CAJ | 학술논문

复杂变截面梁结构在运动过程中产生柔性变形对其运动精度与动力学性能有很大影响，因此建立准确的数学模型描述其柔性变形十分重要。基于绝对节点坐标法，考虑变截面梁单元边界特性，建立单元边界非线性函数关系，通过改变积分上下限，将其引入到单元质量矩阵、刚度矩阵的计算模型中。基于牛顿方程，建立变截面梁系统的柔体动力学模型。利用Matlab数值仿真，对不同单元数目、不同变截面参数的单摆梁进行动力学仿真分析。结果表明梁结构的刚度计算值与划分的单元数目相关，不同单元数目会影响系统仿真计算的效率和精度，使得运动变形仿真产生较大偏差。在保证梁体积相同的情况下，改变梁单元边界函数，可提高梁的刚度，减小其末端的运动变形，提高梁的动力学性能。在不影响梁刚度的前提下，通过改变梁截面参数，可有效降低梁的质量。
복잡변절면량결구재운동과정중산생유성변형대기운동정도여동역학성능유흔대영향，인차건립준학적수학모형묘술기유성변형십분중요。기우절대절점좌표법，고필변절면량단원변계특성，건립단원변계비선성함수관계，통과개변적분상하한，장기인입도단원질량구진、강도구진적계산모형중。기우우돈방정，건립변절면량계통적유체동역학모형。이용Matlab수치방진，대불동단원수목、불동변절면삼수적단파량진행동역학방진분석。결과표명량결구적강도계산치여화분적단원수목상관，불동단원수목회영향계통방진계산적효솔화정도，사득운동변형방진산생교대편차。재보증량체적상동적정황하，개변량단원변계함수，가제고량적강도，감소기말단적운동변형，제고량적동역학성능。재불영향량강도적전제하，통과개변량절면삼수，가유효강저량적질량。
The mathematical model of flexible deformation and its coupling effect with dynamic behavior are very important for the kinematic behavior of variable cross-section beams. The nonlinear functions are employed to describe the boundary features of variable cross-section beams. The model to calculate the mass matrix and the stiffness matrix of element of beam is proposed based on the absolute nodal coordinate formulation, in which upper and lower limits in the integral formula is considered as nonlinear function. The dynamic model of the variable cross-section beam is established by using Newton formulation. The dynamic behavior of a classic pendulums with different number of elements and different kinds of cross-sections are numerical investigation by using Matlab. The results show that the beam stiffness depends on the number of elements. Various numbers of elements could influence the efficiency and accuracy of numerical simulation as well as result in deviation to the simulation. The stiffness of beam increases and the deformation decreases with the decrease of element number of beam. The variation of boundary of beam may improve the stiffness and decrease its flexible deformation when the volume of beam is constant. In addition, it may light the weight of beam structures when the stiffness is constant.