摘要
为了研究截面不均匀系数对梁振动特性的影响,基于Timoshenko梁理论,建立变截面梁自由振动的分析模型.首先,采用傅里叶级数与辅助函数的形式表示Timoshenko梁的位移函数,以解决梁端位移在采用常规傅里叶级数形式时导致的边界位移导数不连续问题.其次,基于拉格朗日函数,利用瑞利-里兹法得到系数满足的线性方程组,进而获得不同边界条件下Timoshenko梁的固有频率及相应的振型模态.最后,分析截面系数对结构固有频率的影响.数值算例表明,该求解方法能够稳定收敛且计算效率高,具有较高的精度.
To investigate the effect of non-uniformity coefficient on the vibration characteristic of beam,an analysis model of free vibration of variable cross-section beams is formulated based on the Theory of Timoshenko Beam.Firstly,the displacement function of Timoshenko beam is expressed as sum of a single Fourier series and auxiliary functions,which can improve the discontinuous issues about the derivatives of displacement at the beam’s ends.Then,the Rayleigh-Ritz methods based on the Lagrange function is used to obtain the linear equations for the coefficients to satisfy,thus the natural frequencies and corresponding modes of Timoshenko beam under different boundary conditions are obtained.Finally,the influence of cross-section coefficient on the natural frequency of the structure is analyzed.The characteristics of generality,convergence,efficiency and accuracy of the proposed method are fully demonstrated and verified through numerical examples.The work of this paper provides a basis for calculating the dynamic characteristics of beams with variable sections in engineering.
作者
常婷婷
鲍四元
Chang Tingting;Bao Siyuan(School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)
出处
《宁夏大学学报（自然科学版）》
CAS
2023年第2期123-130,136,共9页
Journal of Ningxia University(Natural Science Edition)
基金
国家自然科学基金资助项目(11202146)
江苏省普通高校研究生科研创新计划项目。
