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Vibration Modal Analysis of Cantilever Beams with Complicated Elasticity Boundary Constraint

Y.-F. LIU, W. LI, X.-F. YANG


In the classical vibration theory, the foundation is generally idealized as an absolutely rigid body of infinite quality ignoring the dynamic influence of flexibility. Resultingly, the vibration characteristics analysis and control cannot attain the expected high-precision results. In this paper, to fully consider the effect of elasticity, the boundary constraint of the cantilever beam was considered to be a torsional spring and vertical spring system. Combining with the vibration characteristic of the Bernoulli-Euler beam, the dynamic model of cantilever elastic restraint system was established. Subsequently, the bending vibration differential equation and mode were obtained. To investigate the relationship between spring stiffness and modal characteristics, numerical analysis was conducted,moreover,the fixed support and free sustained boundary conditions were combined. The numerical results demonstrated that the natural frequency was increased as the stiffness increases, furthermore,the natural frequency value of elastic constraints was between fixed support and free support within certain stiffness and modal. Finally, in order to verify the effectiveness and correctness of the elastic dynamic model, numerical simulation of the cantilever elastic restraint system was performed using ANSYS software. The analytical results and findings provide a theoretical guidance to study the vibration characteristics and control of the cantilever beam with complicated elasticity boundary constraint

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