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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,验证了所提出的方法。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。
Aiming at the free vibration of the system with the same cross-section, the NAM method is used to calculate the free vibration of the system. The non-dimensional exact solutions with arbitrary anti-rotation dampers and system characteristic equations are derived under various boundary conditions. The complex domain solution of the complex eigenvalue equation is obtained by constructing real function. Numerical examples are compared with the finite element results to verify the proposed method. The system is a non-proportional damping system, the results show that there is a system maximum damping ratio and the optimal damping coefficient. For the vibration system with a single damper, the maximum damping ratio of the system, the optimal damping coefficient and the optimal installation position of the damper are given. Finally, the results of the Torshin beam and the Euler-Bernoulli beam, both connected to the damper, are compared, showing that the former has a slightly lower maximum damping ratio than the latter.