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Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

null

《机械工程前沿（英文）》 2014年第9卷第2期页码 177-190 doi: 10.1007/s11465-014-0288-8

摘要：

In the present paper, three complicated nonlinear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method (AGM). Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method (Runge-Kutte 4th). Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems.

关键词： Algebraic Method (AGM) Angular Frequency Vanderpol Rayleigh Duffing

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Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method

M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI

《机械工程前沿（英文）》 2014年第9卷第1期页码 58-70 doi: 10.1007/s11465-014-0289-7

摘要：

In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

关键词： Algebraic Method (AGM) tower crane oscillating system angular frequency

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On the location of the secondary instantaneous poles in two-degree-of-freedom spherical mechanisms

Soheil ZARKANDI

《机械工程前沿（英文）》 2014年第9卷第1期页码 34-40 doi: 10.1007/s11465-014-0290-1

摘要：

As the instant centers in planar mechanisms, the instantaneous poles (or instant poles, in brief) can be used for kinematic analysis in spherical mechanisms. One of the mandatory steps in this analysis is the determination of the location of these poles. This paper presents a theorem showing analytically that the locus of an unknown secondary instant pole in two-degree-of-freedom (2-DOF) spherical mechanisms is a great circle (GC). The exact location of the pole on its GC is obtained based on the configuration of the mechanism and velocity ratio of the two inputs. Moreover, using the results of the theorem, a geometrical technique is presented to determine the GC of the pole.

关键词： spherical mechanisms instantaneous poles great circle angular velocity

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工程饱和介质中漩涡光的调制不稳定性 Review

D.G. Pires, N.M. Litchinitser

《工程（英文）》 2022年第17卷第10期页码 31-43 doi: 10.1016/j.eng.2022.04.022

摘要：

光束在水下环境、雾、云或生物组织等混浊介质中的传播在科学和技术中有着越来越重要的应用，包括生物成像、水下和自由空间通信技术。虽然这些应用在传统上依赖于常规的线性偏振高斯光束，但光具有许多未被发掘的自由度，如自旋角动量（SAM）和轨道角动量（OAM）。本文提出了具有“旋转”自由度的复杂光束在工程化非线性胶体介质中的非线性光-物质相互作用。利用变分法和摄动法，我们考虑了非圆柱光学涡旋、椭圆光学涡旋和高阶贝塞尔光束在时间上的积分（HOBBIT），来预测这些光束演化的动力学行为和稳定性。这些结果可应用于许多强散射环境下涉及光透射的情况。

关键词： Optical vortex Orbital angular momentum Modulation instability Turbid media

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Shaking-moment balancing of mechanisms with principal vectors and momentum

V. van der WIJK

《机械工程前沿（英文）》 2013年第8卷第1期页码 10-16 doi: 10.1007/s11465-013-0359-2

摘要：

The design of shaking-moment-balanced linkages still is challenging. Considering moment balance in the very beginning of the design process of mechanisms is important for finding applicable solutions. For this purpose, the method of principal vectors is investigated, showing a compact notation of the angular momentum with respect to the center of mass. The moment balance conditions are derived for three elements in series from which balance solutions are synthesized and illustrated. From the application for moment balancing of a 4R four-bar linkage it is shown that the moment balancing of closed kinematic chains remains challenging.

关键词： shaking-moment balancing principal vector linkage angular momentum

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Modeling of large-deflection links for compliant mechanisms

Zhonglei FENG, Yueqing YU, Wenjing WANG,

《机械工程前沿（英文）》 2010年第5卷第3期页码 294-301 doi: 10.1007/s11465-010-0019-8

摘要： The traditional pseudo-rigid-body model (PRBM) has one degree of freedom (DOF) and performs a good simulation to the tip locus of flexible links for compliant mechanisms on the basis of a parametric approximation method. In this study, a new approach of a two-DOF PRBM is proposed to simulate both the tip locus and tip deflection angle of large-deflection links for compliant mechanisms on the basis of the angular deflection approximation technique. A linear regression for the spring stiffness coefficient of the 2R PRBM using the optimization technique is presented. The advantage of the new model is well illustrated through a numerical comparison between the 1R and the 2R PRBM.

关键词： compliant mechanism pseudo-rigid-body model (PRBM) large-deflection link angular deflection approximation

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A frequency error estimation for isogeometric analysis of Kirchhoff–Love cylindrical shells

《结构与土木工程前沿（英文）》 doi: 10.1007/s11709-023-0006-x

摘要： A frequency error estimation is presented for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells using both quadratic and cubic basis functions. By analyzing the discrete isogeometric equations with the aid of harmonic wave assumption, the frequency error measures are rationally derived for the quadratic and cubic formulations for Kirchhoff–Love cylindrical shells. In particular, the governing relationship of the continuum frequency for Kirchhoff–Love cylindrical shells is naturally embedded into the frequency error measures without the need of explicit frequency expressions, which usually are not trivial for the shell problems. In accordance with these theoretical findings, the 2nd and 4th orders of frequency accuracy are attained for the isogeometric schemes using quadratic and cubic basis functions, respectively. Numerical results not only thoroughly verify the theoretical convergence rates of frequency solutions, but also manifest an excellent magnitude match between numerical and theoretical frequency errors for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells.

关键词： isogeometric analysis Kirchhoff–Love cylindrical shell free vibration frequency error convergence

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Calculation of collision frequency function for aerosol particles in free molecule regime in presence

Xiaowei LUO, Yannick BENICHOU, Suyuan YU

《能源前沿（英文）》 2013年第7卷第4期页码 506-510 doi: 10.1007/s11708-013-0275-5

摘要： The collision frequency function for aerosol particles has already been calculated for the free molecule regime and for the continuum range. The present work, taking into account the influence of internal force fields such as magnetic force, electric force and molecular forces, created by particles themselves, recalculated the collision frequency in the case of particles much smaller than the mean free path of the gas (free molecule regime). Attractive forces increase naturally the collision frequency, while repulsive forces decrease it. The calculation was performed for all types of central forces deriving from a potential, including Coulomb forces and Van der Waals forces.

关键词： aerosol particles collision frequency function coagulation

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Fuel variability effect on flickering frequency of diffusion flames

Jizhao LI, Yang ZHANG

《能源前沿（英文）》 2009年第3卷第2期页码 134-140 doi: 10.1007/s11708-009-0034-9

摘要： It is known that fuel variability of different gas suppliers may cause combustion instability in a gas turbine combustor. Mechanisms that control the time scale of the heat release oscillations and acoustic pressure perturbations are both physical and chemical in nature, and thus can be influenced by changes in fuel composition. The intent of this study is to investigate the fuel variability on the flickering frequency of diffusion flames in the hope of understanding some of the fundamental aspects of fuel variability effect on the dynamics of combustion. Experiments were conducted at atmospheric pressure with a matrix of methane and propane blends. An optical fibre system was applied to capture simultaneously the flame flickering at two different light frequencies (430 nm and 516 nm), which provided a means of comparing the chemistry change. It was found that the low frequency oscillation of flow and flame structures depended only weakly on the exit velocities of the fuel, while ambient conditions had a significant effect on flickering frequencies and spectrum. The results of using CH and C H as test fuels at different flow rates showed very little variations, with peak frequencies at 11-13 Hz. When the jet flame was not disturbed, harmonics to at least the third mode were obtained in most of these cases. However, the cases which included CH /C H splits of 90/10, 85/15 and 80/20 by volume showed that unstable flickering frequencies and flame harmonics were not observed. When a mixture of methane/propane at a ratio of 1:1 was used the peak flickering frequency was around 6 Hz, and slight disturbance in the environment would cause the harmonics to disappear. Mechanisms thought to produce changes in the dynamic response and frequency harmonics were discussed.

关键词： fuel variability flickering frequency diffusion flames dynamics of combustion

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Capacity limitation of nuclear units in grid based on analysis of frequency regulation

Yiping DAI, Pan JIANG, Lin GAO, Weimin KAN, Xiaoqing XIAO, Ge JIN

《能源前沿（英文）》 2012年第6卷第2期页码 148-154 doi: 10.1007/s11708-012-0174-1

摘要： The increasing capacity of nuclear units in power grid poses threat to system stability and security. Load disturbance may cause overspeed of the units and trigger the overspeed protection controller (OPC). Repeating actions of valves have a strong impact on the security of the equipment and may result in a collapse of the power system. Based on the analysis of frequency regulation, mathematic models for nuclear units in the grid are established in this paper to simulate the dynamic process when load disturbance occurs. The critical action of the OPC is proposed as the constraint of safe operation for the units. The relationship between different styles of frequency regulation and the allowable capacity of the nuclear units in the grid is discussed. This research can help to estimate the capacity limitation of nuclear units in the grid.

关键词： nuclear units capacity overspeed primary frequency control (PFC) second frequency control (SFC)

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Oscillation frequency of simplified arterial tubes

Hui AN, Fan HE, Lingxia XING, Xiaoyang LI

《机械工程前沿（英文）》 2009年第4卷第3期页码 300-304 doi: 10.1007/s11465-009-0038-5

摘要： To construct the spatial kinetic equation of an arterial tube and obtain its radial natural frequency, a linear-elastic and small deformation condition is assumed. The theoretical analysis is first presented and the finite element method is then used to numerically simulate the spatial kinematics. The results show that the first-order frequency is 15.8 Hz and the obtained exact analytical solutions agree well with numerical solutions, which proves that the theoretical analysis and numerical simulation are both correct.

关键词： spatial kinematics natural frequency finite element method

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Parameter identification of interconnected power system frequency after trip-out of high voltage transmission

Xuzhan ZHOU,Shanshan LIU,Mingkun WANG,Yiping DAI,Yaohua TANG

《能源前沿（英文）》 2014年第8卷第3期页码 386-393 doi: 10.1007/s11708-014-0323-9

摘要： Accurate modeling and parameters of high voltage (HV) grid are critical for stability research of system frequency. In this paper, simulation modeling of the system frequency was conducted of an interconnected power system with HV transmission lines in China. Based on recorded tripping data of the HV transmission lines, system parameters were identified by using genetic algorithm (GA). The favorable agreement between simulation results and recorded data verifies the validity of gird models and the accuracy of system parameters. The results of this paper can provide reference for the stability research of HV power grid.

关键词： high voltage (HV) grid frequency stability parameter identification primary frequency regulation (PFR)

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Dependence of error sensitivity of frequency on bias voltage in force-balanced micro accelerometer

Lili CHEN, Wu ZHOU

《机械工程前沿（英文）》 2013年第8卷第2期页码 146-149 doi: 10.1007/s11465-013-0260-z

摘要：

To predict more precisely the frequency of force-balanced micro accelerometer with different bias voltages, the effects of bias voltages on error sensitivity of frequency is studied. The resonance frequency of accelerometer under closed loop control is derived according to its operation principle, and its error sensitivity is derived and analyzed under over etching structure according to the characteristics of Deep Reaction Ion Etching (DRIE). Based on the theoretical results, micro accelerometer is fabricated and tested to study the influences of AC bias voltage and DC bias voltage on sensitivity, respectively. Experimental results indicate that the relative errors between test data and theory data are less than 7%, and the fluctuating value of error sensitivity under the range of voltage adjustment is less than 0.01 μm . It is concluded that the error sensitivity with designed parameters of structure, circuit and process error can be used to predict the frequency of accelerometer with no need to consider the influence of bias voltage.

关键词： Micro-Electro-Mechanical Systems (MEMS) micro accelerometer force-balanced micro accelerometer frequency error sensitivity

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Potential unreliability of ALK variant allele frequency in the efficacy prediction of targeted therapy

《医学前沿（英文）》 2023年第17卷第3期页码 493-502 doi: 10.1007/s11684-022-0946-x

摘要： Anaplastic lymphoma kinase (ALK) is the most common fusion gene involved in non-small cell lung cancer (NSCLC), and remarkable response has been achieved with the use of ALK tyrosine kinase inhibitors (ALK-TKIs). However, the clinical efficacy is highly variable. Pre-existing intratumoral heterogeneity (ITH) has been proven to contribute to the poor treatment response and the resistance to targeted therapies. In this work, we investigated whether the variant allele frequencies (VAFs) of ALK fusions can help assess ITH and predict targeted therapy efficacy. Through the application of next-generation sequencing (NGS), 7.2% (326/4548) of patients were detected to be ALK positive. On the basis of the adjusted VAF (adjVAF, VAF normalization for tumor purity) of four different threshold values (adjVAF < 50%, 40%, 30%, or 20%), the association of ALK subclonality with crizotinib efficacy was assessed. Nonetheless, no statistical association was observed between median progression-free survival (PFS) and ALK subclonality assessed by adjVAF, and a poor correlation of adjVAF with PFS was found among the 85 patients who received first-line crizotinib. Results suggest that the ALK VAF determined by hybrid capture-based NGS is probably unreliable for ITH assessment and targeted therapy efficacy prediction in NSCLC.

关键词： ALK fusion next-generation sequencing fluorescence in situ hybridization immunohistochemistry variant allele frequency intratumoral heterogeneity targeted therapy

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Remote calibration system for frequency based on in-place benchmark

Xiaobin HONG, Guixiong LIU, Zhuokui WU, Xipeng DU,

《机械工程前沿（英文）》 2010年第5卷第3期页码 316-321 doi: 10.1007/s11465-010-0021-1

摘要： According to the deficiencies of remote calibration mode based on material object reference, a new model of a remote calibration system for frequency based on in-place benchmark is introduced, which is made of a calibration subsystem on the spot and a remote management subsystem. The key technology of some key problems for the remote calibration system is particularly discussed, including the time and frequency benchmark receiving module based on global positioning system (GPS), frequency comparison based on a phase method, frequency division based on dual high-frequency phase locked loop (PLL), and remote calibration based on the web. The results show that the system possesses some characteristics, such as high precision, good versatility, and no limitation of time and place.

关键词： remote calibration in-place benchmark frequency comparison global position system (GPS)