基于样条有限点法的变截面Euler梁横向自由振动分析

刘 鹏1,刘红军1,林 坤1,秦 荣2

振动与冲击 ›› 2016, Vol. 35 ›› Issue (11) : 66-73.

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PDF(1316 KB)
振动与冲击 ›› 2016, Vol. 35 ›› Issue (11) : 66-73.
论文

基于样条有限点法的变截面Euler梁横向自由振动分析

  • 刘 鹏1,刘红军1,林 坤1,秦 荣2
作者信息 +

Free transverse vibration analysis of tapered Bernoulli–Euler beams based on spline finite point method

  • LIU Peng1, LIU Hong-jun1, LIN Kun1, Qin Rong2
Author information +
文章历史 +

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,本文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,本文模型可以取得较高精度且解答趋于稳定。本文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。

Abstract

Based on the Bernoulli–Euler beam theory(EBT), a new model was presented in the paper to study the free transverse vibration problems of tapered Euler beam by using Spline Finite Point method (SFPM)with consideration the effects of breadth and height double linearly tapered along the longitudinal direction. In proposed method, the beam was discretized by a set of uniformly scattered spline nodes along the beam 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 was derived base on the Hamilton Principle, and the global stiffness and mass matrices for tapered beams with varied cross-section were deduced in detail. Results shows that the solutions of natural frequencies of tapered beams based on the proposed method are in agreement with those reported literatures very well with higher accuracy, lower computational cost and easier way of boundary treatment. Solutions with higher accuracy can be achieved by selecting the spline nodes number to be no less than 15. The presented model is suitable for the transverse free vibration of tapered beams with various cross-sections type, 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

Key words

Bernoulli–Euler beam theory / Tapered beam / free transverse vibration / spline finite point method; 

引用本文

导出引用
刘 鹏1,刘红军1,林 坤1,秦 荣2. 基于样条有限点法的变截面Euler梁横向自由振动分析[J]. 振动与冲击, 2016, 35(11): 66-73
LIU Peng1, LIU Hong-jun1, LIN Kun1, Qin Rong2. Free transverse vibration analysis of tapered Bernoulli–Euler beams based on spline finite point method[J]. Journal of Vibration and Shock, 2016, 35(11): 66-73

参考文献

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