The normal modes of non-linear symmetric systems by group representation theory

Abstract

Group representation theory is applied to analyze a symmetric spring mass system of finite degree of freedom for non-linear normal modes of vibration. A set of symmetry operations constituting a group characterises the symmetry of a system. The symmetry adapted basis vectors, corresponding to the irreducible representations present in the reducible representation, are determined. The equations of motion in the symmetry adapted coordinates have a lower order of coupling. An equipotential surface in each invariant subspace is determined from which the normal mode vectors are evaluated in terms of the symmetry adapted basis vectors.