A METHOD OF CALCULATION OF STEADY-STATE OSCILLATIONS IN AUTONOMOUS NON-LINEAR SYSTEMS

作者：QIU SS^*; FILANOVSKY IM

来源：Journal of Sound and Vibration, 1990, 136(1): 35-44.

DOI：10.1016/0022-460X(90)90935-S

• Autonomous Nonlinear Systems
• Harmonic Balance Method
• Nonlinear Conservative System
• Nonlinear Differential Equation
• Steady State Oscillations
• Steady State Solutions

An extension of the harmonic balance method is presented for calculation of the steady state (periodic) solutions in autonomous non-linear systems. The non-linear differential equation is expanded into a system of linear differential equations which are solved consecutively. An approximate solution which includes a few harmonics (the main oscillation) is found from the first equation of this system by the ordinary harmonic balance method. Other harmonics and the corrections of the main oscillation are found as the forced solutions of the second, third and the following equations of the system. To improve the efficiency of correction calculations a systematic method for derivation of the forcing term in these equations is given. As an example, a non-linear conservative system with a non-symmetric non-linearity of the polynomial type is considered.

• 出版日期1990-1-8
• 单位华南理工大学