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Some Problems of Multidegree of Freedom Systems

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Mechanical Vibrations

Part of the book series: Foundations of Engineering Mechanics ((FOUNDATIONS))

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Abstract

The general theory of multidegree of freedom system is considered. The eigenvalue problem that provides the eigenfrequencies for a vibrating finite degree of freedom system is also presented. It is shown what properties these eigenvalue problems have including the fundamental characteristics of the eigenvalues and eigenvectors. Some simple solution procedures are suggested. The concept of the Rayleigh quotient is introduced. Finally the case of forced vibrations is investigated.

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Notes

  1. 1.

    If the matrix in question is symmetric then it is a normal matrix [1] for which the assumption is fulfilled.

  2. 2.

    Also known as the Rayleigh–Ritz ratio, named after Lord Rayleigh (John William Strutt (1842–1919)) and Walther Ritz (1878–1909) [9, 10].

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Authors and Affiliations

  1. Institute of Applied Mechanics, University of Miskolc, Miskolc-Egyetemváros, Hungary

    György Szeidl & László Péter Kiss

Authors
  1. György Szeidl
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  2. László Péter Kiss
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Correspondence to György Szeidl .

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Szeidl, G., Kiss, L. (2020). Some Problems of Multidegree of Freedom Systems. In: Mechanical Vibrations. Foundations of Engineering Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-45074-8_5

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  • DOI: https://doi.org/10.1007/978-3-030-45074-8_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-45073-1

  • Online ISBN: 978-3-030-45074-8

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