文档介绍：CHAPTER 11
ELASTIC WAVE
Elasticity
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第十一章弹性波
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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
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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
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Elastic 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.
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.
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弹性波
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。
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§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 ponent is expressed by ponent , 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.
Elastic wave
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§11-1 弹性体的运动微分方程
弹性波
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