Electrostatic methods in analysis of acoustic beam-forming structures

Tasinkevych, Y.

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Electrostatic methods in analysis of acoustic beam-forming structures

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Tasinkevych Y.

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IPPT_Reports_2012_3_Y_Tasinkevych_online_12_November_2012.pdf

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The work aims to present extensions of the developed methods used in electrostatic analysis of planar periodic and ?nite systems for e?cient solving of variety of the acoustic and electromagnetic wave generation and scattering problems. Specifically, their generalization for application in the acoustic beamforming analysis is reported. Moreover, certain electromagnetic wave scattering problems by periodic waveguiding structures which can be e?ciently approached by these methods are also considered. The monograph consists of seven Chapters. The Chapter 1 presents the introduction where the main objectives of the work are outlined. Mathematical principles of the electrostatic methods which are dealt with in the following are presented in details in the Chapter 2. The cases of in?nite periodic and finite aperiodic systems of in?nitesimally thin electrodes (conducting strips), generally having arbitrary widths and spacings, are considered separately. In the Chapter 3 the electrostatic methods are generalized and extended to the acoustic beam-forming analysis by linear transducer arrays. The mixed boundary-value problem is stated and solved for the cases of infinite periodic and finite aperiodic arrays of rigid baffles. Also, the developed method of the angular directivity function evaluation for a linear transducer array with arbitrary excitation is presented. In the Chapters 4 and 5 several examples illustrating practical applicability of the developed methods are discussed. Specifically, in the Chapters 4 a developed modified multi-element synthetic transmit aperture algorithm for ultrasound imaging, which incorporates the developed method of linear transducer array modeling, is reported. And in the Chapter 5 a two-dimensional electrostrictive transducer array is analyzed. In the Chapter 6 generalization of the electrostatic methods to the electromagnetic wave scattering analysis is presented. Speci?cally, the problems of electromagnetic wave scattering by periodic gratings like a thick-walled parallel-plate waveguide array and a periodic system of conducting electrodes of finite thickness are considered. Finally, the Chapter 7 concludes the monograph.

Podstawowym celem pracy jest przedstawienie opracowanych uogólnionych metod analizy zagadnień elektrostatyki układów planarnych zarówno periodycznych jak i nieperiodycznych, zawierających skończoną ilość elementów, do celów efektywnego rozwiązywania zagadnień brzegowych w teorii generacji i detekcji fal akustycznych oraz analizy zagadnień brzegowych w teorii fal elektromagnetycznych dla przypadku struktur falowodowych. Monografia składa się z siedmiu Rozdziałów. Rozdział 1 stanowi wprowadzenie w którym omówiony został cel i zakres pracy. Matematyczne podstawy metod elektrostatyki, rozwijane i generalizowane w dalszej części monografii, zostały szczegółowo omówione w Rozdziale 2. Tu osobno rozpatrzono przypadki periodycznego oraz nieperiodycznego układów infinitezymalnie cienkich elektrod (przewodzących pasków), w ogólnym przypadku o różnych szerokościach oraz odstępach. W Rozdziale 3 przedstawiono uogólnienie metod elektrostatyki do analizy mieszanego zagadnienia brzegowego dla układów sztywnych przegród, zarówno periodycznych jak i zawierających skończoną ilość elementów, oraz zaprezentowano opracowany model analityczno-numeryczny do obliczania charakterystyki promieniowania liniowych szyków przetworników akustycznych dla dowolnego pobudzenia. Przykłady praktycznego zastosowania opracowanych metod przedstawione zostały w Rozdziałach 4 oraz 5. Mianowicie, w Rozdziale 4 zaprezentowano oryginalny nowoczesny algorytm wieloelementowej syntetycznej apertury nadawczej (ang. multi-element synthetic transmit aperture) dla obrazowania ultrasonograficznego, w którym została zaimplementowana opracowana metoda modelowania liniowych szyków przetworników ultradźwiękowych. Z kolei w Rozdziale 5 przedstawiona została analiza modelu dwuwymiarowej macierzy przetworników elektrostrykcyjnych. W Rozdziale 6 przedstawiono uogólnienie metod elektrostatyki do analizy zjawisk rozpraszania fal elektromagnetycznych dla periodycznych struktur falowodowych takich jak periodyczny układ falowodów płaskich o grubych ściankach oraz periodyczny układ przewodzących elektrod o skończonej grubości. Na koniec, Rozdział 7 przedstawia podsumowanie monografii.

Słowa kluczowe

electromagnetic wave electrostatics

elektrostatyka fale elektromagnetyczne

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

IPPT Reports on Fundamental Technological Research

Rocznik

2012

Tom

nr 3

Strony

3--159

Opis fizyczny

Bibliogr. 134 poz.

Twórcy

autor

Tasinkevych Y.

Instytut Podstawowych Problemów Techniki Polskiej Akademii Nauk

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