用改进的变形参数法求解强参数激励Mathieu方程  

Modified Strained Parameter Method for Strong Parametrical Excitation Mathieu Equation

作　　者：张海燕[1] 唐友刚[1] 谢文会[1] 

机构地区：[1]天津大学建筑工程学院,天津300072

出　　处：《天津大学学报》2006年第11期1289-1292,共4页Journal of Tianjin University(Science and Technology)

基　　金：国家自然科学基金资助项目(50279026);教育部博士点基金资助项目(20050056052)

摘　　要：为了研究大幅值参数激励M ath ieu方程,通过引入新的变换,将强参数激励系统转化为弱参数激励系统,利用改进的变形参数法求解无阻尼项的M ath ieu方程,分别得到具有π和2π方程的周期解和相应的过渡曲线,并利用过渡曲线得到方程的不稳定区域和稳定域.结果表明,该方法与文献[7]得到的过渡曲线基本吻合,通过数值法验证了用该方法得到稳定域比文献[7]的结果更为合理.Parametrical exeitation Mathieu equation with large amplitude is investigated, The strong parametrical excited system was changed into weak parametrical excited system by a new transformation. Using modified strained parameter method, the periodic solutions with periods of π and 2π of undamped Mathieu equation were obtained and the corresponding transition curves were gained, The stability and instability domain of the equation were determined by the transition curves, The results show that the transition curves obtained closely agree with those in Ref. [7], while the stability domain obtained here is more reasonable than that in Ref. [7], which is proved by numerieal method.

关 键 词：MATHIEU方程 强参数激励 过渡曲线 稳定域 

分 类 号：O353[理学—流体力学]