Vol.4, No 16, 2004 pp. 115-120
UDC 537.226.86:53.082.73:62-521

---

MODELLING OF LAMINATE COMPOSITES WITH EMBEDDED PIEZOELECTRIC ACTUATORS AND SENSORS
Dragan Marinković^1,2, Ulrich Gabbert^1
1Otto-von-Guericke-Universität Magdeburg, Fakultät für Maschinenbau,
Institut für Mechanik, Universitätsplatz 2, D-39106 Magdeburg, Germany
²Faculty of Mechanical Engineering, University of Niš
Aleksandra Medvedeva 14, 18000 Niš, Serbia and Montenegro

---

Abstract. The increasing need for lightweight structures requires the development of new kinds of materials. The general requirement of those materials is high specific mechanical properties, i.e. the ratio between mechanical properties and mass density. Laminate fiber reinforced materials, which have a very high strength and stiffness in desired directions and lower characteristics in other directions represent a very good choice, and they are already used in various applications like space structures, transportation applications etc. Further behavior improvement of structures made of laminate composites can be achieved by embedding components made of smart material between layers, like piezoelectric patches. In the paper the governing equations of an active layered plate are described based on the Mindlin-Reissner assumption. For a piezoelectric layer the electromechanical-coupled constitutive equations are introduced and the governing equations of piezoelectric actuating loads and sensor output are developed. Then the paper addresses the problem of the finite element formulation of a laminated piezoelectric plate type element.

---

MODELIRANJE LAMINARIH KOMPOZITNIH MATERIJALA 
SA INTEGRISANIM PIEZOELEKTRIČNIM AKTUATORIMA
I SENZORIMA Sve veća potreba za lakim konstrukcijama zahteva razvoj novih vrsta materijala. Od tih materijala se zahtevaju visoka specifična svojstva, tj.visok odnos mehaničkih karakteristika i specifične gustine. Laminarni vlaknasti kompozitni materijali, koji raspolažu visokom čvrstoćom i krutošću u zeljenim pravcima i nižim karakteristikama u drugim pravcima predstavljaju dobar izbor i već se uveliko koriste u različite svrhe, npr. u konstrukcijama za svemirska istraživanja, transportu itd. Viši kvalitet u ponašanju konstrukcija od ovih materijala može se postići integrisanjem aktivnih komponenti, npr. piezo-pločica, izmedju slojeva materijala. U radu su date osnovne jednačine aktivne kompozitne ploče prema predpostavkama Mindlin-Reissner. Za piezoelektrični sloj su date osnovne jednačine spregnutog mehaničkog i električnog polja, kao i jednačine koje definišu pobudu piezoelektričnog aktuatora, odnosno izlaz senzora. Na kraju rada se razmatra formulacija problema primenom metode konačnih elemenata.