等截面铁摩辛柯梁-抗转阻尼器系统的复模态特性  

Complex modal characteristic of a uniform Timoshenko beam with rotational dampers

作　　者：陈勇[1] 刘盼[1] 

机构地区：[1]浙江大学建筑工程学院,杭州310058

出　　处：《振动与冲击》2012年第23期174-179,共6页Journal of Vibration and Shock

基　　金：浙江省自然科学基金(Y1110143)

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。For the free vibration of a uniform Timoshenko beam with multiple arbitrarily placed rotational dampers, taking advantages of the numerical assembly method （NAM） , its exact solution and characteristic equation were derived under various boundary conditions. The complex-valued natural frequencies of the system were achieved by constructing a real-valued function. Numerical example results were compared with those obtained by the finite element method （FEM）. Good agreement was observed, it verified the validity of the presented method. It was shown that this is a non-proportional damping system, there are a maximum damping ratio and an optimal damping coefficient of the system ; with consideration of a single-rotational-damper case, the curves of the system maximum damping ratio and optimal damping coefficient varying with damper＇s position are illustrated via parametric study. Finally, the comparison of the results attained for a Timoshenko beam and a Euler-Bernoulli beam with the same rotational dampers indicated that the former achieves a slightly smaller damping ratio of the first mode than that of the latter.

关 键 词：自由振动 复模态特性 铁摩辛柯梁 系统最大阻尼比 最优阻尼系数 

分 类 号：TU311.3[建筑科学—结构工程]