OPTIMUM CRITICAL IMPULSE FOR SNAP-THROUGH IN SYSTEMS OF ONE DEGREE OF FREEDOM.
CALIFORNIA UNIV SAN DIEGO LA JOLLA DEPT OF THE AEROSPACE AND MECHANICAL ENGINEERING SCIENCES
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A general procedure is derived for evaluation of the optimum load history which can cause the snap-through of a nonlinear, dissipative dynamical system of one degree of freedom in such a manner that the total impulse delivered by the load is a minimum. For systems in which dissipative force either is absent or else depends linearly on velocity, the optimum load history for minimum impulse is shown to be an ideal Dirac-delta function impulse applied to the system at rest. For nonlinear dissipation, however, the optimum load history has, in general, loads of finite magnitude acting over finite time. A general procedure to determine the optimum load history and the minimum total impulse for nonlinear dissipation is developed. This procedure is illustrated by application to two problems the circulation of a single pendulum with damping the snap-through of a simple, nonlinearly viscoelastic truss. Author