Transfer matrix modeling for asymmetrically-nonuniform curved beams by beam-discrete strategies

Nonuniform and curved beams can be found in extensive engineering scenarios, ranging from big-scale structures of buildings, bridges to small mechanical systems of aerofoils, blades, micromachines, robotics and sensors. However, variable curvature and transverse asymmetry often lead to a complicated dynamic modeling. In this paper, two beam-discrete strategies are comparatively presented for the free vibration analysis of transversely asymmetric and curved beams and even their combinations. The proposed methodology involves discretizing a general nonuniform and curved beams into a sequence of constant beam segments with non-coaxial nodes or inclination angles, which enables a modular transfer matrix modeling process and hence offers a new way to divide the complex modeling into easier steps. A unified transfer matrix is derived for constant beam elements with non-coaxial nodes and inclination angles accounting for the shear deformation, rotary inertia and axial load in any combinations. The proposed beam-discrete strategies with a unified transfer matrix provide a new perspective in contrast to previous investigations. The advantages of easy programming and small degrees of freedom in the traditional transfer matrix method is extended to transversely asymmetric nonuniform and curved beams. Comparative validation with several engineering beams confirms these advantages.