Instability analysis of vibrations of a uniformly moving mass in one and two-dimensional elastic systems

The stability of vertical vibrations of a mass moving uniformly over four different elastic systems has been considered: an Euler–Bernoulli beam, a Kirchhoff plate, a Timoshenko beam and a Mindlin plate that are resting on a linear elastic foundation. It is shown that this vibration can become unstable. Using the fundamental solution approach, the characteristic equation for the vertical vibration of the moving mass is obtained. Starting from the laws of the conservation of energy and momentum the variation of the mass kinetic energy is derived. With the help of this relation, the physical mechanism of instability is discussed.