基于样条有限点法的变截面Euler梁横向自由振动分析  

Free transverse vibration analysis of tapered bernoulli-euler beams based on spline finite point method

作　　者：刘鹏[1] 刘红军[1] 林坤[1] 秦荣[2] 

机构地区：[1]哈尔滨工业大学深圳研究生院,广东深圳518055 [2]广西大学土木建筑工程学院,南宁530004

出　　处：《振动与冲击》2016年第11期66-73,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(51178153)

摘　　要：基于Bernoulli-Euler梁理论,采用样条有限点法建立考虑截面高宽度沿轴线性变化的变截面Euler梁振动分析的计算模型,通过沿梁轴线设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样条函数对梁的位移场进行插值,基于Hamilton原理导出变截面Euler梁的振动方程,推导考虑截面尺寸变化效应的总刚度和总质量矩阵的表达式,并编制计算程序,算例分析表明,模型的变截面梁的横向自振频率解答与文献解答吻合良好,计算精度和计算效率高,且模型边界处理简单,取样条离散节点数为15时,模型可以取得较高精度且解答趋于稳定。模型可适用于不同边界、不同截面变化率和不同截面类型的变截面Euler梁的自由振动分析。Based on Bernoulli-Euler beam theory,a new model was presented here to study free transverse vibration problems of tapered Euler beams by using the spline finite point method(SFPM)considering both width and height of beams' cross section linearly varying along the axial direction.With the proposed method,a beam was discretized by a set of uniformly scattered spline nodes along the axis direction instead of meshes,and the cubic-B spline interpolation functions were utilized to approximate the displacement filed of the beam.The free vibration equation of the beam was derived base on Hamilton Principle,and the global stiffness and mass matrices for the tapered beam were deduced in detail.The results of examples showed that the solutions to natural frequencies of tapered beams based on the proposed method are good in agreement with those reported in literatures;the proposed method has a higher accuracy,a lower computational cost and an easier way for boundary treatment;the solutions with a higher accuracy can be achieved by selecting the spline node number of no less than 15;the presented model is suitable for the free transverse vibration of tapered beams with various cross-section types,tapered ratios and boundary conditions.

关 键 词：欧拉梁理论 变截面梁 横向自由振动 样条有限点法 

分 类 号：TU311.3[建筑科学—结构工程]