二端离散元件动力学特性的矩阵描述法在阻振基座分析中的应用  

Investigation on dynamic characteristics of two pole discrete elements by matrix description approach and applications in analysis of anti-vibration mounting

作　　者：李江涛[1,2] 王纬波[2] 吴有生[2] 

机构地区：[1]上海交通大学海洋工程国家重点实验室,船舶海洋与建筑工程学院,上海200030 [2]中国船舶科学研究中心,江苏无锡214082

出　　处：《船舶力学》2010年第1期148-156,共9页Journal of Ship Mechanics

摘　　要：在元件坐标系下,分别推导了离散元件(质量、弹簧、阻尼、刚体)输入端状态向量与输出端状态向量之间的关系,给出了向前传递矩阵、向后传递矩阵和广义阻抗矩阵的解析公式。并且讨论了点阻抗或点导纳与传递矩阵或广义阻抗矩阵之间的关系。此外,文中还分别采用传递矩阵法和导纳矩阵法推导了阻振基座的纵向振动方程,得到了纵向力传递率的解析公式。两种方法得到的结果相同,但传递矩阵法的推导过程更简洁。文中还采用传递矩阵法推导了阻振基座的横向振动方程,得到了横向力传递率的解析公式。所导得的公式可用于指导阻振基座的动力学设计,计算工作量不大且精度较高。Relationships between input state vectors and output state vectors of discrete elements （mass, spring, damper, rigid body） are deduced respectively in element coordinating system. Analytical formulae of forward transfer matrix, reverse transfer matrix and generalized impedance matrix are derived separately. The correlation respectively between driving point impedance and transfer matrix or generalized impedance matrix and between driving point mobility and transfer matrix or generalized impedance matrix are discussed.Furthermore,the longitudinal vibration equations of the anti-vibration mounting are achieved both by transfer matrix method and mobility matrix method.The analytical formula of the longitudinal force transmissibility is given. Two approaches yield similar results, but the process of transfer matrix method is simpler.The transverse vibration equations of the anti-vibration mounting are also deduced using transfer matrix method. The analytical formula of the transverse force transmissibility is consequently given. Analytical formulae in this paper can be applied in dynamic design of the anti-vibration mounting to achieve good precision with less computation.

关 键 词：阻振基座 刚柔耦合系统 传递矩阵法 广义机械阻抗法 力传递率 

分 类 号：O32[理学—一般力学与力学基础] U661.44[理学—力学]