Asymptotic solutions and stability analysis for generalized non-homogeneous Mathieu equation

作者：Younesian D; Esmailzadeh E^*; Sedaghati R

来源：Communications in Nonlinear Science & Numerical Simulation, 2007, 12(1): 58-71.

DOI：10.1016/j.cnsns.2006.01.005

• Asymptotic solutions
• Mathieu equation
• Stability analysis
• Transition curves
• Multiple scales method
• Strained parameter technique

The asymptotic solutions and transition curves for the generalized form of the non-homogeneous Mathieu differential equation are investigated in this paper. This type of governing differential equation of motion arises from the dynamic behavior of a pendulum undergoing a butterfly-type end support motion. The strained parameter technique is used to obtain periodic asymptotic solutions. The transition curves for some special cases are presented and their corresponding periodic solutions with the periods of 2 pi and 4 pi are evaluated. The stability analyses of those transition curves in the epsilon-delta plane are carried out, analytically, using the multiple scales method. The numerical simulations for some typical points in the epsilon-delta plane are performed and the dynamic characteristics of the resulting phase plane trajectories are discussed.

• 出版日期2007-2