Analysis of strongly non-linear free vibrations of beams using perturbation method = Analiza silnie nieliniowych drgań własnych belek za pomocą metody perturbacji - Lewandowski, Roman (Zielona Góra: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego)
The possibilities of application of the perturbation method to the analysis of strongly non-linear free vibrations of beams are discussed. The geometrical non-linearity is taken into account. The finite element method is used for the description of the dynamic behaviour of beams. The first order perturbation equation is solved and the obtained solution is compared with the solution found with the help of the harmonic balance method which is widely used and applicable to the analysis of strongly non-linear dynamic systems. It was proved that both solutions are almost identical and differences are negligibly small. The numerical procedure enabling determination of backbone curves is also briefly described. Theoretical results are supplemented by a description of the results of typical calculations.
Keywords: belki; drgania nieliniowe; metoda elementów skończonych; metoda perturbacji; strongly non-linear vibrations; free vibrations; perturbation method; beam structures