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Keywords: non-stationary stress strain state, shells of revolution, propagation of waves, asymptotics, approximations, overlap regions.

Summary

The paper deals with the asymptotic methods, developed for creating a mathematical model of non-stationary wave propagation in shells of revolution under shock impacts of tangential bending types and shock impacts of normal type; the methods are also aimed at solving the boundary value problems for the strain-stress state (SSS) components with different values of variability and dynamicity indices. Classification of asymptotic approximations is also presented. This classification defines three different types of separation scheme of non-stationary SSS. This scheme uses the following asymptotic approximations: short-wave and low-frequency ones, boundary layers in the vicinities of the quasi-front, the dilatation and shear wave fronts, and the front of Rayleigh surface waves. The schemes of ranges of applicability of approximate theories and schemes for the longitudinal stress resultant, bending moment and transverse shear force are represented.

Thus the considered methods are characterized:

separating non-stationary SSS into components with different values of variability and dynamic indices,
defining ranges of the applicability of these components and overlap regions between them.

It should be noted that the case of the normal loading is considered for the first time. In this case a new type of boundary layer was considered near the front which is propagated with the speed of the Rayleigh surface waves. Here the disturbances propagate along the boundaries, that is defined by one-dimensional wave operators in the boundary conditions.

Asymptotic methods for constructing the solutions for the SSS components are based on the application of an integral Laplace transform with respect to the time parameter, Fourier transform with respect to longitudinal coordinate, the saddle-point technique and the WKB method.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 207 Dynamics of Shells Under Shock Loading: An Asymptotic Approach L.Yu. Kossovich and I.V. Kirillova Department of Mechanics and Mathematics, Saratov State University, Russia doi:10.4203/ccp.88.207 purchase the full-text of this paper Full Bibliographic Reference for this paper L.Yu. Kossovich, I.V. Kirillova, "Dynamics of Shells Under Shock Loading: An Asymptotic Approach", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 207, 2008. doi:10.4203/ccp.88.207 Keywords: non-stationary stress strain state, shells of revolution, propagation of waves, asymptotics, approximations, overlap regions. Summary The paper deals with the asymptotic methods, developed for creating a mathematical model of non-stationary wave propagation in shells of revolution under shock impacts of tangential bending types and shock impacts of normal type; the methods are also aimed at solving the boundary value problems for the strain-stress state (SSS) components with different values of variability and dynamicity indices. Classification of asymptotic approximations is also presented. This classification defines three different types of separation scheme of non-stationary SSS. This scheme uses the following asymptotic approximations: short-wave and low-frequency ones, boundary layers in the vicinities of the quasi-front, the dilatation and shear wave fronts, and the front of Rayleigh surface waves. The schemes of ranges of applicability of approximate theories and schemes for the longitudinal stress resultant, bending moment and transverse shear force are represented. Thus the considered methods are characterized: separating non-stationary SSS into components with different values of variability and dynamic indices, defining ranges of the applicability of these components and overlap regions between them. It should be noted that the case of the normal loading is considered for the first time. In this case a new type of boundary layer was considered near the front which is propagated with the speed of the Rayleigh surface waves. Here the disturbances propagate along the boundaries, that is defined by one-dimensional wave operators in the boundary conditions. Asymptotic methods for constructing the solutions for the SSS components are based on the application of an integral Laplace transform with respect to the time parameter, Fourier transform with respect to longitudinal coordinate, the saddle-point technique and the WKB method. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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