Engineering Transactions, 18, 4, pp. 615–628, 1970

Drgania Zdeterminowane i Przypadkowe Układu o Jednym Stopniu Swobody Przy Charakterystyce Sprężystości w Postaci Linii Łamanej

K. Piszczek
Politechnika Krakowska

The nonlinear forced vibrations of a system with one degree of freedom are considered, the account having taken of the damping proportional to the first power of velocity. The nonlinear factor
is an elastic force derived from two springs having identical characteristics of elasticity, and where the springs are preliminarily shortened in the state of static equilibrium. The problem is analyzed
in the formulation determined by means of the Krylow-Bogolubow method and in the probabilistic formulation using the Fokker-Planck method.
In the determined case, the system under consideration was found to behave as a mechanical system with a soft characteristic of the elastic forces, whereas in the probabilistic formulation the characteristics obtained correspond to a system with a rigid characteristic. It can be seen also in Fig. 9 that the system reacts markedly to a small nonlinearity (xo/σ<1) and in this case it is
possible to apply the approximate formulae (2.24) and (2.29).

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