DYNAMIC STABILITY OF A BEAM LOADED BY A SEQUENCE OF MOVING MASS PARTICLES

The dynamic stability for the lateral response of a finite Bernoulli-Euler beam loaded by a continuous sequence of identical, equally spaced, mass particles attached to and traveling at a constant speed across the beam is investigated. This paper points out that, in general, multiple regions of unstable response will occur. However, for certain particle spacings and foundation moduli a single region of unstable response occurs. In general, the critical speed ratio Beta cr (or the nondimensional particle speed at which instability of the beam occurs) is increased by decreasing Alpha T, the nondimensional particle mass; increasing rho, the nondimensional particle spacing; increasing gamma, the nondimensional foundation stiffness; increasing P*, the nondimensional axial tensile force on the beam; increasing xi sub n, the damping coefficient.