastics wave 8 11-1 Movement differential equations of elastic objects This chapter we still adopt the assumptions (1) Elastic objects are ideal elastic objects (2) The displacement and distortion are tinny The two assumptions are equal to the basic assumptions when we discuss. static force questions. So the physic and geometry equations and elastic equations where stress component is expressed by displacement component, still are the same with movement equations at any instantaneous time. The only difference is that the equilibrium differential equations of static questions must be substituted by movement differential 7 equations

7 §11-1 Movement differential equations of elastic objects The two assumptions are equal to the basic assumptions when we discuss static force questions. So the physic and geometry equations and elastic equations where stress component is expressed by displacement component , still are the same with movement equations at any instantaneous time. The only difference is that the equilibrium differential equations of static questions must be substituted by movement differential equations . This chapter we still adopt the assumptions: （1） Elastic objects are ideal elastic objects. （2） The displacement and distortion are tinny

弹波 §11-1弹性体的运动微分方程 本章仍然采用如下假设: (1)弹性体为理想弹性体。 (2)假定位移和形变都是微小的。 上述两条假设,完全等同于讨论静力问题的基本假 设。因此,在静力问题中给出的物理方程和几何方程, 以及把应力分量用位移分量表示的弹性方程,仍然适用 于讨论动力问题的任一瞬时,所不同的仅仅在于,静力 问题中的平衡微分方程必须用运动微分方程来代替

8 §11-1 弹性体的运动微分方程 上述两条假设，完全等同于讨论静力问题的基本假 设。因此，在静力问题中给出的物理方程和几何方程， 以及把应力分量用位移分量表示的弹性方程，仍然适用 于讨论动力问题的任一瞬时，所不同的仅仅在于，静力 问题中的平衡微分方程必须用运动微分方程来代替。 本章仍然采用如下假设： （1） 弹性体为理想弹性体。 （2） 假定位移和形变都是微小的

Plastics wave Toward any tiny object, when we apply d Alembert theory, we must consider stress, body force and the inertia force of elastic objects caused by acceleration In space right-angle coordinate system, the x,y, z directions component of inertia force of every unite Ⅴ olume are: a2 02v 02w at at at Where p is the density of elastic objects

9 Toward any tiny object , when we apply d’Alembert theory , we must consider stress , body force and the inertia force of elastic objects caused by acceleration . In space right-angle coordinate system, the x, y, z directions component of inertia force of every unite volume are: Where ρ is the density of elastic objects. 2 2 t u   −  2 2 t  −   2 2 t w   − 

弹篮波 对于任取的微元体,运用达朗伯尔原理,除了 考虑应力和体力以外,还须考虑弹性体由于具有加 速度而产生的惯性力。每单位体积上的惯性力在空 间直角坐标系的xy,方向的分量分别为 a2u 02v 02w O at at at 2 其中p为弹性体的密度。 10

10 对于任取的微元体，运用达朗伯尔原理，除了 考虑应力和体力以外，还须考虑弹性体由于具有加 速度而产生的惯性力。每单位体积上的惯性力在空 间直角坐标系的x,y,z方向的分量分别为: 其中ρ为弹性体的密度。 2 2 t u   −  2 2 t  −   2 2 t w   − 