Metrikine, A.V.

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Parametric Instability of a Moving Mass on a Periodically-Supported Infinitely Long String

 

ASME Journal of Applied Mechanics

 

Summary. A new method is proposed of theoretical analysis of the dynamic instability of a moving object on a periodically supported, infinitely long elastic structure. To demonstrate this method, a simple example is considered of a moving mass on an elastically supported string. The equations are obtained that govern the system parameters which correspond to the boundaries separating stability and instability in the parameter space. These equations are in the form of the determinant of an infinite matrix and are analogous to the Hillís infinite determinant. A parametric analysis of the instability zones is carried out in the plane of the normalized mass magnitude and mass velocity. The focus is placed on the effect of elasticity and viscosity of the supports. An analytical validation is presented of the numerically obtained instability zones. This is done using a simplified model of the string on the corresponding continuous foundation.