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Appl. Sci. 2017, 7(1), 17; doi:10.3390/app7010017

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

1
DICAM - Department, School of Engineering and Architecture, University of Bologna, Bologna 40126, Italy
2
Advanced Computational Mechanics Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Stefano Invernizzi
Received: 24 November 2016 / Revised: 10 December 2016 / Accepted: 14 December 2016 / Published: 22 December 2016
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Abstract

The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry. View Full-Text
Keywords: laminated composites shells; doubly-curved surfaces; natural frequencies; generalized differential quadrature method; higher-order structural theories laminated composites shells; doubly-curved surfaces; natural frequencies; generalized differential quadrature method; higher-order structural theories
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MDPI and ACS Style

Tornabene, F.; Fantuzzi, N.; Bacciocchi, M.; Reddy, J.N. An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells. Appl. Sci. 2017, 7, 17.

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