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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
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
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
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
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
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
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
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
Keywords: isogeometric analysis Kirchhoff–Love cylindrical shell free vibration frequency error convergence
Xiaowei LUO, Yannick BENICHOU, Suyuan YU
Frontiers in Energy 2013, Volume 7, Issue 4, Pages 506-510 doi: 10.1007/s11708-013-0275-5
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
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
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
Keywords: spatial kinematics natural frequency finite element method
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
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
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
Frontiers of Medicine 2023, Volume 17, Issue 3, Pages 493-502 doi: 10.1007/s11684-022-0946-x
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
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