Analysis of Dynamic Interaction Between the Continuous String and Moving Oscillator

The paper presents the analysis of dynamic interaction between a discrete oscillator of two degrees of freedom and a finite continuous string suspended on rigid and visco-elastic concentrated supports. This oscillator moves along the string with a constant sub-critical or super-critical speed. Dynamic transverse displacements of the string as well as the contact force between the oscillator and the string are determined using the d'Alembert solutions of the wave motion equations. Such approach leads to a system of algebraic and ordinary differential equations with a "shifted" argument which are solved numerically in an appropriate sequence. From the performed comparison of numerical results for the sub-critical oscillator speeds with analogous results obtained by means of the finite element method it follows, that the method based on the d'Alembert solutions in the form of travelling waves seems to be more accurate. Moreover, the approach proposed in the paper is numerically very efficient which makes it advantageous for investigations of more complex systems.