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Application of the Averaging Method to the Investigation of Nonlinear Wave Processes in Elastic Systems with Circular Symmetry

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Ukrainian Mathematical Journal Aims and scope

Abstract

We apply asymptotic methods of nonlinear mechanics (the Bogolyubov–Mitropol'skii averaging method) to the construction of approximate solutions of a system of nonlinear equations describing wave processes in elastic systems with circular symmetry. As an example, we study the dynamics of interaction of two flexural waves that propagate in a cylindrical shell under the conditions of free oscillations and periodic excitation.

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REFERENCES

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Kubenko, V.D., Koval'chuk, P.S. Application of the Averaging Method to the Investigation of Nonlinear Wave Processes in Elastic Systems with Circular Symmetry. Ukrainian Mathematical Journal 53, 1645–1656 (2001). https://doi.org/10.1023/A:1015291826531

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  • DOI: https://doi.org/10.1023/A:1015291826531

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