Steady-state nonlinear dynamics of a flexible beam with large deformation under oscillatory flow

Abstract

This work investigates the steady-state nonlinear dynamics of a large-deformation flexible beam model under oscillatory flow. A flexible beam dynamics model combined with hydrodynamic loading is employed using large deformation beam theory. The equations of motion discretised using the high-order finite element method (FEM) are solved in the time domain using the efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method. The arc-length continuation method and Hsu’s method trace stable and unstable solutions. The numerical results are in accordance with the physical experimental results and reveal multiple resonance phenomena. Low-order resonances exhibit hardening due to geometric nonlinearity, while higher-order resonances transition from softening to hardening influenced by inertia and geometric nonlinearity. A strong coupling between tensile and bending deformation is observed. The axial deformation is dominated by inertia, while bending resonance is influenced by an interplay between inertia, structure stiffness, and fluid drag. Finally, the effects of two dimensionless parameters, Keulegan and Carpenter number (KC) and Cauchy number (Ca), on the response of the flexible beam are discussed.