A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomou...A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.展开更多
基金Supported by the National Natural Science Foundation of China(No.11172199)the Key Project of Tianjin Municipal Natural Science Foundation(No.11JCZDJC25400)
文摘A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.
