A Load Accelerating on the Surface of an Acoustic Half Space

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Abstract
The problem of a pressure, distributed as a step function, which moves across the surface of an acoustic half space is discussed. The pressure is suddenly applied and thereafter the step moves as any prescribed continuous function of time. This results in a problem in plane flow. An analytical solution for the pressure and displacements throughout the half space is obtained in terms involving only single integrals. It is shown that if the step moves with the sonic speed for a finite time the displacements beneath the step are discontinuous. This displacement discontinuity increases in proportion with time. (Displacements remain continuous at every point below the surface.) However, if the step accelerates through the sonic speed no displacement discontinuities occur. After the step is moving supersonically, two wave fronts develop. The pressure increases across the leading wave front and decreases across the trailing one.

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