VIBRATION CHARACTERISTICS OF CURVED BEAMS

The paper presents a concise framework studying the coupled vibration of curved beams, whether the curvature is built-in or is caused by loading. The governing equations used are both geometrically exact and fully intrinsic, with a maximum degree of nonlinearity equal to two. For beams with initial curvature, the equations of motion are linearized about the reference state. For beams that are curved because of the loading, the equations of motion are linearized about the equilibrium state. A central difference spatial discretization scheme is applied, and the resulting linearized ordinary differential equations are cast as an eigenvalue problem. Numerical examples are presented, including: (1) validation of the analysis for both in-plane and out-of-plane vibration by comparison with published results, and (2) presentation of results for vibration of curved beams with free-free, clamped-clamped, and pinned-pinned boundary conditions. For coupled vibration, the numerical results also exhibit the low-frequency mode transition or veering phenomenon. Substantial differences are also shown between the natural frequencies of curved beams and straight beams, and between initially curved and bent beams with the same geometry.