Stability of a body supported by a simple vehicular shear suspension system

Abstract

Stability of the oscillatory motion of a body supported by simple shear springs is examined relative to a vehicle that executes a steady circular turn about an arbitrary axis fixed in the vertical plane. The problem is formulated for a general isotropic elastic material whose shear response function is a positive, even function of the amount of shear. A general sufficient condition bounding the normalized vehicle angular speed Ω by a certain critical angular speed Ω c , which depends on the vehicle and load suspension orientation design parameters alone, is obtained for periodic, and hence stable, free relative oscillations of the load for arbitrary initial data. Stability in the forced vibration problem also is discussed. For the special class of materials whose shear response function is a constant, a familiar class that includes the Mooney-Rivlin, Blatz-Ko, and Hadamard material models, for example, the free oscillatory motion of the load is stable if and only if Ω < Ω c . It is shown also for this class that in the forced vibration problem for which the oscillations generally are aperiodic, resonance will occur at an angular speed Ω r smaller than Ω c .