A resonant coupling of a localized harmonic oscillator to an elastic medium

摘要

The motion a point harmonic oscillator coupled to a homogeneous elastic medium and localized either on the medium's surface or embedded in the medium is analzyed. Two new elements are introduced, one regarding the reaction of the oscillator upon the medium and another concerning a coupling function. The present analysis is meant to be relevant for the effects a seismic motion may have upon a localized structure, either natural or man-built. It is shown that the reaction of the oscillator modifies its inertia, which in turn leads to a change in the oscillator's eigenfrequency; this change is controlled by the coupling function. The present treatment opens the way of introducing new, more realistic features in analyzing the effect of the seismic motion upon localized structures, in particular the non-linear features of the coupling of the structure with its local site's motion.