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NATURAL VIBRATIONS OF A RECTANGULAR PLATE WITH MIXED BOUNDARY CONDITIONS

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Natural vibrations of a rectangular plate with two clamped and two freely supported edges are under consideration. The Bubnov — Galerkin method is used to calculate the first eigenvalues, and the first eigenvalue in the case of a single trial function is calculated with an error smaller than 1%. The results are compared with known data, and eigenforms are given.

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REFERENCES

  1. M. Eisenberger and A. Deutsch, “Solution of Thin Rectangular Plate Vibrations for All Combinations of Boundary Conditions," J. Sound Vibrat. 452, 1–12 (2019).

    Article  ADS  Google Scholar 

  2. D. J. Gorman, Free Vibration Analysis of Rectangular Plates (Elsevier North Holland, New York, 1982).

  3. A. W. Leissa, “The Free Vibration of Rectangular Plates," J. Sound Vibrat. 31 (3), 257–293 (1973).

    Article  ADS  Google Scholar 

  4. S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill College, 1959).

    MATH  Google Scholar 

  5. S. Germain, Recherches sur la theorie des surfaces elastiques (Mme ve Courcier, Paris, 1821).

    Google Scholar 

  6. V. N. Barashkov, I. Y. Smolina, L. E. Puteeva, and D. N. Pestsov,Fundamentals of the Plasticity Theory (Tomsk State University of Architecture and Building, Tomsk, 2012) [in Russian].

  7. S. G. Mikhlin, Variational Methods in Mathematical Physics (Pergamon, 1964).

  8. EISPACK. L Collection of Fortran Subroutines that Compute the Eigenvalues and Eigenvectors. https://www. netlib.org/eispack/.

  9. D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra (Fizmatgiz, Moscow, 1963) [in Russian].

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    S. D. Algazin

  2. Lomonosov Moscow State University, 119991, Moscow, Russia

    I. A. Selivanov

Authors
  1. S. D. Algazin
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  2. I. A. Selivanov
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Corresponding authors

Correspondence to S. D. Algazin or I. A. Selivanov.

Additional information

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 2, pp. 70–76.https://doi.org/10.15372/PMTF20210207.

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Algazin, S.D., Selivanov, I.A. NATURAL VIBRATIONS OF A RECTANGULAR PLATE WITH MIXED BOUNDARY CONDITIONS. J Appl Mech Tech Phy 62, 238–244 (2021). https://doi.org/10.1134/S0021894421020073

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  • DOI: https://doi.org/10.1134/S0021894421020073

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