IMPROVED METHODS FOR MEASURING CHARACTERISTIC FUNCTIONS OF UNDERWATER TRANSDUCERS

Abstract

The overall objective of this dissertation is to effectively and efficiently obtain some important characteristic functions of acoustic transducers, such as electrical impedance function, transmitting voltage response (TVR) and beam pattern (BP). Oftentimes, one makes measurements on these functions through traditional ways, e.g., stepped harmonic analysis method and Fourier-based analysis method. To improve the accuracy and efficiency of computing these characteristics, new approaches by pole-residue operations are developed and verified in this dissertation. In this new approach, the poles and residues associated with the input and output signals are extracted with the multi-signal Prony-SS method, which is an extension and improvement of the classical Prony’s method. The system functions can be computed by the operations of those poles and residues from input and output signals. Compared with traditional methods, the new one not only turns out effective and computationally efficient but also overcomes the leakage and the frequency resolution problems, by getting a continuous function in the frequency domain without periodic assumption. In addition, many significant characteristics, such as modal frequencies and modal damping, can be precisely calculated from the system poles other than reading them from the plotting of system functions in traditional ways. When a periodic loading excites the linear system, the calculation of transient response is discussed in manuscript 1. Compared with time-domain methods, frequency-domain methods are more computationally efficient when computing the responses of linear dynamic systems. However, frequency-domain methods can only compute the steady-state response instead of the total response. To the author’s best knowledge, the transient response of a dynamic system to arbitrary periodic loading can not be solved analytically. In the first manuscript, a closed-form solution for the transient responses of linear multi-degree-of-freedom (MDOF) systems to arbitrary periodic excitations is derived. By taking advantage of the fast Fourier transform (FFT) algorithm, a very efficient numerical method is developed to compute the transient and total responses of MDOF systems, suitable for both damped and undamped systems. In the newly developed method, the computational time required for obtaining the transient response is much less than that for the steady state response. Three numerical examples are provided in this manuscript to verify the correctness, and demonstrate the effectiveness as well, of the newly developed method. Discussed in the second manuscript is the impedance function, which is very essential for a transducer. The impedance function contains many important characteristics, such as the resonant frequencies, anti-resonant frequencies, and