Abstract
On the basis of asymptotic analysis of the Kirchhoff-Love cylindrical shell’s element motion equations in displacements a nonintegrable fourth-order quasi-hyperbolic equation with cubic nonlinearity is derived. For the analysis of axisymmetric propagation of small-amplitude flexural-longitudinal waves along the shell, this equation is reduced to the generalized nonlinear Schrödinger equation. A criterion for the modulation instability of the waves is obtained, which clarifies the known Lighthill criterion.
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Acknowledgements
The work was carried out within the Russian state task for conducting fundamental scientific research for 2013–2020 on the topic No. 0035-2014-0402, state registration number 01201458047 and the work was supported of the RFBR (project no. 16-01-00176-a, project no. 18-29-10073).
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Bochkarev, A.V., Erofeev, V.I., Zemlyanukhin, A.I. (2019). Modulation Instability of Flexural Waves in Cylindrical Shells: Modified Criterion. In: Altenbach, H., Belyaev, A., Eremeyev, V., Krivtsov, A., Porubov, A. (eds) Dynamical Processes in Generalized Continua and Structures. Advanced Structured Materials, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-030-11665-1_6
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