Pseudolinear approximation in the averaging method (Q1031826)

This paper considers an averaging method for the investigation of nonlinear systems using the so-called generating system which appears when a small parameter vanishes, and which is essentially nonlinear. In the case of linear approximation the first approximation can be described by sine and cosine functions with frequencies independent of the initial conditions. In the case of nonlinear generating system, the solutions can be represented by special periodic functions with frequencies depending on the initial conditions. The problem can be solved by introduction of a new small parameter determining the deviation of the special functions from sinusoidal form. The author studies such procedure for the second-order essentially nonlinear vibration systems. It is shown that the method simplifies the mathematical treatment of nonlinear vibrations with arbitrary amplitudes.