This paper studies the vibration of beams in 3D space with arbitrary shape. Based on results from differential geometry of curves, a set of beam vibration dynamics equations is developed, comprising six partial differential equations (PDE). The beam dynamics equations account for both the in-plane and out-of-plane beam vibrations simultaneously. In addition, the equations explicitly capture the coupling between different vibration mode types, which occur when the beam exhibits geometric irregularities such as bending, torsion, and twisting. The proposed beam dynamics equations are solved numerically. Comparison between experimental results and numerical results obtained by solving the PDEs proposed in this paper shows a good match for in-plane and out-of-plane curved beam vibrations.

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