In this paper the analysis of vibrations on the basis of two computational models of the crane: the simulating model, worked out with help of the finite elements method (FEM) and the modal model which is the result of the experimental modal analysis conducted on the real object have been presented. The carried out research concern the vibrations of the system in the lifting and rotary plane of the boom. Researchers have been performed by fixed configuration of the system, reflecting the crane position while the load is picked from the foundation. Frequencies and the mode shapes obtained from simulating research have been compared with the results of the experimental modal analysis. The simulation FEM model represents properly the dynamical properties of the real forest crane and it can be used to investigate the dynamic behaviour of the real object in any other than presented in the work cases of working configurations.
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In this paper the discrete-continuous model and one degree of freedom discrete model of vibration of the system consisted of the three member type telescopic boom and hydraulic cylinder of crane radius change have been presented. The formulation and solution of the problem has been based on the Lagrange multiplier formalism. The shown discrete model is useful to describe the lateral motion in the rotary plane of the telescopic boom end where the lifted load is hanged. The mathematical formulation has been completed by the sample numerical results.
W pracy sformułowano i rozwiązano zagadnienie poprzecznych drgań swobodnych układu belkowego z elementami dyskretnymi, stosując metodę mnożników Lagrange'a. Elementy belkowe opisano zgodnie z teorią Bernoulliego-Eulera. Na podstawie zaproponowanego modelu wyznaczono numerycznie częstości oraz odpowiadające im postacie drgań swobodnych.
EN
In this paper the problem of the free transverse vibration of the system consisting of beams with discrete elements has been formulated and solved. The procedure has been based on the Lagrange multiplier formalism. Beam elements have been described according to Bernoulli-Euler theory. The proposed model has been used to determine nuraerical frequencies as well as mode shapes.
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