An investigation of the effects of curvatures on natural vibration characteristics of curved beams and plates

Abstract

Curved structures are mostly investigated through the numerical method. In the numerical model, the curved beam or plate is easily simulated by assembled elements. Although the approximate solution can be obtained, numerical results are inadequate to demonstrate the effect of the curvature on the whole system. In order to reveal such effect and implicative mechanism of the curvature, an analytical way needs to be proved applicable to the curved structure. The present thesis thus develops the perturbation method to analyze the natural behaviour of curved beam structures.

The governing equations for curved beams with the variable and arbitrary curvature are derived. The complex parameter introduced by the curvature is modified by the perturbation method. Simplified equations physically reveal the feature of the mode transition, impacts in terms of boundary conditions, etc. due to the change of curvatures. Based on the asymptotic solutions, the singly curved plate is analyzed by using the Rayleigh- Ritz method. The analysis is further developed to the laminated composite
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curved beam. Examples present extra characteristics brought by the composite materials. In order to support the analytical solutions, finite element models of the curved beam with different type of varying curvatures are established. Numerical results illustrate more phenomena in transition of mode shape following the change of curvatures and the wave propagation behaviour of curved beams.

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