Solutions of Dynamic Problems Based on the Refined Model

  • Alexander Ya. GrigorenkoEmail author
  • Wolfgang H. Müller
  • Yaroslav M. Grigorenko
  • Georgii G. Vlaikov
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


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.


Cylindrical Shells Made Incremental Search Methods Discrete Orthogonalization Natural Vibration Collocation Points 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Alexander Ya. Grigorenko
    • 1
    Email author
  • Wolfgang H. Müller
    • 2
  • Yaroslav M. Grigorenko
    • 1
  • Georgii G. Vlaikov
    • 3
  1. 1.S.P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKievUkraine
  2. 2.Institut für MechanikTechnische Universität BerlinBerlinGermany
  3. 3.Technical CenterNational Academy Sciences of UkraineKievUkraine

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