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1

A quadrature-free Legendre polynomial approach for the fast modelling guided circumferential wave in anisotropic fractional order viscoelastic hollow cylinders

Zhang X., Liang S., Shao S., Yu J.

Archives of Mechanics

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2021

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Vol. 73, nr 2

121--152

EN

Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be advantageous. The characteristics of guided circumferential waves in an anisotropic fractional order Kelvin–Voigt viscoelastic hollow cylinder are investigated by a quadrature-free Legendre polynomial approach combining the Weyl definition of fractional order derivatives. The presented approach can obtain dispersion solutions in a stable manner from an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles of viscoelastic guided wave, which avoids a lot of numerical integration calculation in a traditional polynomial method and greatly improves the computational efficiency. Comparisons with the related studies are conducted to validate the correctness of the presented approach. The full three dimensional spectrum of an anisotropic fractional Kelvin–Voigt hollow cylinder is plotted. The influence of fractional order and material parameters on the phase velocity dispersion and attenuation curves of guided circumferential wave is discussed in detail. Moreover, the difference of the phase velocity dispersion and attenuation characteristics between the Kelvin–Voigt and hysteretic viscoelastic models is also illustrated. The presented approach along with the observed wave features should be particularly useful in non-destructive evaluations using waves in viscoelastic waveguides.

2

Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold

Zeng C., Liang S., Zhang Y., Zhong J., Su Y.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 4

745--757

EN

Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be particular cases of the ideas presented here.

3

Determination of the trace lead in seasoning samples with derivative hydride generation atomic absorption spectrometry

Liang S., Ha J., Sun H., Kang W., Sun J.

Chemia Analityczna

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2003

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Vol. 48, No. 4

723-732

EN

A new method for the determination of lead traces in seasoning by derivative hydride generation atomic absorption spectrometry (D-HGAAS) has been developed. The conditions influencing the derivative absorbance of lead were evaluated and optimised. The detection limit and sensitivity of the proposed method were improved 8.8 times and 26 times, respectively in comparison to those of the conventional hydride generation atomic absorption spectrometry. The characteristic concentration of lead (referring to derivative absorbance of 0.0044) was 0.017 ug L(-1) at maximum sensitivity. The detection limit (3sigma) for lead in the real sample equalled 0.96 ng g(-1) for 5.0 g sample at maximum sensitivity. The method was applied to the determination of lead in seasoning samples with a recovery range of 92-103%.

PL

Opracowano nową metodę oznaczania śladowych ilości ołowiu w przyprawach za pomocą pochodnej absorpcyjnej spektrometrii atomowej z generacją wodorków. Oszacowano i zoptymalizowano warunki wpływające na pochodną absorbancji ołowiu. Granica detekcji i czułość metody były lepsze odpowiednio 8.8 i 22 razy w porównaniu z konwencjonalną atomową spektrometrią absorpcyjną z generacją wodorków. Charakterystyczne stężenie (dla pochodnej absorbancji 0.0044) wynosiło 0.017 ng L(-1) przy maksymalnej czułości układu. Granca detekcji (3 Sigma) dla ołowiu w próbce rzeczywistej wynosiła 0.96 ng g(-1) (przy maksymalnej czułości układu i masie próbki 5.0 g). Metodę zastosowano do oznaczania ołowiu w przyprawach. Strwierdzono, że odzysk ołowiu waha się. w granicach 92-103%.