摘要
基于Euler-Bernoulli梁理论并且考虑几何非线性和纵向振动的影响,研究了纵向和横向振动的FGM梁非线性动力学问题。假设材料的性质沿梁的厚度方向按幂指函数形式连续变化,利用Hamilton变分原理建立了梁的非线性动力学控制微分方程。采用打靶法对方程进行数值求解,结果表明:横向振动的过程中存在着纵向振动,且纵向振动削弱了横向振动,但其影响较小。在此基础上分析了考虑纵向振动时梯度指数、长细比、载荷等对梁的动力响应特性的影响。
Based on Euler-Bernoulti beam theory and considering the effects of geometric nonlinearity and longitudinal vibration,the nonlinear dynamic problems of F G M beams with longitudinal and transverse vibrations were studied.The material properties were assumed to vary continuously along the thickness direction of the beam in the form of power exponential function,the nonlinear dynamic governing differential equation of the beam was established by using the Hamilton variational principle.The numerical solution of the equation was carried out by shooting method,the results showed that there existed in the process of transverse vibration,and the longitudinal vibration weakened the transverse vibration,but its impact was small.On this basis,considering longitudinal vibration,the influence of the gradient index,slenderness ratio and load on the dynamic response features of the beam was analyzed.
作者
梁波
赵永刚
姚世平
Liang Bo;Zhao Yonggang;Yao Shiping(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)
出处
《甘肃科学学报》
2017年第5期1-5,共5页
Journal of Gansu Sciences
基金
国家自然科学基金项目(11472123)
关键词
功能梯度材料
梁
非线性
频率
打靶法
Functionally graded material
Beam
Nonlinearity
Frequency
Shooting method
