2009
DOI: 10.1016/j.ultras.2009.01.001
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Modeling of functionally graded piezoelectric ultrasonic transducers

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Cited by 23 publications
(7 citation statements)
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“…In this Section, numerical results for all cylinders under consideration will be presented and discussed. These waveguides are composed of a PZT-5A material whose properties are given in [2,44,47]. In order to obtain the real and imaginary branches of dispersion curves, the fast and "smart" bisection method was used, which decreases the interval and increases the precision when the roots are very close to each other, and hence, it does not miss them.…”
Section: Numerical Results and Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…In this Section, numerical results for all cylinders under consideration will be presented and discussed. These waveguides are composed of a PZT-5A material whose properties are given in [2,44,47]. In order to obtain the real and imaginary branches of dispersion curves, the fast and "smart" bisection method was used, which decreases the interval and increases the precision when the roots are very close to each other, and hence, it does not miss them.…”
Section: Numerical Results and Discussionmentioning
confidence: 99%
“…The dynamic behavior of piezoelectric cylinders has been studied from different points of view [37][38][39][40][41][42][43][44][45][46][47][48][49][50]. A modern historical outline of the development of these problems and their applications in electro-mechanical devices can be found in [46,48].…”
Section: Introductionmentioning
confidence: 99%
“…Mechanical properties of the matching, backing, and lens layers are given in Table 3. All material properties were taken following previous investigations reported in [37].…”
Section: Materials Propertiesmentioning
confidence: 99%
“…Once the geometry was discretized, material properties were selected, and excitation was defined, the solution was obtained for nodes of the elements. The required solutions for arbitrary positions were obtained using a linear combination of polynomial interpolation functions, as described in [33][34][35][36]. The entire analysis was performed in the time domain using a step-by-step time explicit integration scheme to obtain displacements.…”
Section: Ceramic Modelling-ultrasonic Wave Generationmentioning
confidence: 99%