Localized modes of oscillating structures which lie on the bottom

Abstract

The phenomenon of wave localization in hydroelastic systems leads to the strength concentration of radiation fields. The linear method considers the process of localization to be the formation of nonpropagation waves (trapped modes phenomenon). The presence of such waves in the total wave packet points to the existance of mixed natural spectrum of differential operators describing the behavior of hydroelastic systems. The problem of liquid and oscillating structure interaction caused by the trapped modes phenomenon has been solved (membranes, dies, plates and different liquid models). The areas of wave localization have been determined. These areas depend on both the parameters of oscillating structures and the liquid waveguide parameters (the linear dimensions of the channel filled with liquid; the height from the bottom to the liquid surface; the liquid density gradient according to the height, etc.). Necessary and sufficient conditions for the low-frequency trapped modes and the high-frequency trapped modes have been found. The wave localization in nonlinear elastic structures interacting with liquid has been studied. Cases of weak and strong nonlinearity have been investigated. It has been shown that the slightly decreasing tail is added to nonlinear localized modes depending on the frequency of linear localized modes. The tail is caused by the interaction of the mode’s continuous spectrum and the localized modes.