Fluid–structure interaction of quasi-one-dimensional potential flow along channel bounded by symmetric cantilever beams

An analysis of fluid–structure interaction is presented for incompressible and inviscid flow in a channel bounded by symmetric cantilever beams. Small deflections of the beams and no flows normal to the beams are assumed, thus allowing the governing equations to be defined using quasi-one-dimensional pressure and flow velocity distribution; pressure and velocity are assumed to be uniform across the cross section of the channel. The steady-state solution of the present problem is analytically derived by the linearization of the governing equations. The solution is shown to consist of infinite modes, which is verified by comparing with numerical solutions obtained by the finite element method. The nonlinear effect in the steady-state solution is modeled by numerical method to estimate the error due to linearization. However, only a few leading modes are physically significant owing to the effects of flow compressibility and viscosity. The analytic solutions of the fluid–structure interaction are also presented for dynamic problems assuming harmonic vibration. The steady-state and stationary initial conditions are used, and the equilibrium frequency is determined to minimize the residual error of Euler equation. The fluid–structure interaction is characterized by a phase difference and distortion of waveform shape in the time history of the boundary velocity.