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Variational and Projection Methods for Solving Vibration Theory Equations

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Theory of Elastic Oscillations

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

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Abstract

Exact solutions of equations of the theory of vibrations can only be constructed for a limited class of problems under homogeneous properties of an elastic body. However, if the elastic, inertial and dissipative properties are variable in coordinate, then there is a need to use approximate methods to solve equations of the theory of vibrations.

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References

  1. Fridman, V. M. (1956). On an approximate method for determining the natural frequencies of vibrations. Academy of Sciences of the U.S.S.R., Vibrations in Turbomachinery, pp. 69–76 (in Russian).

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  2. Kukishev, V. L., & Fridman, V. M. (1976). Variational difference method in the theory of elastic vibrations, based on the Reissner variational principle. Academy of Sciences of the U.S.S.R., Mechanics of Solids, 5, 112–119 (in Russian).

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  3. Lurie, A. I. (2005). Theory of elasticity (1050 pp). Berlin: Springer.

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  4. Mikhlin, S. G. (1964). Variational methods in mathematical physics (p. 510). Oxford: Pergamon Press.

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  5. Petrov, G. I. (1940). Application of the Galerkin method to the problem of viscous fluid flow stability. Academy of Sciences of the USSR, Applied Mathematics and Mechanics, 4(3), 3–11 (in Russian).

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  6. Reissner, E. O. (1961). On some variational theorems of the theory of elasticity. Academy of Sciences of the U.S.S.R., Problems of Continuum Mechanics, 328–337 (in Russian).

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  7. Smirnov, V. I. (1964). Course of higher mathematics (Vol. IV, 336 pp). Oxford: Pergamon Press.

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  8. Ritz, W. (1909). Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. Journal für die reine und angewandte Mathematik (Grelle), 135(1), 1–61.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Los Angeles, CA, USA

    Vladimir Fridman

Authors
  1. Vladimir Fridman
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Correspondence to Vladimir Fridman .

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© 2018 Springer Nature Singapore Pte Ltd.

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Fridman, V. (2018). Variational and Projection Methods for Solving Vibration Theory Equations. In: Theory of Elastic Oscillations. Foundations of Engineering Mechanics. Springer, Singapore. https://doi.org/10.1007/978-981-10-4786-2_4

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  • DOI: https://doi.org/10.1007/978-981-10-4786-2_4

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4785-5

  • Online ISBN: 978-981-10-4786-2

  • eBook Packages: EngineeringEngineering (R0)

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