Abstract
Horizontal translational vibrations of a circular disk on an elastic half space are investigated mathematically. The problem is formulated in terms of an integral equation which describes explicitly the relation between the horizontal displacement of the disk and the shearing stress of contact. Its integral kernel is represented in a rigorous but simple form: its singularity is separated and is reduced to an elliptic integral while the regular part is expressed in terms of a definite integral of some higher analytic functions over a finite interval. These higher functions, defined as definite integrals of trigonometric functions over a finite interval, are readily evaluated. The presented formula is proved correct by applying it to a rigid disk and comparing the results with those of conventional methods.
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