均匀温度场中弹性直杆非线性振动解析解  

Analytic solution for nonlinear vibrations of elastics straight bar in uniform temperature fields

作　　者：石晶[1,2] 郝际平[2] 

机构地区：[1]长安大学理学院,陕西西安710064 [2]西安建筑科技大学土木工程学院,陕西西安710055

出　　处：《长安大学学报（自然科学版）》2008年第5期120-122,共3页Journal of Chang’an University(Natural Science Edition)

基　　金：国家自然科学基金项目(50378078)

摘　　要：针对均匀温度场中弹性直杆非线性振动方程,采用迭代法得到对应的算子,导出满足该方程及其初始条件的解答,用不动点理论论证了解答的存在性和唯一性,并给出与近似法对比的计算结果。研究结果表明,该方法迭代格式简洁,对弹性直杆热膨胀状态下的非线性振动问题的研究有一定的实用价值。By using iterative method to construct the operator , the analytic solution for nonlinear vibration equation of elastics straight bar in uniform temperature fields is derived. The solution is satisfied with the equation and the initial condition. By employing the fixed-point theory, the correctness and the uniqueness of the solution are proven. The calculation results of the solution and approximation method are given. The iteration scheme is simple and effective to solve the nonlinear vibration equation of elastic column in state of thermal expansion. 2 tabs, 1 fig, 5 refs.

关 键 词：均匀温度场 弹性直杆 非线性振动方程 不动点理论 解析解 

分 类 号：O322[理学—一般力学与力学基础]