Wave packets in a thin cylindrical shell under a non-uniform axial load. (English. Russian original) Zbl 1010.74578

J. Appl. Math. Mech. 65, No. 2, 301-309 (2001); translation from Prikl. Mat. Mekh. 65, No. 2, 308-316 (2001).
The authors consider a thin cylindrical shell of thickness \(h\). It is assumed that the shell is loaded by slowly varying with respect to time and circular coordinate axial efforts. The compression effort does not reach its critical value. The propagation of localized families of bending-plane waves is studied. As example nonstationary localized vibrations of cylindrical shell are studied. The shell’s crossection is ellipse.


74K25 Shells
74H45 Vibrations in dynamical problems in solid mechanics
74J05 Linear waves in solid mechanics


[1] Mikhasev, G. I.: Localized families of flexural waves in a non-circular cylindrical shell with slanting edges. Prikl. mat. Mekh. 60, No. 4, 635-643 (1996) · Zbl 0920.73176
[2] Tovstik, P. Ye.: The stability of thin shells: asymptotic methods. (1995) · Zbl 0834.73027
[3] Grigolyuk, E. I.; Kabanov, V. V.: The stability of shells. (1978)
[4] Bolotin, V. V.: The dynamic stability of elastic systems. (1956) · Zbl 0125.15301
[5] Mikhasev, G. I.: Free and parametric vibrations of cylindrical shells under static and periodic axial loads. Techn. mech. 17, No. 3, 209-216 (1997)
[6] Kuntsevich, S. P.; Mikhasev, G. I.: Parametric vibrations of viscoelastic cylindrical shell under static and periodic axial loads. Techn. mech. 19, No. 3, 187-197 (1999)
[7] Courant, R.; Helbert, D.: Methoden der mathematischen physik. (1931) · Zbl 0001.00501
[8] Tovstik, P. Ye.: Two-dimensional problems of the stability and vibrations of shells of zero Gaussian curvature. Dokl. akad. Nauk SSSR 271, No. 1, 69-71 (1983)
[9] Bogdanov, Yu.S.; Syroid, Yu.B.: Differential equations. (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.