Original Article Journal of Intelligent Material Systems and Structures 1–7 Ó The Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1045389X15595294 jim.sagepub.com Formulation of a simple distributed- parameter model of multilayer piezoelectric actuators Yangkun Zhang 1 , Tien-Fu Lu 1 and Said Al-Sarawi 2 Abstract A multilayer piezoelectric actuator is a promising linear vibrator. In this article, a simple distributed-parameter analytical model of piezoelectric actuator, which can model vibration characteristics of piezoelectric actuator–based applications, is formulated. Based on the physical analysis of piezoelectric actuator, a simplification is proposed, justified and applied to fundamentals of thickness-extension-mode piezoelectricity. This simplification subtly enables piezoelectric actuator to be effectively modelled as a whole and allows for a formulation of a simple analytical model. Compared with other model- ling methods in the literature, the proposed model with a small number of easily accessible parameters is easy to handle and extend with little compromised accuracy. The effectiveness of the proposed model has been validated by a three- dimensional finite element analysis model of piezoelectric actuator developed in commercial software ANSYS. Keywords Multilayer, piezoelectric, actuators, analytical, model, simplification, piezoelectricity, finite element analysis Introduction A multilayer piezoelectric actuator (PEA) is a widely used linear actuator. It stacks thin piezo layers which can convert electric energy to mechanical force or deformation. Aside from a high resolution in displace- ment, a high stiffness and a large dynamic frequency range, PEA can operate with a low voltage and a com- pact size. Due to those desired features, PEA is widely used as a high-precision positioner (Miri et al., 2014) or a vibrator in high-resolution vibration applications (Lee et al., 2011; Morita et al., 2013; Okamoto and Yoshida, 1998; Peng et al., 2013; Siebenhaar, 2004). In the applications of PEA where multiple resonant modes are required to be modelled (Morita et al., 2013), a distributed-parameter model is required. In this article, a simplification on fundamentals of thickness-extension-mode piezoelectricity is proposed and justified to formulate a simple and effective distributed-parameter analytical model of PEA for modelling the vibration of PEA-based applications. Section ‘Existing models of PEA’ reviews the existing models of PEA. In section ‘Model formulation’, based on the physical analysis of PEA, simplifications are proposed, justified and applied into the complex elec- tromechanical coupled fundamentals of thickness- extension-mode piezoelectricity. Then, based on the simplified fundamentals, a simple distributed- parameter analytical model of PEA is formulated. In section ‘Model validation and discussion’, a case study is carried out for validation of the simplified fundamen- tals and the formulated analytical model. The valida- tion is achieved by checking with a three-dimensional (3D) finite element analysis (FEA) model of PEA developed in commercial software ANSYS. Also, the limitations of the proposed model are discussed in sec- tion ‘Model validation and discussion’. Section ‘Summary and future work’ presents the summary and future work. Existing models of PEA A lot of efforts have been put into modelling PEAs in the literature, especially in its control to overcome some non-linear behaviour such as hysteresis. For online control, lumped-parameter models are often used, as they are easily implemented in practices. A widely 1 School of Mechanical Engineering, The University of Adelaide, Adelaide, SA, Australia 2 School of Electrical & Electronic Engineering, The University of Adelaide, Adelaide, SA, Australia Corresponding author: Tien-Fu Lu, School of Mechanical Engineering, The University of Adelaide, Adelaide, SA 5005, Australia. Email: tien-fu.lu@adelaide.edu.au at UNIVERSITY OF ADELAIDE LIBRARIES on November 6, 2015 jim.sagepub.com Downloaded from