Analysis of a fractal ultrasonic transducer with a range of piezoelectric length scales

摘要: The transmission and reception sensitivities of most piezoelectric ultrasonic transducers are enhanced by their geometrical structures. This structure is normally a regular, periodic one with principal length scale which, due to the resonant nature devices, determines central operating frequency. There engineering interest in building wide bandwidth so it follows that design, resonators have range scales should be used. paper describes mathematical model fractal ultrasound transducer whose components span scales. been many previous studies wave propagation Sierpinski gasket but this first study its complement. critically important development as complement formed from broad distribution triangle sizes whereas triangles equal size. Within structure, electrical mechanical fields fluctuate tune time dependent displacement these substructures. A new set basis functions developed allow us express part finite element methodology. renormalisation approach then used develop recursion scheme analytically key discrete matrices arise. Expressions for transducer's operational characteristics derived analysed function driving It transpires device has significantly higher sensitivity (18 dB) wider (3 MHz) than an equivalent Euclidean (standard) device.