From a chain of nonlinear oscillators to nonlinear longitudinal vibrations of an elastic bar: the case of pure nonlinearity

Abstract

This study is concerned with a chain of oscillators in which discrete masses are connected mutually and with a base with purely nonlinear springs whose power of nonlinearity is assumed to be any real (non-integer or integer) number higher than unity. Similar nonlinear normal modes are determined and found to be associated with different bifurcations. These results are extended to a continuous system and used to provide insights into longitudinal vibrations of a bar whose material is characterized by purely nonlinear stress-strain relationship.