样条有限点法分析旋转变截面Euler梁弯曲自由振动问题

发布时间：2018-03-07 02:33

本文选题：Euler-Bernoulli梁理论　切入点：旋转变截面梁　出处：《湖南大学学报(自然科学版)》2016年09期 　论文类型：期刊论文

【摘要】：基于Euler-Bernoulli梁理论,采用样条有限点法建立旋转变截面梁弯曲振动分析新模型.通过沿梁轴线均匀布置一定数量的样条节点对变截面梁样条离散化,采用三次B样条函数对变截面梁的位移场进行插值.考虑截面尺寸变化和旋转离心刚化效应的影响,基于Hamilton原理推导出旋转变截面梁计算模型的总刚度和总质量矩阵表达式,编制程序对旋转变截面梁动力特性进行分析,并建立ANSYS有限元模型进行比较验证.结果表明:本文解答与文献和有限元解答吻合良好,本文模型具有计算精度好、建模效率高、边界条件简单和程序编制方便的优点,可适用于不同边界约束、截面变化率、截面变化类型、旋转角速度和轮毂半径条件下的旋转变截面梁的弯曲自由振动问题.参数分析表明截面变化率和旋转角速度对旋转变截面梁动力特性有重要影响.
[Abstract]:Based on Euler-Bernoulli beam theory, a new model of bending vibration analysis of rotating variable section beam is established by using spline finite point method. A certain number of spline nodes are uniformly arranged along the axis of the beam to discretize the spline of the variable section beam. The cubic B-spline function is used to interpolate the displacement field of a beam with variable cross section. Considering the effect of the change of section size and the effect of centrifugal rotation, the expressions of total stiffness and total mass matrix of the calculation model of rotating variable section beam are derived based on the Hamilton principle. A program is compiled to analyze the dynamic characteristics of rotating beams with variable cross-section, and a ANSYS finite element model is established for comparison and verification. The results show that the solutions in this paper are in good agreement with the literature and the finite element solutions, and the model has good calculation accuracy and high modeling efficiency. The advantages of simple boundary conditions and convenient programming can be applied to different boundary constraints, cross-section change rates, and cross-section variation types. Under the condition of rotating angular velocity and hub radius, the bending free vibration of rotating beam with variable cross section is discussed. The parameter analysis shows that the rate of change of cross section and the speed of rotation angle have important influence on the dynamic characteristics of rotating variable section beam.
【作者单位】：哈尔滨工业大学深圳研究生院;广西大学土木建筑工程学院;
【基金】：国家自然科学基金资助项目(51178153)~~
【分类号】：O327

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