Instability of vibrations of a moving two-mass oscillator on a flexibly supported Timoshenko beam

Transversal vibrations of a uniformly moving two-mass oscillator on a Timos henko beam of infinite length supported by a viscoelastic foundation are st udied. By using integral transforms, the characteristic equation for the os cillator'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 em ploying the method of D-decomposition, the instability domains are found in the space of the system parameters.