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Shock and Vibration
Volume 16, Issue 5, Pages 495-503

Free Vibration of Sandwich Plates and Shells by Using Zig-Zag Function

S. Brischetto,1 E. Carrera,1 and L. Demasi2

1Department of Aeronautics and Space Engineering, Politecnico di Torino, Torino, Italy
2Department of Aerospace Engineering, San Diego State University, San Diego, CA, USA

Received 30 June 2008; Revised 4 September 2008

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper analyses the free vibration response of sandwich curved and flat panels by introducing the zig-zag function (—1)kζk (ZZF) in the displacement models of classical and higher order two-dimensional shell theories. The main advantage of ZZF is the introduction of a discontinuity in the first derivative, zig-zag effect, of the displacements distribution with correspondence to the core/faces interfaces. Results including and discarding ZZF are compared. Several values of face-to-core stiffness ratio (FCSR) and geometrical plate/shell parameters have been analyzed. Both fundamental vibration modes and those corresponding to high wave numbers are considered in the analysis. It is concluded that: (1) ZZF is highly recommended in the free vibration analysis of sandwich plates and shells; (2) the use of ZZF makes the error almost independent by FCSR parameter; (3) ZZF is easy to implement and its use should be preferred with respect to other `more cumbersome' refined theories.