弹性力学(双语版)西安交通大学.pptVIP

* 由于 ，故不计体力的运动微分方程，简化后得等容波的波动方程： 其中 就是等容波在无限大弹性体中的传播速度。 * According to without rotating wave and equal volume wave , we give the conclusion without proving that :in elastic objects , stress , strain and speed of particle transmit in the same way and the same speed as displacement. * 对于无旋波和等容波，我们不加证明地给出如下结论：在弹性体中，形变、应力以及质点速度，都将和位移以相同的方式与速度进行传播。 * 1. vertical wave [definition] The particle movement direction of elastic objects is parallel to the transmitting direction of elastic wave. （seen in the Fig.） Transmitting format of vertical wave §11-3 Vertical wave and transverse wave * 一、纵波 [定义] 弹性体的质点运动方向平行弹性波的传播方向（图示） 纵波的传播形式 §11-3 纵波与横波 * Let x axis be the transmitting direction of waves, then the displacement components of any point in elastic objects are: So: And: * 将x轴取为波的传播方向，则弹性体内任取一点的位移分量都有： 从而 而 * Substitute them into movement differential equations without including body force, we can find that the second and third formulas are identical equations. So the first formula can be simplified as: where is transmitting speed of vertical wave in elastic objects. It is obvious that transmitting speed of vertical waves is the same as without rotating waves’ . In fact vertical wave is a kind of without rotating wave. * 代入不计体力的运动微分方程，可见其第二、第三式成为恒等式，而第一式简化为： 其中 为纵波在弹性体中的传播速度。 显然纵波的传播速度与无旋波相同。事实上，纵波就是一种无旋波。 * The general solution of wave movement equations of vertical wave is: The physic meaning of the general solution is: let us take the first item for example, function at a fixed time is function of x, and can be expressed by curve abc in Fig.(a) (suppose the form is like this ). After , the function becomes: If let ，then function becomes . Its format is similar to the original function . From the Fig we can see the only difference is transverse coordinate moves in level . So