Nonlinear Equations with a Retarded Argument in Discrete-Continuous Systems

Abstract

The paper deals with dynamic problems of discrete-continuous systems with local nonlinearities, the analysis of which is reduced to solving nonlinear differential equations with a retarded argument. This concerns the discrete-continuous systems subject to torsional, longitudinal, or shear deformations, where the equations of motion for elastic elements are classical wave equations. It is assumed that the characteristics of local nonlinearities are of a soft-type and in the paper they are described by four nonlinear functions. After a short general description of the approach used, the detailed considerations and numerical results are presented for a multimass discrete-continuous system with a local nonlinearity having the characteristics of a soft-type subject to shear deformations.