Transversal vibrations of a uniformly moving two-mass oscillator on a Timoshenko beam of in®nite length supported by a viscoelastic foundation are studied. By using integral transforms, the characteristic equation for the oscillator's vibrations is obtained. It is shown that the equation may have a root with a positive real part. The existence of such a root leads to the exponential increase of the amplitude of the oscillator vibrations, i.e. to instability. The reasons for the instability to occur are discussed. By employing the method of D-decomposition, the instability domains are found in the space of the system parameters.
IntroductionThe rapid development of high-speed railways has stimulated the research to take a new look at the classical``moving load problem'', [7]. The necessity to do so was based on the fact that in earlier studies on this problem, it was usually assumed that the load speed is much smaller than the wave velocity in an elastic system, which the load perturbs. This assumption is no longer acceptable, since modern high-speed trains are able to move with speeds comparable with the wave velocity in a railway track, [6, 9±11, 16].There exists a large number of papers that are dealing with the``moving load problem'' by considering different models of the load-structure interaction.With respect to the type of the elastic structure, papers on this topic can be subdivided into two large groups. The ®rst group is concerned with analysis of ®nite-length structures (see [7] and references in this book), that may be exempli®ed by railway bridges. In papers of the second group, attention is focused on the dynamic behavior of in®nitely long structures like open-®eld railway tracks [6,9,10,16] and overhead power lines [1,12].Limiting the discussion to the case of in®nitely long structures, one can provide a further subdivision of papers on the topic, sorting them by the model chosen to describe the moving object. Globally, two approaches in modeling the moving load are known. In the framework of the ®rst approach, internal degrees of freedom (DOFs) of the load are neglected, and an elastic structure is considered to be subjected to a moving force, which magnitude is prescribed in a certain manner. The second approach is more adequate and assumes that the load has its own DOFs and is modelled as a mass, an oscillator, or as any other multi-DOF discrete system. In this case, the contact force between the moving load and the elastic structure is unknown and has to be de®ned by considering their interaction.
