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Solutions of Dynamic Problems Based on the Refined Model

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Recent Developments in Anisotropic Heterogeneous Shell Theory

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSCONTINU))

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Abstract

A wide class of problems on natural vibrations of anisotropic inhomogeneous shells is solved by using the refined model. Shells with constructional (with variable thickness) and structural inhomogeneity (made of functionally gradient materials) are considered. Initial boundary-value, eigenvalue, and partial derivative problems with variable coefficients are solved by spline-collocation, discrete-orthogonalization, and incremental search methods. In the case of hinged shells, the results obtained by means of analytical and proposed numerical methods are compared and analyzed. It is studied how the geometrical and mechanical parameters as well as the type of boundary conditions influence the distribution of dynamical characteristics of the shells under consideration. The frequencies and modes of natural vibrations of an orthotropic shallow shell of double curvature with variable thickness and various values of a radius of curvature are determined. The dynamical characteristics have been calculated for the example of cylindrical shells made of a functionally gradient material with thickness varying differently in circumferential direction. The values of natural frequencies obtained for this class of shells under some boundary conditions are compared with the data calculated by means of three-dimensional theory of elasticity.

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Authors and Affiliations

  1. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    Alexander Ya. Grigorenko & Yaroslav M. Grigorenko

  2. Institut für Mechanik, Technische Universität Berlin, Berlin, Germany

    Wolfgang H. Müller

  3. Technical Center, National Academy Sciences of Ukraine, Kiev, Ukraine

    Georgii G. Vlaikov

Authors
  1. Alexander Ya. Grigorenko
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  2. Wolfgang H. Müller
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  3. Yaroslav M. Grigorenko
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  4. Georgii G. Vlaikov
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Correspondence to Alexander Ya. Grigorenko .

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Grigorenko, A.Y., Müller, W.H., Grigorenko, Y.M., Vlaikov, G.G. (2016). Solutions of Dynamic Problems Based on the Refined Model. In: Recent Developments in Anisotropic Heterogeneous Shell Theory. SpringerBriefs in Applied Sciences and Technology(). Springer, Singapore. https://doi.org/10.1007/978-981-10-1596-0_1

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  • DOI: https://doi.org/10.1007/978-981-10-1596-0_1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-1595-3

  • Online ISBN: 978-981-10-1596-0

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