Structural Vibration of A Flexible Complex System Under A Harmonic Oscillation Moving Force

Abstract

This paper focuses on the free and forced transverse vibration of a double-string complex system with elastic interlayer under a harmonic oscillation moving force. The paper includes the study of a dynamic behaviour of a finite, simply supported double-string flexible complex system subject to harmonic force moving with a constant velocity on the top string. The strings are identical, parallel one upon the other. The elastic interlayer is described by the Winkler’s model consists of a Hookean resilient spring distributed in parallel. The classical solution of the response of complex systems subjected to harmonic oscillation force moving with a constant velocity has a form of an infinite series. But also, it is possible to show that in the considered case part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method to search for a solution in a closed-form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations. The double string connected in parallel by linear elastic elements can be studied as a theoretical model of composite structure in which impact of layer interaction, interlayer coupling effects and transverse wave effects is taken into account.