等截面铁摩辛柯梁-抗转阻尼器系统的复模态特性

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (23) : 174-179.

论文

等截面铁摩辛柯梁-抗转阻尼器系统的复模态特性

陈勇, 刘盼

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Complex modal characteristic of a system of a uniform Timoshenko beam with rotational dampers

Chen Yon , Liu Pan

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摘要

针对等截面铁摩辛柯梁-抗转阻尼器系统的自由振动，在复数域采用NAM法，推导了多种边界条件下带有任意个抗转阻尼器的无量纲精确解及系统特征方程。采用构造实函数的方法获得该复特征方程的复数域解。数值实例分析中与有限元结果进行了比较，验证了本文方法。该系统为非比例阻尼系统，研究结果表明存在系统最大阻尼比和最优阻尼系数。针对带有单个阻尼器的振动系统，研究给出了系统最大阻尼比、最优阻尼系数与阻尼器的最优安装位置。最后将均连接阻尼器的铁摩辛柯梁和欧拉-伯努利梁的结果进行了比较，表明前者获得的第一阶模态最大阻尼比略小于后者。

Abstract

For the free vibration of a uniform Timoshenko beam with multiple arbitrarily placed rotational dampers, taking advantage of the numerical assembly method (NAM), the exact solution and characteristic equation for a Timoshenko beam with any number of rotational dampers are presented, in a range of various boundary conditions. The complex-valued natural frequencies of the system were achieved by constructing a real-valued function. Numerical study results were compared with those obtained by finite element method (FEM). Good agreement is observed, which confirms the validity of the present solution. As a non-proportional damping system, it is evident that there is a system maximum damping ratio and optimum damping coefficient of the system. With consideration of a single-rotational-damper case, the curves of the system maximum damping ratios and optimum damping coefficients varying with damper’s position are illustrated via parametric study. Finally, the comparison of the results attained via Timoshenko beam and Euler-Bernoulli beam indicates that the latter would achieve a slightly higher damping ratio that corresponds to the first mode.

导出引用

陈勇;刘盼. 等截面铁摩辛柯梁-抗转阻尼器系统的复模态特性[J]. 振动与冲击, 2012, 31(23): 174-179

Chen Yon;Liu Pan. Complex modal characteristic of a system of a uniform Timoshenko beam with rotational dampers [J]. Journal of Vibration and Shock, 2012, 31(23): 174-179