MODELLING OF FGM PIEZOELECTRIC TRANSDUCERS USING GRADED FINITE ELEMENT CONCEPT Wilfredo Montealegre Rubio, wilfredo.rubio@poli.usp.br Emilio Carlos Nelli Silva, ecnsilva@usp.br Flavio Buiochi, fbuiochi@usp.br Julio C. Adamowski, jcadamow@usp.br Department of Mechatronics and Mechanical Systems Engineering, Escola Politécnica da Universidade de São Paulo, Av. Prof. Mello Moraes, 2231 - Cidade Universitária, São Paulo – SP – 05508-900, Brazil Abstract. Piezoelectric materials generate displacements when an electric potential is applied and, electric potential when they are subjected to forces or pressure. Functionally Graded Materials (FGM) are composite advanced materials, which are made by changing gradually the properties with position inside material domain. The application of FGM concept to piezoelectric transducer design allows designing composite transducers without interface between materials (e.g. PZT and Aluminum), due to the continuous change of property values. Thus, large improvements can be achieved, as reduction of stress concentration, increasing bonding strength and fatigue-lifetime. Recent works about piezoelectric FGM show lack of computational methods to model these transducers and evaluate their performance considering property gradation function, futhermore, FE comercial softwares have no “tools” to simulate graded continuous materials for while. Thus, this work proposes the development of Finite Element (FE) algorithms to model FGM piezoelectric ceramics and to explore the FGM potential on piezoelectricity field. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element concept, where these material properties are interpolated inside the finite element using the FE shape functions. A software based on 4-node graded finite element (Q4) is implemented. Dynamic and static analyses are performed. In the examples, the material properties are graded along thickness direction to illustrate the influence of gradation on the output displacements, vibration modes, and resonance frequencies. These examples are compared with results of a homogeneous piezoceramic to show FGM advantages. Keywords: Graded Finite Element, Functionally Graded Material, Piezoelectric ceramic, Dynamic Performance, Static Performance 1. INTRODUCTION Piezoelectric materials have the property to convert an electrical energy (electric field and electric potential) into a mechanical energy (stress and strain) and vice-versa. Examples of piezoelectric materials include quartz, ceramics (PZT) and polymers (PVDF). Its main applications are in sensors and electromechanical actuators, as resonators in electronic equipment and acoustic applications, as ultrasound transducers, naval hydrophones, and sonars. Ultrasound transducers are used in medical imaging (Akhnak et al., 2000) and non-destructive tests. Other applications include pressure sensors; piezoelectric actuators for the structural vibration control; performance of nanopositioning and micromanipulation devices as: electronic microscopy instruments; laser interferometry; cell manipulation equipment; microelectromechanical systems "MEMS"; nanotechnology and precision mechanics equipment (Kögl and Silva, 2005). A brief review of piezoelectric applications is offered by Newnham and Ruschau (Newman and Ruschau, 1991). In order to improve the conventional piezoceramic performance (single and homogeneous materials) are fabricated as piezocomposite materials. However, the interface between materials produces an uneven distribution of stresses which reduces the electric-field-induced displacement characteristics, reliability and lifetime. Other modern approach is to change the piezoelectric properties of ceramic disk through its thickness, specifically, to reduce one echo wave of two produced in each piezoceramic surface and to increase the induced piezoelectric stress gradient. Functionally Graded Material concept has arisen as a solution to reduce the ultrasonic wave generated at one piezoceramic surface (Yamada et al., 1998; Ichinose et al., 2004; Samadhiya and Mukherjee, 2006). Functionally Graded Materials (FGM) are materials that possess continuously graded properties with gradual change in microstructure (Hirai, 1996; Suresh and Mortensen, 1998). The materials are made to take advantage of desirable features of its constituent phases. For instance, in a thermal protection system, FGMs take advantage of heat and corrosion resistance, typical of ceramics, and mechanical strength and toughness, typical of metals. A soft property variation supplies advantages such as stress concentration reduction (Suresh and Mortensen, 1998), since they do not present interface among inclusion and matrix materials, therefore, it reduces a common problem in composite materials, the crack arising or damages in these interfaces. Specifically, in Functionally Graded Piezoelectric (FGP) ceramics, the conventional and homogeneous piezoelectric material is replaced by a functionally graded piezoelectric one, see Fig. 1. Therefore, all or some properties vary along a specific Cartesian direction, usually along thickness. Several gradation functions can be used, see Fig. 1. Thus, if the piezoelectric properties change from low to high values, only one ABCM Symposium Series in Mechatronics - Vol. 3 - pp.552-561 Copyright c  2008 by ABCM