Free vibration analysis of a composite cantilever beam using a Timoshenko beam model: analytical, numerical, and experimental approaches
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Abstract
This study investigates the free vibrations of a glass/polyester composite cantilever beam through an integrated analytical, numerical, and experimental approach. An analytical formulation, based on the Timoshenko beam model and incorporating bending-torsion coupling, was developed to compute natural frequencies and mode shapes. Numerical modeling, using finite element methods, simulated the vibrations while accounting for transverse shear and rotary inertia effects. Concurrently, an experimental modal analysis was performed by exciting the beam at multiple points and measuring natural frequencies via frequency response functions. The findings reveal strong agreement between the analytical and numerical approaches, with a relative error below 0.15%, but notable discrepancies with experimental data, exceeding 15%. These discrepancies are attributed to two main physical factors neglected in idealized models: the inherent material damping and the imperfect stiffness of the experimental support system. Adjusting the numerical model reduced these discrepancies, enhancing the method’s reliability. This approach provides a robust framework for designing composite structures, while highlighting the need to incorporate quantified damping and accurately defined material and boundary characteristics in future research for improved predictive accuracy.
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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