Papers by Keyword: Power Series

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Authors: Rui Hua Zhuo, Shu Wang Yan, Lei Yu Zhang
Abstract: The unification differential equation of buckling and motion of viscoelastic beam subjected to the uniformly distributed follower forces in time domain was established by differential operators including extension viscosity, shearing viscosity and moment of inertia. According to the unification differential equation, dynamic stability of three-parameter model of viscoelastic beams subjected to follower forces with clamped-free supported boundary condition was firstly analyzed by power series. The relations of the follower force versus vibration frequency and decay coefficient were obtained, so was the effect of viscous coefficient on the critical load of beams.
Authors: Yao Jun Yu
Abstract: Calibration is an important operation in the instrumentation industry for determining the relationship between the output (s) (or response) of a measuring instrument and the value of the input (s). This paper proposes a nonlinear calibration method based on least squares support vector regression (LS-SVR) with the output voltage of thermocouple sensor as input and the measured temperature output to eliminate the nonlinear errors in detection process. Firstly, the nonlinear calibrator, expressed by power series, was established based on the principle of inverse model. And then the parameters of the calibrator were identified by LS-SVR. Through this calibrator, the desired linear characteristics of thermocouple sensor could be obtained. Finally, platinum-rhodium 30– platinum-rhodium 6-thermocouple (B-type) was taken as an example, and experimental results show that the proposed calibration method is efficient in the temperature range from 400°C to 1800°C. And the method has an advantage of analytical expression of the calibration model.
Authors: Chang Jiang Liu, Zhou Lian Zheng, Wei Ju Song, Yun Ping Xu, Jun Long
Abstract: Nonlinear vibration computational problem of isotropic thin plates in large amplitude was investigated here. We applied the Von Kármán’s theory of thin plates to derive the governing equations of nonlinear free vibration of isotropic thin plates, and solved the governing equations by direct integration method combined with power series expansion method. We obtained the power series solution of the nonlinear vibration frequency of the rectangular thin plates with four edges simply supported. Finally, the paper gave the computational example and compared the two results from the large amplitude theory and the small one, respectively. Results obtained from this paper provide a new analytical computational approach for calculating the frequency of nonlinear free vibration of isotropic thin plates in large amplitude, and provide more accurate theoretical basis for the vibration control and dynamic design of plate structures.
Authors: Vitaly Viktorovich Pivnev, Sergey Nikolaevich Basan
Abstract: The way of calculating the currents and voltages in nonlinear resistive electrical circuits , based on the use of power series (Taylor, Maclaurin) is considered . The advantage of this method lies in the fact that while it implementation it is not necessary to a system of nonlinear equations. To determine the numerical values ​​of the coefficients of the power series corresponding system of linear algebraic equations are solved. Nonlinear operations are limited to the calculation of the numerical values ​​of currents, voltages and their derivatives with respect to the pole equations of nonlinear elements.
Authors: Sheng Ma, Qin Jiang
Abstract: In the paper, the specific issues is discussed whether or not the points on the convergence circle are the singular point of a sum function of a class of power series. Whats more, the relationship between divergence of the power series on the convergence circle and the pole of its function on the convergence circle is explored. And a new result is obtained that there exists the pole of its function on the convergence circle, the power series has the characteristic of everywhere divergence on the convergence circle.
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