Nonlinear forced vibrations of rotating anisotropic beams

Abstract

This work deals with forced vibration of nonlinear rotating anisotropic beams with uniform cross sections. Coupling the Galerkin method with the balance harmonic method, the nonlinear intrinsic and geometrically exact equations of motion for anisotropic beams subjected to large displacements, are converted into a static formulation. This latter is treated with two continuation methods. The first one is the asymptotic-numerical method, where power series expansions and Pade approximants are used to represent the generalized vector of displacement and the frequency. The second one is the pseudo-arclength continuation method. Numerical tests dealing with isotropic and anisotropic beams are considered. The natural frequencies obtained for prismatic beams are compared with the literature. Response curves are obtained and the nonlinearity is investigated for various geometrical conditions, excitation amplitudes and kinematical conditions. The nonlinearity related to the angular speed for prismatic isotropic beam is thus identified. The stability of the solution branch is examined, in the frequency domain using the Floquet theory.