The extended Durbin method and its application for piezoelectric wave propagation problems

Ing, Yi‐Shyong; Liao, H.-F.; Huang, Kuo-Shu

doi:10.1016/j.ijsolstr.2013.08.009

Cited by 8 publications

(6 citation statements)

References 42 publications

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“…Finally, it is essential to note that authors such as Ing, Liao, and Huang [24]; Li and Wu [25]; Lv, Chen, and Cheng [26]; and Shurui, Jingyou, Lei, and Zhong [27], use space econometric models, including the Durbin model, to investigate the impact of different policy mechanisms on economic variables at the sector level. At the same time, with its purpose, they have been able to determine the effects of overflow and spatial autocorrelation, which have served as a guide to suggest regional and sectoral policies.…”

Section: Introductionmentioning

confidence: 99%

Economic and Spatial Determinants of Energy Consumption in the European Union

et al. 2019

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In recent decades, various policies have been implemented to reduce energy consumption, as well as a considerable increase in research that analyzes the determinants of energy consumption, both with a standard feature, mitigating environmental degradation. However, few studies investigate the economic and spatial determinants of energy consumption in the European Union (EU). Therefore, to cover the knowledge gap, based on the review of the existing literature, this document is designed to analyze the determinants and energy policy in energy consumption in the EU. For this reason, the objective of this research is to analyze the effect of human capital, the price of oil, and Kyoto Protocol policy on energy consumption. In addition, the effect of contiguity and spatial concentration on energy consumption is studied for 34 European countries, of which 26 belong to the EU, for the period 2000–2016. For this, data collected from the World Bank (2017) and the World Energy Statistical Review (2017) were used. The work methodology is based on the application of econometric techniques for panel data, and spatial econometrics, based on the application of a Spatial Durbin Model (SDM), through which the existence of “spillovers” was determined in the implementation of the energy policy. The results of the estimates show a negative effect of the price of oil and human capital concerning energy consumption, and the variable "Policy" reflects a reduction in the energy consumption of the EU countries in the period analyzed. Additionally, the space panel confirms that the behavior of a country's energy consumption depends on its past values and the level of consumption presented by its neighbors, corroborating the importance of territorial contiguity in the success of environmental policy in the case of the European Union.

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Section: Introductionmentioning

confidence: 99%

Economic and Spatial Determinants of Energy Consumption in the European Union

et al. 2019

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“…The formula of the double Laplace inversions of a function f ðk; sÞ can be expressed as follows (Ing et al, 2013):…”

Section: Numerical Laplace Inversionmentioning

confidence: 99%

“…It was found that a t T t = 5 to 10 and a x T x = 0.01 to 0.1 can be used to obtain accurate numerical results (Ing et al, 2013). By substituting Eqs.…”

Section: Numerical Laplace Inversionmentioning

confidence: 99%

“…Lin and Ma (2012) found that the transient responses of the continuously distributed multilayered media can be simulated by the effective material concept and are applicable to analyze the wave propagation problem in a functionally graded slab. Ing et al (2013) presented an extended Durbin method for a two-sided Laplace inversion, and evaluated the transient stress and electric displacement of a two-layered piezoelectric medium.…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional transient analysis of wave propagation in functionally graded piezoelectric slabs using the transform method

Lin

Ing

2015

International Journal of Solids and Structures

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a b s t r a c tIn this study, the transient responses of a functionally graded piezoelectric slab were analyzed using the transform technique. The slab was subjected to a dynamic anti-plane concentrated force and an in-plane point electric displacement on the top surface, and the bottom surface was assumed to be open-circuit or grounded. The analytical solutions were obtained in the Laplace transform domain, and a numerical inversion was performed using the Durbin method. The numerical results showed that an applied point electric displacement may instantaneously induce shear stress waves due to the piezoelectricity for both open-circuit and grounded cases. When the bottom surface was grounded, a visible electric wave was induced by the grounded boundary and the influence of this wave was significant when the gradient coefficient of the functionally graded piezoelectric materials (FGPMs) was large enough.

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“…The propagating nature of the elastic and electric wave in bone and porous PZT was investigated by Chakraborty (2009). Using the extended Durbin method, Ing et al (2013) investigated the transient elastic waves propagating in a two-layered piezoelectric medium The wave propagation behavior in layered piezoelectric structures and functionally graded piezoelectric material structures has also been studied by many researches with different methods, such as the transfer matrix method (Cai et al, 2001), the layer element method (Han et al, 2004), the orthogonal polynomial series method (Yu and Ma, 2008;Yu et al, 2013;Singh and Rokne, 2013), and so on.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in piezoelectric rings with rectangular cross-sections

Zhang

Wang

Chen

2015

jtam

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The ring ultrasonic transducers are widely used in the ocean engineering and medical fields. This paper employs an extended orthogonal polynomial approach to solve the guided wave propagation in two-dimensional structures, i.e. piezoelectric rings with rectangular cross-sections. The extended polynomial approach can overcome the drawbacks of the conventional orthogonal polynomial approach which can be used to solve wave propagation in one-dimensional structures. Through numerical comparison with the available results for a rectangular aluminum bar, the validity of the present approach is illustrated. The dispersion curves and displacement and electric potential distributions of various rectangular piezoelectric rings are calculated, and the effects of different radius to thickness ratios, width to height ratios and polarizing directions on the dispersion curves are illustrated.

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The extended Durbin method and its application for piezoelectric wave propagation problems

Cited by 8 publications

References 42 publications

Economic and Spatial Determinants of Energy Consumption in the European Union

Economic and Spatial Determinants of Energy Consumption in the European Union

Two-dimensional transient analysis of wave propagation in functionally graded piezoelectric slabs using the transform method

Wave propagation in piezoelectric rings with rectangular cross-sections

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