Linear and Nonlinear Analysis of a Curved Timoshenko Beam Using Geometrically Exact Formulation

This study investigates the mechanisms of nonlinear modal interactions in a circularly curved cantilever beam, utilizing the geometrically exact Timoshenko beam formulation. The governing equations take into account shear deformation, rotary inertia, and the geometric nonlinearities associated with significant deflections. A Chebyshev pseudospectral scheme is employed to achieve highly accurate linear eigenvalues, which are subsequently used in a nonlinear modal projection to develop a reduced-order model. Explicit expressions for the quadratic and cubic modal coupling coefficients are derived. The Harmonic Balance Method is then applied to explore internal resonance phenomena, frequency modulation behavior, and the transfer of energy between non-commensurate lateral and normal vibration modes.