摘要
通过Chebyshev谱方法对变截面欧拉梁动态特性进行研究。采用Chebyshev多项式逼近欧拉梁弯曲位移函数的表达式,借助梁结构的拉格朗日函数,由Ritz方法将欧拉梁的固有频率问题转化为求解特征值问题,得到变截面欧拉梁在任意弹性边界条件下的自振频率。与解析解及已有文献解进行比较,验证Chebyshev谱方法在欧拉梁的动态特性分析中的准确性和优越性。所得结果可为欧拉梁在不同边界和不同截面类型下动态特性的分析提供理论参考。
The dynamic characteristics of Euler beams with variable section are studied by Chebyshev spectral method. The Chebyshev polynomials are used to approximate the expression of bending displacement function of Euler beams. With the help of Lagrange function of the beam structure, Ritz method is used to convert theEuler beam frequency problem into an eigenvalue problem, and the natural vibration frequencies of beams with variable cross-section under arbitrary elastic boundary conditions are obtained. The accuracy and superiority of Chebyshev spectral method in dynamic characteristic analysis of Euler beams are verified by comparison with analytical solution and existed solutions in literature. The results can provide theoretical reference for analyzing the dynamic characteristics of Euler beams with different boundary conditions and different section types.
作者
陶彦鸣
张旭鹏
鲍四元
TAO Yanming;ZHANG Xupeng;BAO Siyuan(College of Civil Engineering, Suzhou University of Science and Technology, Jiangsu Suzhou 215011, China)
出处
《低温建筑技术》
2019年第9期24-28,共5页
Low Temperature Architecture Technology
基金
国家自然科学基金(11202146)
