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The extended Durbin method and its application for piezoelectric wave propagation problems

机译:扩展的Durbin方法及其在压电波传播问题中的应用

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摘要

Based on the well-known Durbin method, an efficient numerical method was developed for the inversion of the two-sided Laplace transform. The accuracy of the method was verified using examples. As an application of the method, transient elastic waves propagating in a two-layered piezoelectric medium subjected to anti-plane concentrated loading and in-plane electric displacement loading were investigated. One-sided and two-sided Laplace transforms were applied to determine the shear stresses and electric displacements in the double Laplace transform domain. Subsequently, the Durbin method for one-sided Laplace transform inversion and the extended Durbin method for two-sided Laplace transform inversion were used to implement the numerical inversions. Additionally, the numerical results of the transient stresses and electric displacements were evaluated and discussed. It showed that the arrival time of transient waves satisfies physical phenomena, and the transient solution oscillates near the static solution and rapidly approximates the static solution.
机译:基于众所周知的Durbin方法,开发了一种有效的数值方法来对双面Laplace变换进行反演。通过实例验证了该方法的准确性。作为该方法的一种应用,研究了在两层压电介质中承受反平面集中载荷和平面内电位移载荷时传播的瞬态弹性波。应用一侧和两侧拉普拉斯变换来确定双拉普拉斯变换域中的切应力和电位移。随后,将用于单面Laplace变换反演的Durbin方法和用于双面Laplace变换反演的扩展Durbin方法用于实现数值反演。另外,对瞬态应力和电位移的数值结果进行了评估和讨论。结果表明,瞬态波的到达时间满足了物理现象,瞬态解在静态解附近振荡并迅速逼近静态解。

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