Abstract. This study formulates and solves the problem of transverse damped vibration in the system of changing the boom radius in a truck crane with advanced cylinder design for controlling the boom radius. The dissipation of vibration energy in the model adopted in the study occurs as a result of internal damping of the viscoelastic material (rheological Kelvin-Voigt model) of the beams that model the system and movement resistance in the supports of the cylinder and crane boom to the bodywork frame of the crane. Damped frequencies of vibrations and degree of vibration amplitude decay were calculated. The study also presents eigenvalues of system vibration with respect to changes in damping coefficients and system geometry for a selected load.

Abstract. In this paper, the problem of transverse and longitudinal damped vibration of the Γ type frame was formulated and solved. The effect of constructional damping of the column support and fixing bolt frame support on degree of vibration amplitude decay was presented. The vibration energy dissipation in the model (modelled by the rotational viscous dampers) is a result of the movement resistance taken into account in the frame supports. The eigenvalues of the system with respect to changes in system geometry and for a selected and variable damping coefficient values were calculated.

This paper discusses the formulation and solution for the problem of damped transverse vibrations of the Γ type frame with open cracks. Dissipation of vibration energy in the frame results from the movement constraint in the column and bolt support (constructional damping) and internal damping of viscoelastic material of the frame (rheological model by Kelvin-Voigt). Presence of a crack impacts local flexibility that has an effect on frame vibration response. The boundary problem for the above system was formulated based on the Hamilton's principle and solved numerically for the complex eigenvalues * . The effect of the crack depth and its location on damped vibration was presented. The effect of both types of damping on the degree of amplitude decay was also presented.

Abstract. In the present work a problem pertaining to the damped lateral vibrations of the truck crane radius change system with the developed hydraulic cylinder model that changes the radius has been formulated and solved. In the adopted model the vibration energy dissipation derives from the internal damping of the viscoelastic material (the Kelvin-Voigt rheological model) of beams that model the system. Damped vibration frequency and the vibration amplitude decay level have been calculated. Changes of the eigenvalues of system vibrations with the damping ratio change and the change of the system geometry with different loads observed on it have been presented.

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