基于样条有限点法的变截面Euler梁横向自由振动分析

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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。

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	刘鹏1
	刘红军1
	林坤1
	秦荣2

关键词 ：欧拉梁理论, 变截面梁, 横向自由振动, 样条有限点法

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..

Key words： Bernoulli–Euler beam theory Tapered beam free transverse vibration spline finite point method;

收稿日期: 2015-09-17 出版日期: 2016-05-25

引用本文:

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. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(11): 66-73.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2016/V35/I11/66

[1] Shahba A, Rajasekaran S. Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials[J]. Applied Mathematical Modelling, 2012,36(7):3094-3111.
[2] 周叮. 一类变截面梁横向自由振动的精确解析解[J]. 振动与冲击, 1996, 15(03):12-15.
ZHOU Ding, the exact analytical solution of transverse free vibration of a type of beams with variable cross-sections[J]. Journal of Shock and vibration, 1996, 15(03):12-15.
[3] 朱由锋, 朱由国. 基于有限差分法的变截面旋转梁弯曲振动[J]. 噪声与振动控制, 2014, 34(03):6-10.
ZHU You-feng, Zhu You-guo, Analysis of bending vibration of rotating tapered beams base on finite difference method[J] Noise and Vibration Control, 2014, 34(03):6-10.
[4] 钱波, 岳华英. 变截面梁横向振动固有频率数值计算[J]. 力学与实践, 2011, 33(06):45-49.
QIAN Bo, Yue Hua-ying, Numerical calculation of natural frequency of transverse vibration of non-uniform beams[J].Mechanics in Engineering, 2011, 33(06):45-49.
[5] Ozgumus O O, Kaya M O. Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli–Euler beam by differential transform method[J]. Journal of Sound and Vibration, 2006,289(1):413-420.
[6] Şimşek M, Kocatürk T, Akbaş Ş D. Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory[J]. Composite Structures, 2013,95(0):740-747.
[7] 崔灿, 蒋晗, 李映辉. 变截面梁横向振动特性半解析法[J]. 振动与冲击, 2012, 31(14):85-88.
CUI Can, Jiang Huan, Li Ying-hui, Semi-analytical method for calculating vibration characteristics of variable cross-section beam [J]. Journal of Shock and vibration, 2012, 31(14):85-88.
[8] Huang Y, Li X. A new approach for free vibration of axially functionally graded beams with non-uniform cross-section[J]. Journal of Sound and Vibration, 2010,329(11):2291-2303.
[9] 秦荣. 样条有限点法[J]. 广西大学学报, 1980, 5(02):18-35.
QIN Rong. Spline finite point method[J].Journal of Guangxi University, 1980,5(02):18-35
[10] 秦荣. 结构力学中的样条函数方法[M]. 南宁: 广西人民出版社, 1984：
QIN Rong, Spline Function Method on Structural Mechanics, Nanning: Guangxi People Press. 1984.
[11] 秦荣. 样条无网格法[M]. 北京: 科学出版社, 2012：
QIN Rong, Spline meshless method[M].Beijin: Science Press. 2012.
[12] 李秀梅, 李萍, 黄幸, 等. 连续梁分析的样条有限点法及程序设计[J]. 广西大学学报(自然科学版), 2014, 39(04):732-739.
LI Xiu-mei, Li Ping, Huang Xing, et. al, Spline finite point method for continuous beam analysis and program design[J] .Journal of Guangxi University, 2014, 39(04):732-739.
[13] 秦荣. 复合材料板壳分析的样条有限点法[J]. 工程力学, 2001,18(01):14-22.
QIN Rong, Analysis of composite plate and shell based on spline finite element method [J].Engineering Mechanics, 2001,18(01):14-22
[14] 秦荣, 王建军, 李秀梅. 箱拱桥梁地震反应分析的新方法研究[J]. 工程力学, 2009, 26(05):148-152.
QIN Rong, Wang Jianjun, Li Xiumei. Study on new method for seismic response analysis of box arch bridge [J]. Engineering Mechanics, 2009, 26 (05):148-152.
[15] 崔灿. 变截面梁振动特性快速算法及其应用[D]. 西南交通大学, 2012:1-78.
CUI Can, A fast calculation methods application for vibration characteristics for beam with variable cross-section. [D]. Master dissertation of Southwest Jiaotong University, 2012.