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Modal Analysis of a Plate Compliant in Transverse Shear

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Mechanics of Composite Materials Aims and scope

A finite-element solution of the problem on natural vibrations of a plate compliant in transverse shear is considered. A four-node rectangular finite element whose basic nodal kinematic parameters include the angles of transverse shear deformations is used. A comparative analysis of frequencies and modes of natural vibrations of composite and sandwich plates is performed for two variants of boundary conditions on their contour: the classical clamping and clamping with free transverse shear deformations.

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References

  1. E. Carrera, “Theories and finite elements for multilayered, anisotropic, composite plates and shells,” Arch. Comput. Meth. Eng., 9, No. 2, 87-140 (2002).

    Article  Google Scholar 

  2. E. Carrera, “Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking,” Arch. Comput. Meth. Eng., 10, No. 3, 215-296 (2003).

    Article  Google Scholar 

  3. E. Reissner, “The effect of transverse shear deformation on the bending of elastic plates,” Trans. ASME, J. Appl. Mech., 12, No. 2, 69-77 (1945).

    Google Scholar 

  4. R. D. Mindlin, “Influence of rotary inertia and shear on flexural motions of elastic plates,” Trans. ASME, J. Appl. Mech., 18, 31-38 (1951).

    Google Scholar 

  5. V. V. Vasil’ev, Mechanics of Composite Structures [in Russian], Mashinostroenie, Moscow (1988).

    Google Scholar 

  6. V. A. Nesterov, “Stiffness matrix of the finite element of a plate compliant in transverse shear,” Mech. Compos. Mater., 47, No. 3, 271-284 (2011).

    Article  Google Scholar 

  7. A. J. M. Ferreira, G. E. Fasshauer, R. C. Batra, and J. D. Rodrigues, “Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter,” Compos. Struct., 86, 328-343 (2008).

    Article  Google Scholar 

  8. D. J. Dawe and O. L. Roufaeil, “Rayleigh–Ritz vibration analysis of Mindlin plates,” J. Sound and Vibration, 69, Iss. 3, 345-359 (1980).

    Article  Google Scholar 

  9. K. M. Liew, J. Wang, T. Y. Ng, and M. J. Tan, “Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method,” J. Sound Vibrat., 276, 997-1017 (2004).

    Article  Google Scholar 

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Authors and Affiliations

  1. Reshetnev Siberian State Aerospace University, Krasnoyarsk, Russia

    V. Nesterov

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  1. V. Nesterov
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Correspondence to V. Nesterov.

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Translated from Mekhanika Kompozitnykh Materialov, Vol. 51, No. 1, pp. 59-76, January-February, 2015.

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Nesterov, V. Modal Analysis of a Plate Compliant in Transverse Shear. Mech Compos Mater 51, 43–54 (2015). https://doi.org/10.1007/s11029-015-9475-x

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  • DOI: https://doi.org/10.1007/s11029-015-9475-x

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