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Forced vibrations of a body supported by viscohyperelastic shear mountings. (English) Zbl 1040.74027
The authors study damped, finite-amplitude forced vibrations of a load supported symmetrically by simple shear springs and by smooth inclined bearing surface. For the class of viscohyperelastic material having a quadratic shear-response function, the equation of motion of the load is forced Duffing equation for which an approximate solution is obtained by the method of harmonic balance. Regions of stable motion are identified in terms of the amplitude of the motion, driving-force intensity, driving frequency and system design parameters. Bifurcation limits on the driving frequency for stable motion of the system are identified analytically and illustrated graphically.

74H45 Vibrations in dynamical problems in solid mechanics
74H55 Stability of dynamical problems in solid mechanics
74B20 Nonlinear elasticity
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