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A Complex-valued Solution of Free Vibration for Tapered Beams with Any Number of Rotational Dampers |
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PP: 749-758 |
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Author(s) |
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Yong Chen,
Pan Liu,
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Abstract |
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| Exact analytical solution of free vibration for a linearly tapered beam with multiple arbitrarily placed rotational dampers is developed by taking advantage of the numerical assembly method (NAM) and Bessel functions. A characteristic equation for a tapered beam with any number of rotational dampers is therefore addressed in complex domain. Corresponding results for beams with different boundary conditions are also presented. The presence of the rotational dampers renders the solution of the characteristic equation complex valued. Therefore, a method is proposed to solve the equation in complex domain. To ensure the reliability of this method, the finite elements method (FEM) is used to verify the results achieved via the characteristic equation. Furthermore, with consideration of a single-rotational-damper case, the curves of the total maximum damping ratios and total optimal damping coefficients varying with taper ratios are also depicted for convenience of engineering application. |
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