Mechanics of Composite Materials

, Volume 49, Issue 2, pp 171–180 | Cite as

Axisymmetric Vibrations of Stepped Cylindrical Shells Made of Composite Materials. Part 21

  • J. Lellep
  • L. Roots

Axisymmetric vibrations of stepped cylindrical shells are studied. The shells are made of elastic unidirectionally reinforced composite materials and have a piecewise constant (stepped) thickness. It is assumed that, at the reentrant corners of steps, stable circumferential cracks of constant depth are located. The method of a “massless rotational spring” developed in earlier papers for investigation of homogeneous shells made of isotropic materials is extended to the case of anisotropic composite materials. Analytical expressions are derived for shells with an arbitrary number of steps, and numerical results are presented for shells with one and two steps.


anisotropy shell vibration crack 


Acknowledgements. A partial support from the Grant 9110 of the ESF “Optimization of structural elements” and from the target financed project SF0180081s08 “Models of applied mathematics and mechanics” is acknowledged.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.University of Tartu, Institute of MathematicsTartuEstonia

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