Hong Gong

This paper is concerned with electric–acoustic/acoustic–electric conversions of thin-wafer piezoelectric transducers polarized in the thickness direction. By introducing two mechanical components with frequency-dependent values, i.e., radiation resistance and radiation mass, into the equivalent circuit of the thin-wafer piezoelectric transducer, we established a frequency-dependent dynamic mechanic-electric equivalent network with four terminals for an arbitrary given frequency, an enhancement from the conventional circuit networks. We derived the analytic expressions of its electric–acoustic and acoustic–electric conversion impulse responses using the four-terminal equivalent circuit to replace the traditional six-terminal equivalent circuit for a thin-wafer transducer with harmonic vibrational motion. For multifrequency electrical/acoustic signals acting on the transducer, we established parallel electric–acoustic/acoustic–electric conversion transmission networks. These two transmission network models have simple structures and clear physical and mathematical descriptions of thin-wafer transducers for electric–acoustic/acoustic–electric conversion when excited by a multifrequency electric/acoustic signal wavelet. The calculated results showed that the transducer’s center frequency shift relates to its mechanical load and vibration state. The method reported in this paper can be applied to conventional-sized and small-sized piezoelectric transducers with universal applicability.

The traditional acoustic attenuation coefficient is derived from an analogy of the attenuation of an electromagnetic wave propagating inside a non-ideal medium, featuring only the attenuation of wave propagation. Nonetheless, the particles inside viscous solids have mass, vibrating energy, viscosity, and inertia of motion, and they go through transient and damping attenuation processes. Based on the long-wavelength approximation, in this paper, we use the energy conservation law to analyze the effect of the viscosity of the medium on acoustic attenuation. We derive the acoustic attenuation coefficient by combinations of the dynamical equation of a solid in an acoustic field with conventional longitudinal wave propagation under a spring oscillator model. Considering the attenuation of propagating waves and the damping attenuation of particle vibration, we develop a frequency dispersion relation of phase velocity for the longitudinal wave propagating inside viscous solid media. We find that the acoustic impulse response and vibrational system function depends on the physical properties of the viscous solid media and their internal structure. Combined with system function, the impulse response can be an excellent tool to invert the physical properties of solids and their internal structures. We select a well-known rock sample for analysis, calculate the impulse response and vibrational system function, and reveal new physical insight into creating acoustic attenuation and frequency dispersion of phase velocity. The results showed that the newly developed acoustic attenuation coefficients enjoy a substantial improvement over the conventional acoustic attenuation coefficients reported in the literature, which is essential for industrial applications; so are the dispersion characteristics.

In solving piezoelectric equations of motion, we established an electric–acoustic equivalent circuit of tangentially polarized thin cylindrical transducers and derived analytical expressions of the electric-acoustic response from the harmonic driving-voltage excitation. To experimentally verify the findings, we manufactured a parallel electric-acoustic transmission network for transducers excited by multifrequency driving signals. We found that the tangentially polarized thin cylindrical transducers achieved a much higher electric-acoustic conversion efficiency than the radially polarized thin cylindrical transducers. The electric-acoustic impulse response of the transducers consisted of a direct-current damping with lower-frequency components, a damping oscillation with higher-frequency elements, and a higher resonant frequency of the transducer over its center frequency. The characteristics of radiated acoustic signals included contributions from the geometrical shape and size of the transducer, the physical parameters of piezoelectric material, the type of driving-voltage signals, and the polarization mode of the transducers. In comparison, our theoretical predictions are in good agreement with experimental observations. It is plausible that using the tangentially polarized thin cylindrical transducers as sensors in the acoustic-logging tool may significantly improve the signal-to-noise ratio of the measured acoustic-logging signals.