考虑端部质点的中心刚体-楔形梁系统动力特性研究

对带有端部质点的中心刚体-楔形梁系统的动力学特性进行了研究．楔形梁为Euler Bernoulli 梁，其宽度与高度随着长度方向改变．采用假设模态法对楔形梁的变形场进行离散，在考虑梁的横向和纵向变形以及由于横向弯曲而引起的纵向缩短量的条件下，运用第二类拉格朗日方程推导出系统的动力学方程，并编制动力学仿真软件．通过仿真算例对系统的动力学特性进行研究，结果表明：同等条件下梁的形状与有无端部质点对系统的刚柔耦合动力学响应以及系统频率的影响十分明显．因此采用楔形梁结构进行仿真更具实际意义且仿真结果更加精确．

Dynamic Study of Central Rigid Body - Tapered Beam System with Tip Mass

This paper focuses on studying the dynamic characteristics of the Wedge Hub-Beam System with the tip mass. The Euler Bernoulli beam is the type of tapered beam used in this study, whose width and height vary with the length. The assumed-mode method is adopted to disperse the deformation field of the tapered beam and Lagrange's equations of second kind is used to deduce the kinetic equations of the system, as well as to compile the dynamics simulation software. The lateral and longitudinal deformations of the beam and the longitudinal shrinking due to lateral bending deformation are considered. Comparisons are made between the simulation results of three structures, i.e., the tapered beam with tip mass, the tapered beam and the uniform beam. The results show that: under the same conditions, the shape of the beam with or without tip mass have a very obvious influence on the rigid-flexible coupling dynamical response of the system; the influence of adding a tip mass on the vibration response of the tip of beam is very obvious and the tip mass will reduce the natural frequency of the beam. Therefore, the use of tapered beam structure for simulation is of more practical significance, and can get more accurate simulation results.