Abstract
The elastodynamic field of N rigid strips, lying parallel on the surface of an elastic half-space and harmonically excited in time by vertical forces, was calculated. It is assumed (1) the contact between the rigid strips and the surface of the half-space is maintained during the motion of the strips, and (2) the horizontal component of the traction is zero on the surface of the half-space. Calculation of the elastodynamic field is based on the integral representation of the particle displacement in the half-space, together with the dynamic equations for the strip. From the integral representation and the dynamic equations, a set of coupled integral equations for the vertical component of the traction under the strips can be derived. This set of integral equations was solved numerically by the method of moments.The influence of the hold-down mass and its spring system is also investigated. It is shown that its action can be accounted for by introducing a frequency-dependent effective mass of the strips. At the resonance frequency of the hold-down mass/spring system, the power radiated into the half-space, is shown to be zero.Numerical results show that for a fixed strip width and fixed parameters of the elastic half-space, the frequency at which the peak in the radiated power occurs decreases as the mass/unit length of the strip increases, whereas the ratio of the radiated P-, S-, and Rayleigh waves does not change at all.Since the frequency at which the peak in the radiated power occurs depends upon the mass/unit length of the strip, and since the influence of the hold-down mass/spring is actually a frequency-dependent effective mass of the strip, theoretically it is possible to optimize the radiated power of a vibrator for a frequency band of interest. Such a vibrator, if ever constructed, will most likely depend upon a feedback and control system. I show that the phase difference between the driving force and the velocity of the strip is a suitable feedback signal.
