Hydroelastic Oscillations of Three-Layered Channel Wall Resting on Elastic Foundation

Abstract

The hydroelastic bending oscillations of a three-layered wall of narrow parallel-plate channel with viscous flow were studied. We analyze the hydroelastic problem of a plane type and consider the upper channel wall as a rigid vibrating stamp and the bottom channel wall as a three-layered beam resting on elastic foundation. The flow in the channel is studied within the viscous incompressible fluid model. We investigate flow as a creeping one and assume a Winkler model for elastic foundation. The three-layered beam is a sandwich construction, which consists of outer layers and a stiff lightweight core, as well as three-layered beam kinematics is described by using the postulate of broken normal. The mathematical model of the investigated parallel-plate channel consists of dynamic equations of the three-layered beam with stiff lightweight-core, dynamic equations of the creeping flow and boundary conditions. We assume boundary conditions at the channel walls are no-slip ones, as well as boundary conditions at the channel edges are pressure difference. We studied the stationary oscillation problem under loading harmonic vibrating stamp. The analytical solution of the considered problem was obtained. We suggest the frequency-dependent function of three-layered beam deflection distribution along the channel and make calculations of the channel wall amplitude-frequency response.