Studies on Analytical Determination of the Vibrations of a Load, Twice Elastically Suspended from an Elastic Beam via Another Load

The dynamics of mechanical systems with suspended loads, such as bridge cranes, monorail hoists, mining machines, and so on, are examined in this chapter. A load is hung twice elastically from an elastic beam via another load in the mechanical system under consideration. The purpose is to determine the mechanical system’s vibrations with suspended loads. The system is developed with two dynamical models that respect the kinetic energy of the elastic ropes, and their corresponding differential equations of motion are produced. The vibration of the mechanical system is described by a coupled system of two ordinary and n(n=1,2,….) partial differential equations. Using general start conditions, the nonlinear restoring forces are linearized using the equivalent linearization method, and an analytical solution for the differential equations of both dynamical models is found concurrently. The integration constants are calculated analytically for a specific instance of the start conditions, which indicates a common application. The mechanical system is numerically simulated using initial circumstances that correspond to common operating regimes of real systems with suspended loads.

Author(s) Details

Vassil Zlatanov
Department of Technical Mechanics, University of Food Technologies, Plovdiv, Bulgaria.

Stefan Bachvarov
Department of Mechanics, Technical University, Sofia, Bulgaria.

Snezhana Atanasova
Department of Technical Mechanics, University of Food Technologies, Plovdiv, Bulgaria.

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