Impulse and Resonant Response in Systems Showing Secular and Leaky Excitations

A model consisting of a string embedded in an elastic medium and terminated by a harmonic oscillator has been studied in the frequency and time domains to elucidate the physical effects of supersonic and subsonic leaky waves as well as that of true surface waves. A supersonic leaky wave manifests itself by a resonant maximum of the local density of states within the band of bulk waves and by an anomalous dispersion of the real part of the frequency dependent response function. The time domain impulse response then contains mainly resonant contribution from the poles of the response function in analogy to ordinary resonances. True surface waves show generally analogous behaviour. Here, however, the phenomenon is governed by dissipation mechanisms different from the radiation into the bulk. An important difference is that the impulse response contains equilibrated contributions due to the poles and due to the stop frequency gap in the case of true surface waves. The main manifestation of a subsonic leaky wave, i.e. a surface resonance with the frequency situated in the stop gap, is a sharp peak of the real part of the frequency-dependent response function just at the bottom of the bulk waves band. This is in certain analogy with a large reactive power in electric circuits. A strong destructive interference of the resonant part of the impulse response with the part due to the gap makes the time domain response fast attenuated.