Nonlinear Oscillation of a 3 DOF Elastically Mounted Rigid Body with Superharmonic Resonance : Application of the Method of Normal Forms with the Aid of Computer Algebra

Abstract

The concept of modal analysis is well developed for linear systems. However, we are not aware of the way of dealing with nonlinear dynamical problems along this method. The basic idea underlying the method of normal forms is the use of local coordinate transformations so that the dynamical system can take the "simplest form". For nonlinear systems, the coordinate transformation will generally be nonlinear. This technique is demanded for us to find application in engineering, but most of the previous works on normal forms deal exclusively with simple dynamical systems such as autonomous systems. In this paper, we examine more practical systems. As an example of these systems we give an elastic mounting of four-stroke engine for marine use at low speed ; consequently we consider the problem of an elastically mounted rigid body having three degrees of freedom which can include a rotating oscillator.