Finite-Element Solution of Periodic Waveguides for Acoustic Waves

Abstract

Abslract-A n umerical approach based on the finite-element method is described for the analysis of periodic waveguides for acoustic waves. The va lidity of the method is confirmed by comparing the nume rical results for the dispersion curves of horizontal shear (SH) waves in a groove grating on an isotropic material with the experimental results. The application of this approach is also demonstrated by investigating the propagation characteristics of SH surface waves in a groove grating on a layered isotfopic material. Furthermore, ror a groove grating on a piezoelec tric material, the stop-band width and the center-rrequency shift in the dispen ion d iagram ror Rayleigh waves are calculated, which afe important parameters ro r design of a reflector, and the Influences or groove shape on these parameters are examined. I. IN TRODUCTION IN recent years, attention has been given to the use of gratings on solid surfaces to reduce the propagation velocity of acoustic waves and to introduce bandgaps and cutoff frequencies into their dispersion relations for the purpose of producing delay lines and filtering devices [ 1]- [6]. Several methods for the analysis of periodic waveguides in Fig. I have been proposed , and the coupledmode theory, which derives the coupled-mode equations under the assumption of small perturbations , is widely used [7]- [12]. The calculation procedure of this method is relatively simple, but the accuracy is degraded for large perturbations. On the other hand, it is possible to increase the accuracy by expanding the acoustic and electromagnetic fields in terms of Fourier series by means of the Floquet theorem and deriving the homogeneous linear equations of infinite order [13]-[19J. However, it seems to be difficult to apply this approach to arbitrarily shaped periodic waveguides.In this paper a numerical approach based on the finiteelement method is described for the analysis of arbitrarily shaped periodic waveguides for acoustic waves. The validity of the method is confirmed by comparing {he numerical results for the dispersion curves of horizontal shear (SH) waves in a groove grating on an isotropic material with the experimental results [4]. We also demonstrate the application of this approach by investigating the propagation characteristics of SH slIrface waves in a groove grating on a layered isotropic material. Further-, Manuscript received April 22, 1986; revised September 12, 1986. The authors are with' the Department of Electronic Engineering, Hokhido Unive rsity, Sapporo, 060 Japan.IEEE Log Number 8612862. more, for a groove grating on a piezoelectric material, the stop-band width and the center-frequency shift in the dispersion diagram for Rayleigh waves are calculated, which are important parameters for· design ofa reflector, and the influences of groove shape on these parameters are examined. II . BASIC EQUATIONSThe structure under study is periodic in the x direction with period d as shown in Fig. I . The region n surrounded by boundaries r I to r 4 is the basic cell. The mechani...

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