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

M. R. AKBARI,D. D. GANJI,A. MAJIDIAN,A. R. AHMADI

Frontiers of Mechanical Engineering 2014, Volume 9, Issue 2,   Pages 177-190 doi: 10.1007/s11465-014-0288-8

Abstract:

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.

Keywords: Algebraic Method (AGM)     Angular Frequency     Vanderpol     Rayleigh     Duffing    

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

Frontiers of Mechanical Engineering 2014, Volume 9, Issue 1,   Pages 58-70 doi: 10.1007/s11465-014-0289-7

Abstract:

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.

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

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

Soheil ZARKANDI

Frontiers of Mechanical Engineering 2014, Volume 9, Issue 1,   Pages 34-40 doi: 10.1007/s11465-014-0290-1

Abstract:

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.

Keywords: spherical mechanisms     instantaneous poles     great circle     angular velocity    

Modulational Instability of Optical Vortices in Engineered Saturable Media Review

D.G. Pires, N.M. Litchinitser

Engineering 2022, Volume 17, Issue 10,   Pages 31-43 doi: 10.1016/j.eng.2022.04.022

Abstract: Gaussian beams, light possesses many degrees of freedom that are still largely unexplored, such as spin angularmomentum (SAM) and orbital angular momentum (OAM).

Keywords: Optical vortex     Orbital angular momentum     Modulation instability     Turbid media    

Shaking-moment balancing of mechanisms with principal vectors and momentum

V. van der WIJK

Frontiers of Mechanical Engineering 2013, Volume 8, Issue 1,   Pages 10-16 doi: 10.1007/s11465-013-0359-2

Abstract: For this purpose, the method of principal vectors is investigated, showing a compact notation of the angular

Keywords: shaking-moment balancing     principal vector linkage     angular momentum    

Modeling of large-deflection links for compliant mechanisms

Zhonglei FENG, Yueqing YU, Wenjing WANG,

Frontiers of Mechanical Engineering 2010, Volume 5, Issue 3,   Pages 294-301 doi: 10.1007/s11465-010-0019-8

Abstract: locus and tip deflection angle of large-deflection links for compliant mechanisms on the basis of the angular

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

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

Frontiers of Structural and Civil Engineering doi: 10.1007/s11709-023-0006-x

Abstract: A frequency error estimation is presented for the isogeometric free vibration analysis of Kirchhoff–LoveBy analyzing the discrete isogeometric equations with the aid of harmonic wave assumption, the frequencyIn particular, the governing relationship of the continuum frequency for Kirchhoff–Love cylindrical shellsis naturally embedded into the frequency error measures without the need of explicit frequency expressionsNumerical results not only thoroughly verify the theoretical convergence rates of frequency solutions

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

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

Xiaowei LUO, Yannick BENICHOU, Suyuan YU

Frontiers in Energy 2013, Volume 7, Issue 4,   Pages 506-510 doi: 10.1007/s11708-013-0275-5

Abstract: The collision frequency function for aerosol particles has already been calculated for the free moleculeforce, electric force and molecular forces, created by particles themselves, recalculated the collision frequencyAttractive forces increase naturally the collision frequency, while repulsive forces decrease it.

Keywords: aerosol particles     collision frequency function     coagulation    

Fuel variability effect on flickering frequency of diffusion flames

Jizhao LI, Yang ZHANG

Frontiers in Energy 2009, Volume 3, Issue 2,   Pages 134-140 doi: 10.1007/s11708-009-0034-9

Abstract: The intent of this study is to investigate the fuel variability on the flickering frequency of diffusionIt was found that the low frequency oscillation of flow and flame structures depended only weakly onWhen a mixture of methane/propane at a ratio of 1:1 was used the peak flickering frequency was aroundMechanisms thought to produce changes in the dynamic response and frequency harmonics were discussed.

Keywords: fuel variability     flickering frequency     diffusion flames     dynamics of combustion    

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

Frontiers in Energy 2012, Volume 6, Issue 2,   Pages 148-154 doi: 10.1007/s11708-012-0174-1

Abstract: Based on the analysis of frequency regulation, mathematic models for nuclear units in the grid are establishedThe relationship between different styles of frequency regulation and the allowable capacity of the nuclear

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

Oscillation frequency of simplified arterial tubes

Hui AN, Fan HE, Lingxia XING, Xiaoyang LI

Frontiers of Mechanical Engineering 2009, Volume 4, Issue 3,   Pages 300-304 doi: 10.1007/s11465-009-0038-5

Abstract: To construct the spatial kinetic equation of an arterial tube and obtain its radial natural frequencyThe results show that the first-order frequency is 15.8 Hz and the obtained exact analytical solutions

Keywords: spatial kinematics     natural frequency     finite element method    

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

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

Frontiers in Energy 2014, Volume 8, Issue 3,   Pages 386-393 doi: 10.1007/s11708-014-0323-9

Abstract: Accurate modeling and parameters of high voltage (HV) grid are critical for stability research of system frequencyIn this paper, simulation modeling of the system frequency was conducted of an interconnected power system

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

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

Lili CHEN, Wu ZHOU

Frontiers of Mechanical Engineering 2013, Volume 8, Issue 2,   Pages 146-149 doi: 10.1007/s11465-013-0260-z

Abstract:

To predict more precisely the frequency of force-balanced micro accelerometer with different biasvoltages, 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 operationsensitivity with designed parameters of structure, circuit and process error can be used to predict the frequency

Keywords: Micro-Electro-Mechanical Systems (MEMS)     micro accelerometer     force-balanced micro accelerometer     frequency    

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

Frontiers of Medicine 2023, Volume 17, Issue 3,   Pages 493-502 doi: 10.1007/s11684-022-0946-x

Abstract: 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.

Keywords: next-generation sequencing     fluorescence in situ hybridization     immunohistochemistry     variant allele frequency    

Remote calibration system for frequency based on in-place benchmark

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

Frontiers of Mechanical Engineering 2010, Volume 5, Issue 3,   Pages 316-321 doi: 10.1007/s11465-010-0021-1

Abstract: calibration mode based on material object reference, a new model of a remote calibration system for frequencysome key problems for the remote calibration system is particularly discussed, including the time and frequencybenchmark receiving module based on global positioning system (GPS), frequency comparison based on aphase method, frequency division based on dual high-frequency phase locked loop (PLL), and remote calibration

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

Title Author Date Type Operation

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

M. R. AKBARI,D. D. GANJI,A. MAJIDIAN,A. R. AHMADI

Journal Article

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

Journal Article

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

Soheil ZARKANDI

Journal Article

Modulational Instability of Optical Vortices in Engineered Saturable Media

D.G. Pires, N.M. Litchinitser

Journal Article

Shaking-moment balancing of mechanisms with principal vectors and momentum

V. van der WIJK

Journal Article

Modeling of large-deflection links for compliant mechanisms

Zhonglei FENG, Yueqing YU, Wenjing WANG,

Journal Article

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

Journal Article

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

Xiaowei LUO, Yannick BENICHOU, Suyuan YU

Journal Article

Fuel variability effect on flickering frequency of diffusion flames

Jizhao LI, Yang ZHANG

Journal Article

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

Journal Article

Oscillation frequency of simplified arterial tubes

Hui AN, Fan HE, Lingxia XING, Xiaoyang LI

Journal Article

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

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

Journal Article

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

Lili CHEN, Wu ZHOU

Journal Article

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

Journal Article

Remote calibration system for frequency based on in-place benchmark

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

Journal Article