Abstract
The new classification of nonlinear vibrations is shown in Parts 1 and 2. In this paper we analyse the typical vibrations classified as accompanying type, branching type (1) and branching type 2. The numerical results corresponding to accompanying type ascertain the behaviour of the accompanying oscillation components which is expected by the form of nonlinear terms in the algebraic equations derived by applying the method of harmonic balance. The numerical results for 1/2-subharmonic oscillation classified as branching type (1) show that there is instability region for the oscillation. Then, we analyse nonlinear vibrations classified as branching type (2). In conventional treatment of the vibrations in elastic systems, they are dealt with as parametric excitations which occur in the Mathieu-Hill equation. The results obtained here are compared with the reuslts which are obtained by applying conventional treatment. In order to examine whether obtained periodic solutions are stable or unstable we solve complex eigenvalue problem.
