周期弹性波作用下一维非线性裂纹的弹塑性
Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave
摘要：
在一维情况下研究了线弹性波与有限压缩非线性裂纹的相互作用。对正弦载荷作用下的双曲线接触模型的数值研究表明，裂纹上离散的弹性位移的平均值是不连续的。裂纹的平均扩张也随加载水平的幅值而增大。目前的理论研究的目的是分析这些非线性过程在更大范围的非线性跳跃条件下。为此目的，该问题被减少到一个非线性微分方程。在正弦强迫条件下，周期解对强迫振幅的依赖性被量化。的平均值，最大值和最小值的解决方案的界限。最后，与零平均值的周期强迫解决。在这种情况下，得到了关于裂纹平均扩张的一个结果。
英文摘要：
The interactions between linear elastic waves and a nonlinear crack with finite compressibility are studied in the one-dimensional context. Numerical studies on a hyperbolic model of contact with sinusoidal forcing have shown that the mean values of the scattered elastic displacements are discontinuous across the crack. The mean dilatation of the crack also increases with the amplitude of the forcing levels. The aim of the present theoretical study is to analyse these nonlinear processes under a larger range of nonlinear jump conditions. For this purpose, the problem is reduced to a nonlinear differential equation. The dependence of the periodic solution on the forcing amplitude is quantified under sinusoidal forcing conditions. Bounds for the mean, maximum and minimum values of the solution are presented. Lastly, periodic forcing with a null mean value is addressed. In that case, a result about the mean dilatation of the crack is obtained.
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