Optimum transmitter pulse shapes for maximum acoustical excitation of mechanical vibrations

This thesis contains the results obtained in modeling the acoustic response of an M-10 solid which has been momentarily excited by an ultrasonic signal. The model is implemented with a high Q series RCL network which is excited by the same form of signal used in the transmitted ultrasonic signal.

The objective of this investigation was to optimize the duration of the transmitted ultrasonic signal with respect to the maximum vibrational energy remaining in the solid after the transmitted signal terminates.

Since the transmitted signal is windowed and can be either at or near one of the vibrational mode frequencies, a complete analysis is made for the particular window with the transmitted signal at and near the vibrational mode frequencies. Rectangular, Hanning, and triangular are the type of windows used.

Experimental, theoretical, and SPICE analyses are used to verify the final results, and plots of each analysis are well illustrated in the thesis. The theoretical analysis combines classical methods and Laplace transform techniques to solve the differential equations that govern the high Q series RCL model. Also, the Fourier series expansion for an even function together with trigonometric identities are implemented to simplify the calculations.

The experimental data taken from the M-IO solid are in good agreement with the analytical results obtained from the electrical model. The optimum window widths for the rectangular, Manning, and triangular cases at and near one of the vibrational frequencies were within a reasonable range compare with the results from the model.