# Propagation and excitation of ultrasonic Lamb waves in piezoelectric materials

#### Abstract

This thesis studies the propagation and excitation of ultrasonic Lamb waves in single crystal piezoelectric plates as well as in composite structures that consist of two piezoelectric plates in contact with each other. The propagation characteristics of Lamb waves in a piezoelectric plate and their relation to the surface acoustic wave under different electrical boundary conditions is investigated both theoretically as well as experimentally. It is found that when both surfaces are either metallized or unmetallized, the surface acoustic wave is obtained by a linear superposition of the lowest two modes, the $A\sb0$ and $S\sb0$ modes. On the other hand, if only one surface is metallized, then the surface acoustic wave is equivalent to just one of the modes (either the $A\sb0$ or $S\sb0$ mode, depending on which surface is metallized). The beating phenomenon, whereby wave energy launched on one surface transfers periodically back and forth between opposite plate surfaces, is present when both surfaces are either metallized or unmetallized, but is absent if only one surface is metallized. The excitation of ultrasonic Lamb waves by an interdigital transducer deposited on a piezoelectric plate is analyzed using the Green's function method. The amplitudes of the generated Lamb waves are obtained in terms of the charge density on transducer electrodes. This is then used to calculate the radiation conductance of the transducer. Experimentally measured characteristics of interdigital transducers deposited on Y-Z lithium niobate plates are found to be in good agreement with theoretical calculations. The analysis is also used to calculate the performance of Lamb wave delay lines taking into account the excitation of fundamental as well as higher-order Lamb wave modes. Experimental results obtained on delay lines fabricated on 128$\sp\circ$ Y-X lithium niobate plates are compared with theoretical calculations. The resonant frequencies and time delays of the modes are found to be in fair agreement with calculated values. It is shown that delay lines fabricated on acoustically thin plates $(h/\lambda < 1,$ where h = plate thickness, and $\lambda$ = acoustic wavelength) can efficiently excite Lamb waves at frequencies greater than 10 times the resonant frequency of the lowest order mode. The Green's function method used for single piezoelectric plates is extended to analyze the excitation of Lamb waves in composite structures. The analysis is used to calculate the coupling coefficient, $K\sp2,$ of the IDT to the $A\sb0$ and $S\sb0$ modes. For the case of a zinc oxide film deposited on a silicon membrane, it is found that by proper choice of the film and membrane thickness, values of $K\sp2$ greater than 1.8% can be obtained.

#### Recommended Citation

Yu Jin, "Propagation and excitation of ultrasonic Lamb waves in piezoelectric materials" (January 1, 1993). Dissertations (1962 - 2010) Access via Proquest Digital Dissertations. Paper AAI9411503.
http://epublications.marquette.edu/dissertations/AAI9411503

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