Abstract
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.
Highlights
Nowadays sandwich structures are used to build large portions of advanced structural elements for aerospace, automotive and ship vehicles
As significant features sandwich structures are characterized by a soft core between two stiffer faces
The present paper has demonstrated the convenience of using the Zig-Zag function to build higher order theories to evaluate the free vibration response of sandwich plates and shells
Summary
Nowadays sandwich structures are used to build large portions of advanced structural elements for aerospace, automotive and ship vehicles. The discontinuity of mechanical properties between faces and core introduces a discontinuity of deformed core-faces planes at the interfaces, see Fig. 1 This is known as Zig-Zag effect in laminated structures [5]. Called layer-wise models, in which the three layers are treated as three independent layers, can be used to capture the above ZZ form, see the overviews by Burton and Noor [4], Noor, Burton and Bert [19], Altenbach [1], Librescu and Hause [17], Vinson [23], Carrera and Brischetto [8], Demasi [13]. Brischetto et al / Free vibration of sandwich plates and shells by using Zig-Zag function
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