HOMOCLINIC ORBIT OF STRONGLY NONLINEAR AUTONOMOUS OSCILLATOR VIA GENERALIZED PADÉ APPROXIMATION METHOD
-
摘要: 在经典Padé逼近理论的基础上进行了相应推广,提出了广义Padé逼近方法,并针对强非线性自治振子同宿轨的求解问题,利用双曲函数构造了一种新的广义Padé逼近式. 首先,该广义Padé逼近式有着较简单的泰勒展开式,与现有的Padé逼近式相比,在计算同阶逼近时,计算量更少;其次,该方法在强非线性时,依然有着较高的精度;第三,该方法并不局限于某些特定的系统,而是有着较广的适用范围. 因此对于广义Padé逼近方法的研究具有一定的实际意义和理论价值.Abstract: The generalized Padé approximate definition is proposed based on classical definition of Padé approximation. By utilizing the hyperbolic function, a new form of generalized Padé approximation is constructed for determining the homoclinic orbit of strongly nonlinear autonomous oscillator. The Taylor expansion of generalized Padé approximation in this paper is simpler than existing ones, which means that the proposed method has less complexity in calculation. The precision of the solutions is high when the nonlinear parameters are large. The proposed method is not restricted to solve some certain systems. It can be utilized in many kinds of systems, which means that the proposed method is generally applicable. So the investigation in generalized Padé approximation is meaningful.
-
Key words:
- generalized Padé /
- approximate /
- homoclinic orbit /
- strongly nonlinear
-
Nayfeh AH,Balachandran B. Applied Nonlinear Dynamics,Analytical,Computational,and Experimental Methods. New York: Wiley, 1995 Melnikov VK. On the Stability of the Center for Time Periodic Perturbations. Moscow: Trans Moscow Math, 1963 Chen SH, Chen YY, Sze KY. A hyperbolic perturbation method for determining homoclinic solution of certain strongly nonlinear autonomous oscillators. Journal of Sound and Vibration, 2009, 322: 381-392 Chen YY, Chen SH, Sze KY. A hyperbolic Lindstedt-Poincaré method for homoclinic motion of a kind of strongly nonlinear autonomous oscillators. Acta Mechanica Sinica, 2009, 25(5): 721-729 Xu Z, Chan HSY, Chung KW. Separatrices and limit cycles of strongly nonlinear oscillators by the perturbation-incremental method. Nonlinear Dynamics, 1996, 11: 213-233 Mikhlin YV. Matching of local expansions in the theory of non-linear vibrations. Journal of Sound and Vibration, 1995, 182: 577-588 Manucharyan GV, Mikhlin YV. The construction of homo- and heteroclinic orbits in non-linear systems. Journal of Applied Mathematics and Mechanics, 2005, 69: 39-48 张琪昌,冯晶晶,王炜. 类Padé逼近方法在二维振动系统的应用. 力学学报, 2011, 43(5): 914-921 (Zhang Qichang, Feng Jingjing, Wang Wei. The construction of homoclinic and heterclinic orbit in two-dimensional nonlinear system based on the quasi-Padé approximation. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 914-921 (in Chinese)) Emaci E, Vakakis AF, Andrianov IV, et al. Study of two-dimensional axisymmetric breathers using Padé approximants. Nonlinear Dynamics, 1997, 13: 327-338 Martín P, Baker GA. Two-point quasifractional approximant in physics. Truncation error. Journal of Mathematical Physics, 1991, 32: 1470-1477 -
点击查看大图
计量
- 文章访问数: 1191
- HTML全文浏览量: 58
- PDF下载量: 820
- 被引次数: 0
下载:
