Periodic composite ultrasonic transducers offer many advantages but the periodic pillar architecture can give rise to unwanted modes of vibration which interfere with the piston like motion of the fundamental thickness mode. In this paper, viscoelastic loss is incorporated into a three-dimensional plane wave expansion model (PWE) of these transducers. A comparison with experimental and finite element data is conducted and a design to damp out these lateral modes is investigated. Scaling and regularisation techniques are introduced to the PWE method to reduce ill-conditioning in the large matrices which can arise. The identification of the modes of vibration is aided by examining profiles of the displacements, electrical potential and Poynting vector. The dispersive behaviour of a 2-2 composite transducer with high shear attenuation in the passive phase is examined. The model shows that the use of a high shear attenuation filler material improves the frequency band gap surrounding the fundamental thickness mode.

Ultrasonic transducers composed of a periodic piezoelectric composite are generally accepted as the design of choice in many applications. Their architecture is normally very regular and this is due to manufacturing constraints rather than performance optimisation. Many of these manufacturing restrictions no longer hold due to new production methods such as computer controlled, laser cutting, and so there is now freedom to investigate new types of geometry. In this paper, the plane wave expansion model is utilised to investigate the behaviour of a transducer with a self-similar architecture. The Cantor set is utilised to design a 2-2 configuration, and a 1-3 configuration is investigated with a Sierpinski Carpet geometry. * Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, U.K., Tel: ++44 (0)141 548 2971, Fax: ++44 (0)141 548 3345, email: ajm@maths.strath.ac.uk 1 Ideally a single longitudinal mode in the thickness direction will drive the transducer in a piston like fashion. In this paper it was found that by increasing the fractal generation level, the bandwidth surrounding the main thickness mode will increase, but there will be a corresponding reduction in the amplitude of the electrical conductance. It is also shown that a shift in the frequency of operation of the device can be achieved by altering the spatial periodicity of the electrical excitation.

The large number of degrees of freedom in the design of piezoelectric transducers requires a theoretical model that is computationally efficient so that a large number of iterations can be performed in the design optimisation. The materials used are often lossy, and indeed loss can be used to enhance the operational characteristics of these designs. Motivated by these needs, this paper extends the one-dimensional linear systems model to incorporate frequency dependent elastic loss. The reception sensitivity, electrical impedance and electromechanical coupling coefficient of a 1-3 composite transducer, with frequency dependent loss in the polymer filler, are investigated. By plotting these operating characteristics as a function of the volume fraction of piezoelectric ceramic an optimum design is obtained. A device with a non-standard, high shear attenuation polymer is also simulated and this leads to an increase in the electromechanical coupling coefficient. A comparison with finite element simulations is then performed. This shows that the two methods are in reasonable agreement in their electrical impedance profiles in all the cases considered. The plots are almost identical away from the main resonant peak where the frequency location of the peaks are comparable but there is in some cases a 20% discrepancy in the magnitude of the peak value and in its bandwidth. The finite element model also shows that the use of a high shear attenuation polymer filler damps out the unwanted, low frequency modes whilst maintaining a reasonable impedance magnitude.

The Plane Wave Expansion (PWE) method has been proposed as a theoretical model for periodic composite ultrasonic transducers. This paper extends previous work by importantly including viscoelastic loss in the material parameters. Some of the issues with model formulation, such as ill-conditioning in the large matrices, have been addressed through parameter scaling and Tikhonov regularisation. Identification of each mode of vibration has been carried out by visualising the spatial and temporal profiles of the displacement, electrical potential and Poynting vector. A comparison between the theoretical predictions and experimental data from a piezoelectric composite device is presented. The effect that the elastic properties of the passive phase have on device performance is also investigated. It is found that high shear attenuation in the passive phase gives rise to a large frequency stop band gap around the fundamental thickness mode.