Strongly Nonlinear Vibrations

Abstract

This chapter presents analytical successive approximations algorithms for different oscillators with strongly nonlinear characteristics. In general terms, such algorithms approximate temporal mode shapes of vibrations by polynomials and other simple functions of the triangular sine wave. In order to develope the algorithms, the triangular wave is introduced into dynamical systems as a new temporal argument. The corresponding manipulations with dynamical systems are described in the first three sections. Then the description focuses on the algorithm implementations for different essentially unharmonic cases including oscillators whose characteristics may approach nonsmooth or even discontinuous limits.