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The discrete-continual model of the rod of variable section for the analysis of oscillations of telescopic rotor systems of cranes is substantiated. As methods for solving the basic equations (for bending type oscillations), the methods of Ritz and Budnov-Galerkin using the Relay formula are used to calculate the proper frequency of oscillations of the considered system using a model with lumped parameters (discrete models) and taking into account the distributed properties of the systems being studied. The approaches used for the thorough analysis of the continual (distributed) properties of telescopic boom systems of mobile cranes and the analysis of variations of oscillations (longitudinal, twisting and bent) of telescopic boom systems of autocranes taking into account the circumstances of mass distribution along the arrow (rod) with a variable section of the rod along its length. Approximate methods of analysis and improvement of methods for calculating various types of oscillations that arise in the rods of a variable section are presented, within the framework of consideration of telescopic boom systems of cranes as having discrete continual properties. Equations are constructed using the BubnovGalerkin method in the problems of longitudinal or steep oscillations of telescopic rotor systems of cranes.

Use moded bar of variable cross section in vibration analysis of telescopic boom system of truck-mounted cranes