Estudo de um problema de “snap" dinâmico, mediante o Método Direto de Liapunov

Abstract

Liapunov's direct method is used to study the domain of attraction of one of the stable equilibrium positions of a simple structure which presents a "snap-through” behavior. The mechanical model studied is a plane simple strut which has already been used by many other authors for the discussion of some aspects which are typical for “snap-through" problems. Two different damping laws are considered and for each case Liapunov functions are constructed using several different methods, among which the methods of Szego , Willems and Infante receive special attention. In order to compare the estimates of the domain of attraction obtained by this procedure with the actual domain, the equations of motion were also solved on an analogue computer. Finally it is shown how the direct method can also be used to solve the problem of dynamic "snap-through" under loading. Step and impulsive-loading are considered.