Investigation of Free Vibrations of Multilayer Shallow Shells and Plates of Complex Shape in Plan

We propose an algorithm for the solution of the problem of free vibrations of multilayer shallow shells and plates based on the variational methods and the theory of R-functions. By using this algorithm, we solve the problems posed for shallow shells (spherical and cylindrical) and plates of complex shape in plan. We present the results of investigation of the dependences of the natural frequencies of vibrations of shallow shells and plates with different number of layers on the angle of rotation of the principal directions of each layer.     

Special-purpose interactive programming shell for the “pole” system

Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 154–161, January–February, 1995.     

Free vibration analysis of laminated shallow shells with complex shape using the R-functions method

The vibration problems of composite laminated shallow shells resting on an arbitrary planform are studied. In order to develop the effective numerical–analytical method, the first-order shear deformation theory (FSDT) is used. The proposed method involves the use of the R-functions theory and variational methods. A number of problem have been solved to study the effects of various parameters such as planform geometry, lamination scheme, curvatures and boundary conditions on the dynamical behavior of the shell. The obtained results are verified by way of comparison with available results for square planform shells.     

Investigation into nonlinear vibrations of composite plates using the <Emphasis Type="Italic">R</Emphasis>-function theory

We have developed an effective approach to the solution of problems on geometrically nonlinear vibrations of orthotropic multilayer plates of irregular shapes in a classical statement based on the use of the R-function theory, Ritz variational method and Bubnov-Galerkin method. Using the proposed method, problems of vibrations of both multilayer rectangular plates and plates of complex geometries have been solved. The effect of the domain geometry and boundary conditions on the amplitude-frequency characteristics has been investigated. __________ Translated from Problemy Prochnosti, No. 5, pp. 101–113, September–October, 2007.