Archive of Applied Mechanics

, Volume 83, Issue 5, pp 765-781

First online:

Three-dimensional free vibration analysis of rotating laminated conical shells: layerwise differential quadrature (LW-DQ) method

  • Mostafa TalebitootiAffiliated withCenter of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology Email author 

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This paper focuses on the free vibration analysis of thick, rotating laminated composite conical shells with different boundary conditions based on the three-dimensional theory, using the layerwise differential quadrature method (LW-DQM). The equations of motion are derived applying the Hamilton’s principle. In order to accurately account for the thickness effects, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the shells. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equation applying the DQM in the meridional direction. This study demonstrates the applicability, accuracy, stability and the fast rate of convergence of the present method, for free vibration analyses of rotating thick laminated conical shells. The presented results are compared with those of other shell theories obtained using conventional methods and a special case where the angle of the conical shell approaches zero, that is, a cylindrical shell and excellent agreements are achieved.


Rotating conical shell Layerwise theory Natural frequency Differential quadrature method