摘要
基于非局部理论,对任意弹性边界Euler-Bernoulli梁的横向振动特性进行分析。在结构两端边界引入横向位移弹簧和旋转约束弹簧,通过设置其刚度大小来模拟从自由到固支的各种边界条件。计算中先将梁的位移函数以改进傅里叶级数形式表示,然后采用基于Lagrange泛函的瑞利-里兹法建立关于改进傅里叶级数系数的线性方程组。根据此方程组有非零解的条件,通过求解广义特征值问题得到梁的固有频率和振型曲线。算例结果表明所提方法具有合理性且具有良好的精度,并进一步探究非局部影响系数与弹性边界约束刚度对非局部梁振动的影响。
The transverse vibration of nonlocal Euler-Bernoulli beams with arbitrary elastic boundary is analyzed based on the nonlocal theory.The transverse spring and the rotational spring are introduced at both ends of the beam structure.The stiffness of the two ends is properly chosen to simulate the different boundary conditions.First,the displacement function of the beam is represented by the improved Fourier series.Then,the Rayleigh-Ritz method based on the Lagrange function is used to create a system of linear equations about the spectro-geometric coefficients.According to the condition for non-zero solution,the natural frequencies and vibration modes of the beam structure are obtained by solving the generalized eigenvalue problem.Finally,the characteristics of generality,accuracy and efficiency of the proposed method are fully demonstrated and verified through numerical examples.The influence of nonlocal characteristic parameters and restraint stiffness on vibration of the nonlocal beam is further studied.
作者
鲍四元
曹津瑞
周静
BAO Si-yuan;CAO Jin-rui;ZHOU Jing(School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2020年第2期276-284,共9页
Journal of Vibration Engineering
关键词
结构振动
横向振动
非局部理论
谱几何法
弹性边界条件
structural vibration
transverse vibration
nonlocal theory
spectro-geometric method
elastic boundary condition
