Two- and three-dimensional finite element time and frequency domain analysis for the complex 1-3 type piezocomposite material transducer

Piezocomposites of the 1-3 type have become the transducer material of choice for medical imaging and nondestructive evaluation, where the half wavelength thickness mode has typical frequency in the megahertz range. For marine applications, transducers resonant in the kilohertz range are typical. The objective of this work is to apply the FEM simulation for a new complex 1-3 type composite and verify the predictions by experiment. To retain the advantages of the conventional 1-3 type composite material around (or below) 100 kHz, we devised a complex rod configuration for 1-3 type with composite. Each rod contained a ceramic sandwiched between an aluminum head mass and steel tail mass. To simulate the new complex 1-3 type composite material transducer in both frequency and time domains, we apply quantum mechanics Dirac notation to derive a complete set of finite element constitutive equations with damping. Solving equations in frequency domain, we compute transducer electrical impedance, resonant and antiresonant frequencies, transmitting voltage response (TVR), receiving voltage response (RVR) and figure of merit (insertion loss), etc. By utilizing the numerical discrete fast Fourier transform (DFFT) and inverse discrete fast Fourier transform (IDFFT), we are also able to calculate the impulse response, sound pressure field, wave forms due to different driving voltages, etc. A typical time domain analysis example for the new complex 1-3 type composite transducer is presented.