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Free vibration of a sagged cable with attached discrete elements

  • W. PakosEmail author
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Abstract

An algorithm is presented to analyze the free vibration in a system composed of a cable with discrete elements, e.g., a concentrated mass, a translational spring, and a harmonic oscillator. The vibrations in the cable are modeled and analyzed with the Lagrange multiplier formalism. Some fragments of the investigated structure are modeled with continuously distributed parameters, while the other fragments of the structure are modeled with discrete elements. In this case, the linear model of a cable with a small sag serves as a continuous model, while the elements, e.g., a translational spring, a concentrated mass, and a harmonic oscillator, serve as the discrete elements. The method is based on the analytical solutions in relation to the constituent elements, which, when once derived, can be used to formulate the equations describing various complex systems compatible with an actual structure. The numerical analysis shows that, the method proposed in this paper can be successfully used to select the optimal parameters of a system composed of a cable with discrete elements, e.g., to detune the frequency resonance of some structures.

Key words

free vibration sagged cable with attachments continuous discrete model 

Chinese Library Classification

O342 O325 

2010 Mathematics Subject Classification

74H50 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringWrocław University of Science and TechnologyWroclawPoland

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