一类单自由度非自治系统的非线性振动
A Kind of Nonlinear Oscillations of Single Degree of Non-Autonomy System
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摘要: 本文用奇异摄动理论多尺度法的导数展开法[1],求解了在微粘性阻尼作用下,连结在一个非线性弹簧上的一个质点的受迫振动方程.研究的是四次非线性问题,讨论了四种情况:非共振的软激发;非共振的硬激发;共振的软激发;共振的硬激发.Abstract: In this paper we use the method of derivative expansion of multiple scales of singular perturbations, and we have solve the forced vibration equation of a particle attached to a nonlinear spring under the influence of slight viscous damping. The problem is of the fourth order nonlinearity. The four cases discussed are the soft excitation of non-resonance, the hard excitation of non-resonance, the soft excitation of resonance, the hard excitation of resonance.
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[1] 钱伟长主编,《奇异摄动理论及其在力学中的应用》,科学出版社(1981) [2] 钱伟长,《奇异摄动理论》,讲义应用数学和力学编辑部翻印(1980). [3] 丁一飞,Duffing方程次谐共振的分析,《全国非线性力学会议论文集》,第四册(1982). [4] Shaker, B. S., Nonlinear oscillations of single-degree of freedom systems, Int. Cong, on Recent Advances in Structure Dynamics (1980), U. of Southampton, Vol. 2 (1980), 569-578. [5] 冯登泰,《应用非线性振动力学》,中国铁道出版社,北京(1982). [6] 古屋茂、南云仁,《非线性振动论》,上海科学技术出版社.(1962). -
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