Verichev S.N., Metrikine A.V. |
Instability of vibrations of a mass that moves along a beam on a periodically inhomogeneous foundation |
Journal of Sound and Vibration 260, 901-925, 2003 doi:10.1016/S0022-460X(02)00936-7 |
Summary. The stability of vibrations of a mass that uniformly moves along
an Euler-Bernoulli beam on a periodically inhomogeneous continuous foundation
is studied. The inhomogeneity of the foundation is caused by a slight
periodical variation of the foundation stiffness. The moving mass and the
beam are assumed to be always in contact. With the help of a perturbation
analysis it is analytically shown that vibrations of the system may become
unstable. The physical phenomenon that lies behind this instability is
parametric resonance that occurs because of the periodic (in time) variation
of the foundation stiffness under the moving mass. The first instability zone
is found in the space of the system parameters within the first approximation
of the perturbation theory. The location of the zone is strongly dependent on
the spatial period of the inhomogeneity and on the weight of the moving mass.
The smaller this period and/or the smaller the mass, the higher is the
velocity at which the instability occurs. |