#### Date of Award

2018

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy in Ocean Engineering

#### Specialization

Acoustics

#### Department

Ocean Engineering

#### First Advisor

Harold Vincent

#### 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 maximum/ minimum impedance values. In addition, the modal damping can also be calculated through impedance function. It is usually measured first under air loading and then under water loading. When the transducer is operated in water, some characteristics, such as resonant and anti-resonant frequencies, are changed because the acoustic medium becomes denser in water, and the added radiation mass in water is much greater than that in air. This new method by pole-residue operations is applied to estimate impedance functions of acoustic transducers. With this new method, the poles of the impedance function can be used to precisely compute some characteristics of the transducer, such as modal frequencies and modal damping. Four numerical examples show the procedures to calculate impedance functions of the transducer under air and water loadings through both finite element model and experiments. Together with their comparisons, the influence of water to the transducer, the radiating mass, has been quantified.

Transmitting voltage response (TVR) and beam pattern (BP) are two of the most important measures of a transducer’s ability to perform the functions of radiating sound. Traditionally, there are two kinds of methods for measuring TVR and BP, namely, single-frequency harmonic analysis method and Fourier-based analysis method. But, both methods have drawbacks. The former one is too time-consuming while the latter one suffers from the leakage and frequency resolution problems. Additionally, both of them are usually influenced by the reflecting waves from boundaries, such as water surface and acoustic tank walls. In manuscript 3, a new approach by pole-residue operations is developed to estimate TVR and BP, which overcomes the above drawbacks. Unlike the traditional methods, continuous characteristic functions in the frequency domain can be obtained by one-time measurement with the new method. Since very short signal is needed in this approach, the calculation of characteristic functions can be finished before the sound waves travel back from the boundaries. Two numerical examples are provided to show the procedures to compute TVR and BP of an underwater transducer. The effectiveness is verified by the harmonic analysis method. The accuracy and the efficiency are also demonstrated by the comparisons with traditional methods.

#### Recommended Citation

Gao, Bin, "IMPROVED METHODS FOR MEASURING CHARACTERISTIC FUNCTIONS OF UNDERWATER TRANSDUCERS" (2018). *Open Access Dissertations.* Paper 766.

https://digitalcommons.uri.edu/oa_diss/766

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