Axially Symmetric Vibrations of Elastic Annular Bases and a Perfect Two-Layer Liquid in a Rigid Annular Cylindrical Vessel

Abstract

We deduce a frequency equation for the natural coupled axially symmetric vibrations of elastic bases (in the form of annular plates) and a heavy two-layer incompressible perfect liquid in a rigid annular cylindrical vessel. We consider different limiting cases: the case of degeneration of annular plates into membranes, the case of absolutely rigid or circular plates, and the case of absence of the upper plate (liquid with free surface). For a broad range of parameters of the analyzed mechanical system, we investigate the frequency spectra and obtain a series of mechanical effects in the problem of hydroelasticity.