Zastosowanie metody linearyzacji do analizy nieliniowego oscylatora poddanego działaniu przypadkowych impulsów

A single degree of freedom system with non-linear stiffness and damping subjected to Poissonian impulse excitation is examined.

The stochastic linearization technique is used to obtain a system of equations for equivalent linear stiffness and damping. The generalized Fokker – Planck – Kolmogorov equation and the characteristic function method allow to obtain general formulae for the characteristic function and moments of the system response probability distribution.

The dependence of equivalent linear stiffness and damping upon system and excitation parameters is investigated for the case of zero mean Gaussian probability distribution of the linear impulse. The behaviour of system displacement variance as time function is also exammed.

A digital simulation method is applied to verify the results obtained.