Higher Order Model for Analysis of Magneto-Electro-Elastic Plates

In the recent years the study of smart structures has attracted significant researchers. The use of smart materials, such as piezoelectric and/or piezomagnetic materials, in the form of layers or patches embedded and/or surface bonded on laminated composite structures, can provide the so-called adaptive structures. In these cases, the structure behaviour is not defined by the geometry and material properties, but also by the electric and magnetic fields that are applied to the structures, because the piezomagnetic materials have the ability of converting energy from one form to the other (among magnetic, electric, and mechanical energies).

In this paper we present a finite element model, based in the third-order shear deformation theory, for static and free vibration analysis of plate structures integrating piezoelectric/piezomagnetic layers. A simple and efficient three-node triangular fat plate element is used. The formulation introduces one electric potential and one magnetic potential degree of freedom for each piezoelectric and piezomagnetic layer of the finite element. The solutions given by the proposed model for illustrative numerical examples, in static and free vibration, are presented and discussed. elastic plate magneto-electro-elastic plate Mode B only F only B/F/B F/B/F B only F only B/F/B F/B/F 1 12600.01 14882.24 12751.45 14738.18 12631.77 14905.91 12783.17 14761.57 2 24926.81 27965.02 25211.44 27664.41 24964.69 27987.31 25249.50 27686.12 3 25147.20 28198.62 25433.88 27895.27 25185.42 28221.14 25472.28 27917.20 4 34176.64 37478.54 34566.57 37048.92 34210.58 37496.29 34601.21 37065.91 5 39204.94 42568.46 39657.88 42059.00 39234.02 42582.32 39687.79 42072.00 6 39963.98 43475.44 40422.48 42960.06 39995.27 43490.76 40454.58 42974.49 Table 1. Natural Frequencies (rad/s) : L=1 m ; H=0.3 m. .. HSDT