Short communication Transverse surface waves in a piezoelectric material carrying a gradient metal layer of finite thickness Zheng-Hua Qian a,b, * , Feng Jin a , Tianjian Lu a , Sohichi Hirose b a MOE Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, PR China b Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, Tokyo 152-8550, Japan article info Article history: Received 26 December 2008 Accepted 17 April 2009 Available online 24 May 2009 Keywords: Layered structure Gradient metal layer WKB method Transverse surface waves abstract The existence and propagation behavior of transverse surface waves in a layered structure concerning a piezoelectric substrate and a gradient metal layer are theoretically investi- gated in this paper. The Wentzel–Kramers–Brillouin (WKB) method is applied to obtain the analytical solutions in the gradient metal layer. The dispersion equation for transverse surface waves in such structure is obtained in a quite simple mathematical form, where the material gradient of the metal layer assumes arbitrary functions. Effects of material gradi- ent on three types of dispersion behavior are discussed in detail based on a proper classi- fication. Numerical results show that the material gradient in the metal layer evidently affects the fundamental mode shape of the transverse surface waves but has negligible effects on the higher order modes. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Transverse surface wave in piezoelectric materials or layered piezoelectric structures has been of a major concern due to their high performance and simple particle motion in technological applications such as SAW (surface acoustic wave) sen- sors, filters, delay lines, and so on [1]. One type of transverse surface wave is the Love wave which exists only when a sub- strate surface carries a finite-thickness layer of a second material and when the bulk shear wave velocity in this second material is less than that in the substrate. The Love wave is always dispersive and has more than one mode, which has been extensively studied and used in signal-processing devices in recent years [2–9]. Another type of transverse surface wave is called Bleustein–Gulyaev (B–G) wave, which exists and propagates only at the free surface of a piezoelectric half-space due to the interconnection between the elastic and electric fields in piezoelectric materials [10,11]. It is closely related to a bulk shear wave and, although seldom used in practice at present, may have certain advantages over SAW devices currently used due to its simple particle motion. Much earlier, Curtis and Redwood [12] carried out a theoretical study on the propagation of transverse surface waves in a piezoelectric substrate carrying a finite-thickness metal layer. Such a wave is related both to the B–G wave and to the Love wave, and would have great importance in the practical application to SAW devices. Recently, the potential applications of gradient materials to SAW devices have been extensively considered to improve their efficiency and natural life [13–16]. However, to our best knowledge, there exists no study on transverse surface waves in a piezoelectric substrate coated with a gradient metal layer of finite thickness. Furthermore, it is much easier to tune the propagation behavior of transverse surface wave in layered structures by introducing material gradient in metal layer than in piezoelectric substrate, which motivated our work in this paper too. Dispersion equations for the existence of transverse 0020-7225/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijengsci.2009.04.002 * Corresponding author. Address: Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, Tokyo 152-8550, Japan. Tel./ fax: +81 3 57342692. E-mail addresses: qian.z.aa@m.titech.ac.jp, zhenghua_qian@hotmail.com (Z.-H. Qian). International Journal of Engineering Science 47 (2009) 1049–1054 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci