Mathematical and Computational Applications

80 KiB

Open AccessArticle

Nonlinear Vibration Analysis of a Rigid Rod on a Circular Surface via Hamiltonian Approach

by Y. Khan, Q. Wu, H. Askari, Z. Saadatnia and M. Kalami-Yazdi

Math. Comput. Appl. 2010, 15(5), 974-977; https://doi.org/10.3390/mca15050974 - 31 Dec 2010

Cited by 26 | Viewed by 1551

This paper applies the Hamiltonian approach a nonlinear oscillator of a rigid rod on a circular surface without slipping, and its natural frequency is obtained. Comparison of the obtained result with the exact one shows good agreement even for large amplitudes and strong [...] Read more.

This paper applies the Hamiltonian approach a nonlinear oscillator of a rigid rod on a circular surface without slipping, and its natural frequency is obtained. Comparison of the obtained result with the exact one shows good agreement even for large amplitudes and strong nonlinearities. Full article

66 KiB

Open AccessArticle

Fractional Complex Transform for Fractional Differential Equations

by Zheng-Biao Li and Ji-Huan He

Math. Comput. Appl. 2010, 15(5), 970-973; https://doi.org/10.3390/mca15050970 - 31 Dec 2010

Cited by 275 | Viewed by 5237

Abstract

Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily applied to fractional calculus. Two examples are given. Full article

83 KiB

Open AccessArticle

Soft Compressible Porous Mat For "Flying" Vehicles

by Yang-Shuai Liu and Ji-Huan He

Math. Comput. Appl. 2010, 15(5), 967-969; https://doi.org/10.3390/mca15050967 - 31 Dec 2010

Cited by 2 | Viewed by 1107

Abstract

This paper explores the performance of a flying vehicle on a soft porous blanket at a high speed. The flying vehicle employs the basic principle of lubrication theory. An airplane can fly in air, because air is strong enough to support the airplane. [...] Read more.

This paper explores the performance of a flying vehicle on a soft porous blanket at a high speed. The flying vehicle employs the basic principle of lubrication theory. An airplane can fly in air, because air is strong enough to support the airplane. The flying vehicle can also fly on the soft porous blanket if the moving body pushes air in the soft compressible porous mat. A model is established. Full article

102 KiB

Open AccessArticle

Analytical Solutions of Nano Boundary Layer Flows by Using He's Homotopy Perturbation Method

by M. Khaki and D.D. Ganji

Math. Comput. Appl. 2010, 15(5), 962-966; https://doi.org/10.3390/mca15050962 - 31 Dec 2010

Cited by 4 | Viewed by 1132

Abstract

The aim of this article is to examine nano boundary layer. The equations governing the flow on wedge are derived from continuity and Navier-Stoks equations. The boundary conditions for the governing equations are obtained from the nonlinear Navier slip condition. This boundary condition [...] Read more.

The aim of this article is to examine nano boundary layer. The equations governing the flow on wedge are derived from continuity and Navier-Stoks equations. The boundary conditions for the governing equations are obtained from the nonlinear Navier slip condition. This boundary condition contains an arbitrary index parameter, denoted by n > 0, which appears in the coefficients of the ordinary differential equation to be solved. The coupled equations are transformed into one differential equation by similarity solution. The transformed equation is then solved by He’s Homotopy perturbation method and an analytical solution will be achieved. The validity of results is verified by comparing results with existing numerical results. Results are presented for the x and y components of the velocity profiles. Results are in reasonable agreement with those provided by other numerical methods and demonstrate a good accuracy of the obtained analytical solutions. Full article

181 KiB

Open AccessArticle

Analytical Solution of Two-Dimensional Viscous Flow Between Slowly Expanding or Contracting Walls with Weak Permeability

by Z.Z. Ganji, D.D. Ganji and A. Janalizadeh

Math. Comput. Appl. 2010, 15(5), 957-961; https://doi.org/10.3390/mca15050957 - 31 Dec 2010

Cited by 9 | Viewed by 1120

Abstract

In this article the problem of two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability is presented and Homotopy Perturbation Method are employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. [...] Read more.

In this article the problem of two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability is presented and Homotopy Perturbation Method are employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. Comparisons are made between the Numerical solution (NM) and the results of the He's Homotopy Perturbation Method (HPM). The results reveal that these methods are very effective and simple and can be applied for other nonlinear problems. Full article

178 KiB

Open AccessArticle

Exact Three-Wave Solutions for the (3+1)-Dimensional Boussinesq Equation

by Zheng-Biao Li

Math. Comput. Appl. 2010, 15(5), 953-956; https://doi.org/10.3390/mca15050953 - 31 Dec 2010

Viewed by 1204

Abstract

In this paper, the three-wave method is used for seeking periodic kink-wave and cross-kink soliton solutions. The (3 + 1)-dimensional Boussinesq equation is chosen as an example to illustrate the effectiveness and convenience the proposed method. Full article

176 KiB

Open AccessArticle

Correlation Properties of Chaos: Cumulant Approach

by V. Kontorovich, Z. Lovtchikova and F. Ramos-Alarcon

Math. Comput. Appl. 2010, 15(5), 946-952; https://doi.org/10.3390/mca15050946 - 31 Dec 2010

Cited by 5 | Viewed by 989

Abstract

The current trend in the statistical analysis of chaos shows certain gaps particularly regarding the engineering applications. This paper, which is a sequel of previous publications from the authors [1-5], develops an application of the cumulant approach to the analysis of the covariance [...] Read more.

The current trend in the statistical analysis of chaos shows certain gaps particularly regarding the engineering applications. This paper, which is a sequel of previous publications from the authors [1-5], develops an application of the cumulant approach to the analysis of the covariance properties of chaotic signals. A general approach for the analysis of two-moment cumulants is considered, particular emphasis is made in the covariance function and the third order cumulant behavior. The cumulant functions of the Lorenz and Chua strange attractors are considered as examples. Full article

89 KiB

Open AccessArticle

Hard Fling Objector Contact with Surface of Fluid as a Ricochet

by Jian-Hua Xiao

Math. Comput. Appl. 2010, 15(5), 940-945; https://doi.org/10.3390/mca15050940 - 31 Dec 2010

Viewed by 1068

Abstract

For a hard flying objector contacts with the surface of fluid, there exists a critical contact angle between the flying direction and the surface direction. When the actual contact angle is less than the critical angle, the flying objector will get additional moment [...] Read more.

For a hard flying objector contacts with the surface of fluid, there exists a critical contact angle between the flying direction and the surface direction. When the actual contact angle is less than the critical angle, the flying objector will get additional moment in flying direction and be rebounded up to tens grades. This critical angle is determined by the flying velocity and elastic constants of fluid. These phenomena are named as ricochet which essentially is due to the dynamic pressure of the fluid acting upwards on the flying objector to overcome its gravity force. Although the skipping of a flat stone on water surface is well known practices, the essential theoretic interpretation is not suitably formulated. In this research, it is shown that the fluid has two typical deformation modes: one is orthogonal rotational deformation (which is related with conventional contact), another is orthogonal rotation with intrinsic volume expansion. For the first kind of deformation, the dynamic pressure is inward direction, so the objector will sink into the fluid. However, for the second of deformation, the dynamic pressure is upward direction, so the flying objector will be raised up. It is this mechanism that produces the ricochet phenomenon. In this paper, the dynamic stress is determined by the fluid deformation. Then the contact condition equations are used to establish the related phenomenon. Based on these formulations, the critical angle is expressed by the flying velocity, mass and the fluid viscosity parameters. The related mechanic equations are formulated also. These results may promote the researches on the dynamic contact problem with bifurcation, such as ricochet and/or emerging. Full article

167 KiB

Open AccessArticle

Study on the Stability of Steiner Tree Structure of Explosion-Proof Textiles

by Ling-Ye Wu and Ji-Huan He

Math. Comput. Appl. 2010, 15(5), 936-939; https://doi.org/10.3390/mca15050936 - 31 Dec 2010

Cited by 5 | Viewed by 1019

Abstract

The stability of Steiner tree structure of explosion-proof textiles by studying on the tearing strength. We conclude that the Steiner tree structure has good stability. Full article

103 KiB

Open AccessArticle

The Variational Approach Coupled with an Ancient Chinese Mathematical Method to the Relativistic Oscillator

by Lin-Hong Zhou and J.H. He

Math. Comput. Appl. 2010, 15(5), 930-935; https://doi.org/10.3390/mca15050930 - 31 Dec 2010

Cited by 10 | Viewed by 1003

Abstract

This paper applies the variational approach to the relativistic oscillator. In order to effectively deal with the irrational term, an ancient Chinese mathematics is introduced. Comparison of the obtained result with the numerical one elucidates the efficiency of the present treatment. Full article

87 KiB

Open AccessArticle

The Extended G'/G-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations

by Shundong Zhu

Math. Comput. Appl. 2010, 15(5), 924-929; https://doi.org/10.3390/mca15050924 - 31 Dec 2010

Cited by 15 | Viewed by 1163

Abstract

In this Letter, the G’/G-expansion method [M.L. Wang, X.Z. Li, J.L. Zhang, Phys. Lett. A 372 (2008) 417] is improved and an extended G’/G -expansion method is proposed to seek the travelling wave solutions of nonlinear evolution equations. We choose the mKdV equation [...] Read more.

In this Letter, the G’/G-expansion method [M.L. Wang, X.Z. Li, J.L. Zhang, Phys. Lett. A 372 (2008) 417] is improved and an extended G’/G -expansion method is proposed to seek the travelling wave solutions of nonlinear evolution equations. We choose the mKdV equation to illustrate the validity and advantages of the proposed method. Many new and more general solutions are obtained. Our solutions naturally include those in open literature. Full article

164 KiB

Open AccessArticle

Variational Approach to Solitary Solutions Using Jacobi-Elliptic Functions

by Yue Wu

Math. Comput. Appl. 2010, 15(5), 910-923; https://doi.org/10.3390/mca15050910 - 31 Dec 2010

Cited by 5 | Viewed by 1021

Abstract

Partial differential equations are transformed into ordinary differential equations, and a variational formulation is then established. The trial function is chosen using Jacobi-elliptic function with some unknown parameters similar to the exp-function method. Various approximate solitary solutions are obtained when making the obtained [...] Read more.

Partial differential equations are transformed into ordinary differential equations, and a variational formulation is then established. The trial function is chosen using Jacobi-elliptic function with some unknown parameters similar to the exp-function method. Various approximate solitary solutions are obtained when making the obtained variational principle stationary with respect to each unknown parameter in the trial-function. The coupled Zakharov-Kuznetsov equations are used as an example to elucidate the solution procedure. Full article

105 KiB

Open AccessArticle

Frequency-Amplitude Relationship for Nonlinear Oscillator with Discontinuity

by Ting Zhong and Jingjing Zhang

Math. Comput. Appl. 2010, 15(5), 907-909; https://doi.org/10.3390/mca15050907 - 31 Dec 2010

Cited by 2 | Viewed by 1083

Abstract

The Hamiltonian approach is used to find an approximate amplitude-frequency relationship of a nonlinear oscillator with discontinuity. The solution procedure is simple while the result is of acceptable accuracy. Full article

91 KiB

Open AccessArticle

Application of Hamiltonian Approach to an Oscillation of a Mass Attached to a Stretched Elastic Wire

by Lan Xu

Math. Comput. Appl. 2010, 15(5), 901-906; https://doi.org/10.3390/mca15050900 - 31 Dec 2010

Cited by 22 | Viewed by 1200

Abstract

This paper applies Hamiltonian approach to a nonlinear oscillation of a mass attached to a stretched wire. Comparison of the obtained results with those of the exact solution shows that the approximate solutions are accurate and valid for the whole solution domain. Full article

71 KiB

Open AccessArticle

Backward Stochastic Differential Equation on Hedging American Contingent Claims

by Ruili Song and Bo Wang

Math. Comput. Appl. 2010, 15(5), 895-900; https://doi.org/10.3390/mca15050895 - 31 Dec 2010

Viewed by 1015

Abstract

We consider a general wealth process with a drift coefficient which is a function of the wealth process and the portfolio process with convex constraint. Existence and uniqueness of a minimal solution are established. We convert the problem of hedging American contingent claims [...] Read more.

We consider a general wealth process with a drift coefficient which is a function of the wealth process and the portfolio process with convex constraint. Existence and uniqueness of a minimal solution are established. We convert the problem of hedging American contingent claims into the problem of minimal solution of backward stochastic differential equation, and obtain the upper hedging price of American contingent claims. Full article

188 KiB

Open AccessArticle

Nonlinear Analysis of Damage Evolution for Steel Structures under Earthquake

by Hongxia Duan, Shouju Li and Yingxi Liu

Math. Comput. Appl. 2010, 15(5), 889-894; https://doi.org/10.3390/mca15050889 - 31 Dec 2010

Viewed by 1105

Abstract

The evolution of plastic deformation and damage in steel frame buildings caused by seismic action is simulated based on a modified damage model. This model combines nonlinear isotropic and kinematic hardening criteria with a damage evolution law expressed in terms of plastic displacement. [...] Read more.

The evolution of plastic deformation and damage in steel frame buildings caused by seismic action is simulated based on a modified damage model. This model combines nonlinear isotropic and kinematic hardening criteria with a damage evolution law expressed in terms of plastic displacement. A nine-story steel frame is chosen as a reference structure, and a nonlinear damage analysis is performed using ABAQUS with the El Centro earthquake accelerogram as input. The results reveal that the beam ends on the upper floors exhibit more obvious plastic deformation and form damage domains, which is consistent with the observed seismic damage of high-rise steel structures during the Northridge earthquake. Full article

178 KiB

Open AccessArticle

Mechanics Analysis of 3D Braided Composites Based on the Helix Geometry Model

by Tao Zeng and Lili Jiang

Math. Comput. Appl. 2010, 15(5), 883-888; https://doi.org/10.3390/mca15050883 - 31 Dec 2010

Cited by 12 | Viewed by 1198

Abstract

The helix geometry model of 3D braided composites has been presented, which truly reflects the braided manner and coincides with the actual configuration of the braided composites. The longitudinal tensile stress-strain relationships and the strength of 3D braided composites under the tension loading [...] Read more.

The helix geometry model of 3D braided composites has been presented, which truly reflects the braided manner and coincides with the actual configuration of the braided composites. The longitudinal tensile stress-strain relationships and the strength of 3D braided composites under the tension loading have been predicted by a finite multiphase element method (FMEM) based on the helix geometry model. Comparisons are conducted for those from the present model and experiment. The results obtained from the present model are supported by the experimental data. The numerical results show that the braiding angle has a significant influence on the strength of 3D braided composites. Full article

136 KiB

Open AccessArticle

New Periodic Solitary-Wave Solutions to the (3+1)- Dimensional Kadomtsev-Petviashvili Equation

by Zitian Li, Zhengde Dai and Jun Liu

Math. Comput. Appl. 2010, 15(5), 877-882; https://doi.org/10.3390/mca15050877 - 31 Dec 2010

Cited by 1 | Viewed by 1058

Abstract

By the extended homoclinic test technique, explicit solutions of the (3+1)-dimensional Kadomtsev-Petviashvili(KP) equation are obtained. These solutions include doubly periodic wave solutions, doubly soliton solutions and periodic solitary-wave solutions. It is shown that the extended homoclinic test technique is a straightforward and powerful [...] Read more.

By the extended homoclinic test technique, explicit solutions of the (3+1)-dimensional Kadomtsev-Petviashvili(KP) equation are obtained. These solutions include doubly periodic wave solutions, doubly soliton solutions and periodic solitary-wave solutions. It is shown that the extended homoclinic test technique is a straightforward and powerful mathematical tool for solving nonlinear evolution equation. Full article

220 KiB

Open AccessArticle

Application of the Phase Space Reconstruction in Ecology

by Yuzhi Wang, Bo Li, Renqing Wang, Jing Su and Xiaoxia Rong

Math. Comput. Appl. 2010, 15(5), 872-876; https://doi.org/10.3390/mca15050872 - 31 Dec 2010

Cited by 2 | Viewed by 1548

Abstract

A brief introduction to phase space reconstruction in ecology is given, and the application of the method to rodent populations is illustrated. Results show that phase space reconstruction is highly convenient and effective when utilized in short-term predictions in natural population. Full article

86 KiB

Open AccessArticle

Controlling Chaos by an Improved Estimation of Distribution Algorithm

by Xingli Huang, Peifa Jia and Bo Liu

Math. Comput. Appl. 2010, 15(5), 866-871; https://doi.org/10.3390/mca15050866 - 31 Dec 2010

Cited by 11 | Viewed by 1413

Abstract

Control and synchronization of chaotic systems are important issues in nonlinear sciences. This paper proposes an effective estimation of distribution algorithm (EDA)-based memetic algorithm (MA) to direct the orbits of discrete chaotic dynamical systems as well as to synchronize chaotic systems, which could [...] Read more.

Control and synchronization of chaotic systems are important issues in nonlinear sciences. This paper proposes an effective estimation of distribution algorithm (EDA)-based memetic algorithm (MA) to direct the orbits of discrete chaotic dynamical systems as well as to synchronize chaotic systems, which could be formulated as complex multi-modal numerical optimization problems. In EDA-based MA (EDAMA), both EDA-based searching operators and simulated annealing (SA)–based local searching operators are designed to balance the exploration and exploitation abilities. On the other hand, global information provided by EDA is combined with local information from SA to create better solutions. In particular, to enrich the searching behaviors and to avoid premature convergence, SA-based local search is designed and incorporated into EDAMA. To balance the exploration and exploitation abilities, after the standard EDA-based searching operation, SA-based local search is probabilistically applied to some good solutions selected by using a roulette wheel mechanism with a specified probability. Numerical simulations based on Hénon Map demonstrate the effectiveness and efficiency of EDAMA, and the effects of some parameters are investigated as well. Full article

493 KiB

Open AccessArticle

Nonlinear Transient Analysis for Large-Scale Dynamics of Microelectromechanical Systems with the MOR-PIM Method

by Le Guan, Jinkui Chu, Jiali Gao and Ran Zhang

Math. Comput. Appl. 2010, 15(5), 859-865; https://doi.org/10.3390/mca15050859 - 31 Dec 2010

Cited by 5 | Viewed by 1256

Abstract

Microelectromechanical Systems (MEMS) is difficult to take transient analysis due to the tight coupling between the multiple energy domains, typically nonlinear. An effective increment-dimensional precise integration method (PIM) combined with the model order reduction (MOR) technique based on Krylov subspace is present to [...] Read more.

Microelectromechanical Systems (MEMS) is difficult to take transient analysis due to the tight coupling between the multiple energy domains, typically nonlinear. An effective increment-dimensional precise integration method (PIM) combined with the model order reduction (MOR) technique based on Krylov subspace is present to solve large-scale nonlinear finite element dynamics systems. The numerical example of V-beam electro-thermal actuator is shown to demonstrate that the MOR-PIM method can achieve high precision and fast speed when solving the nonlinear dynamic equation with large-scale freedom. Full article

223 KiB

Open AccessArticle

Matematical Model for Yarn Unwinding from Packages

by Stanislav Praček and Sluga Franci

Math. Comput. Appl. 2010, 15(5), 853-858; https://doi.org/10.3390/mca15050853 - 31 Dec 2010

Cited by 5 | Viewed by 1120

Abstract

Yarn unwinding from a package is important in many textile processes. The stability of the unwinding process has a direct influence on the efficiency of the process and on the quality of the end product. During the unwinding, the tension is oscillating. This [...] Read more.

Yarn unwinding from a package is important in many textile processes. The stability of the unwinding process has a direct influence on the efficiency of the process and on the quality of the end product. During the unwinding, the tension is oscillating. This is especially noticeable in over-end unwinding from a static package, where the yarn is being withdrawn with a high velocity in the direction of the package axis. The optimal form of the package allows an optimal shape of the yarn balloon and low and steady tension even at very high unwinding velocities.The purpose of this work is to write down the equations that describe the motion of yarn during unwinding and to construct a mathematical model whichwould permit to simulate the process of unwinding. Full article

357 KiB

Open AccessArticle

Numerical Simulations of Yarn Unwinding from Packages

by Stanislav Praček and Sluga Franci

Math. Comput. Appl. 2010, 15(5), 846-852; https://doi.org/10.3390/mca15050846 - 31 Dec 2010

Cited by 4 | Viewed by 1073

Abstract

We derive a system of coupled nonlinear differential equations that govern the motion of yarn in general. The equations are written in a (non-uniformly) rotating observation frame and are thus appropriate for description of over-end unwinding of yarn from stationary packages. We comment [...] Read more.

We derive a system of coupled nonlinear differential equations that govern the motion of yarn in general. The equations are written in a (non-uniformly) rotating observation frame and are thus appropriate for description of over-end unwinding of yarn from stationary packages. We comment on physical significance of virtual forces that appear in a non-inertial frame and we devote particular attention to a lesser known force, that only appears in non-uniformly rotating frames. We show that this force should be taken into account when the unwinding point is near the edges of the package, and the quasi-stationary approximation is not valid because the angular velocity is changing with time. The additional force has an influence on the yarn dynamics in this transient regime where the movement of yarn becomes complex and can lead to yarn slipping and even breaking. Full article

389 KiB

Open AccessArticle

Effects of Time Delay on Chaotic Neuronal Discharges

by Wuyin Jin, Ruicheng Feng, Zhiyuan Rui and Aihua Zhang

Math. Comput. Appl. 2010, 15(5), 840-845; https://doi.org/10.3390/mca15050840 - 31 Dec 2010

Cited by 7 | Viewed by 1113

Abstract

Effects of time delay on Hindmarsh-Rose(HR) model neuron are studied. For an individual neuron, with the scaling delay time and synaptic intensity, neuronal firing pattern’s transform among tonic spiking, busting and resting firing state, and the neuronal chaotic spike could be controlled. Furthermore, [...] Read more.

Effects of time delay on Hindmarsh-Rose(HR) model neuron are studied. For an individual neuron, with the scaling delay time and synaptic intensity, neuronal firing pattern’s transform among tonic spiking, busting and resting firing state, and the neuronal chaotic spike could be controlled. Furthermore, two coupled HR neuronal system could be fully synchronized under certain coupled strength and delay time. Full article

96 KiB

Open AccessArticle

Variational Iteration Method for Delay Differential-Algebraic Equations

by Hongliang Liu, Aiguo Xiao and Yongxiang Zhao

Math. Comput. Appl. 2010, 15(5), 834-839; https://doi.org/10.3390/mca15050834 - 31 Dec 2010

Cited by 3 | Viewed by 1339

Abstract

Variational iteration method is applied to solve a class of delay differential-algebraic equations. The obtained sequence of iteration is based on the use of Lagrange multipliers. The corresponding convergence results are obtained and successfully confirmed by some numerical examples. Full article

216 KiB

Open AccessArticle

Nonlinear Dynamic Responses of Arch Dam with Shear Keys

by Chengbin Du and Shouyan Jiang

Math. Comput. Appl. 2010, 15(5), 828-833; https://doi.org/10.3390/mca15050828 - 31 Dec 2010

Cited by 9 | Viewed by 1187

Abstract

The purpose of this paper is to obtain an insight into the effects of shear keys with different slopes on the nonlinear seismic responses of an arch dam. The nonlinear exponential dynamic contact constitutive model is proposed for simulating the normal interactions of [...] Read more.

The purpose of this paper is to obtain an insight into the effects of shear keys with different slopes on the nonlinear seismic responses of an arch dam. The nonlinear exponential dynamic contact constitutive model is proposed for simulating the normal interactions of the two surfaces separated by contraction joints, along with the standard Coulomb friction model to simulate the tangential interactions. After the shear key’s real configuration is established, the seismic responses of the arch dam are discussed in detail to understand the effects of shear keys on the behavior of the contraction joints and the stress and deformation of the dam. The results indicate that the dam without the shear keys shows comparatively narrow joint opening, and that the maximum joint opening decreases when the slope of shear keys increases. In addition, the slope of shear keys exerts an obvious effect on the sliding displacement along the radial direction and the stress of the dam. Full article

217 KiB

Open AccessArticle

Cylindrical Microparticle Transport and Deposition from Electrokinetic Microflow in a 90 Degree Bend

by Kai Zhang, Lizhong Huang and Deming Nie

Math. Comput. Appl. 2010, 15(5), 822-827; https://doi.org/10.3390/mca15050822 - 31 Dec 2010

Cited by 2 | Viewed by 1072

Abstract

Cylindrical microparticle transport and deposition from electrokinetic microflow in a 90 degree bend have been numerically simulated. Under the effect of dielectrohporetic force, gravity and stokes force, it’s found that microparticles with larger size deposit on the lower region of the bend’s outer [...] Read more.

Cylindrical microparticle transport and deposition from electrokinetic microflow in a 90 degree bend have been numerically simulated. Under the effect of dielectrohporetic force, gravity and stokes force, it’s found that microparticles with larger size deposit on the lower region of the bend’s outer wall. An exponential curve of deposition efficiency versus the product of stokes number and shape factor is fitted based on large number of numerical results. Full article

172 KiB

Open AccessArticle

Analytical Approach to Investigation of Deflection of Circular Plate Under Uniform Load by Homotopy Perturbation Method

by Yasser Rostamiyan, A. Fereidoon, M. R. Davoudabadi, H. Yaghoobi and D.D. Ganji

Math. Comput. Appl. 2010, 15(5), 816-821; https://doi.org/10.3390/mca15050816 - 31 Dec 2010

Cited by 4 | Viewed by 1205

Abstract

In this paper Homotopy-Perturbation method (HPM) is introduced to obtain the approximate solution of the governing differential equation of deflection of thin circular plate under uniform loads with two different types of boundary conditions. The edge of the plate is either simply supported [...] Read more.

In this paper Homotopy-Perturbation method (HPM) is introduced to obtain the approximate solution of the governing differential equation of deflection of thin circular plate under uniform loads with two different types of boundary conditions. The edge of the plate is either simply supported or clamped and the plate is assumed to be geometrically perfect. He's Homotopy-Perturbation method is implemented for solving the differential equations. From comparison the results obtained that HPM is very rapid convergence and it can be widely applicable in engineering and especially for the cases have not exact solution, this method can be used as semi-exact solution. The results for both types of boundary conditions were compared with the results obtained by finite element method and exact solution. Full article

145 KiB

Open AccessArticle

Analytical Solution to Determine Displacement of Nonlinear Oscillations with Parametric Excitation by Differential Transformation Method

by A. Fereidoon, N. Kordani, Y. Rostamiyan and D. D.Ganji

Math. Comput. Appl. 2010, 15(5), 810-815; https://doi.org/10.3390/mca15050810 - 31 Dec 2010

Cited by 2 | Viewed by 1027

Abstract

In this study, sub-harmonic displacement of nonlinear oscillations with parametric excitation is solved using a simulation method called the Differential Transformation Method (DTM). We employed this method to derive solutions of nonlinear oscillations with parametric excitation equation. Also Runge-Kutta as numerical method is [...] Read more.

In this study, sub-harmonic displacement of nonlinear oscillations with parametric excitation is solved using a simulation method called the Differential Transformation Method (DTM). We employed this method to derive solutions of nonlinear oscillations with parametric excitation equation. Also Runge-Kutta as numerical method is exerted to this equation too. The obtained results from DTM are compared with those from the numerical solution to verify the accuracy of the proposed method. The results specify that the technique introduced here is accurate and achieve suitable results in predicting the solution of such problems. Full article

282 KiB

Open AccessArticle

Variational Iteration Method for Conservative Oscillators with Complicated Nonlinearities

by Y. M. Chen, G. Meng and J. K. Liu

Math. Comput. Appl. 2010, 15(5), 802-809; https://doi.org/10.3390/mca15050802 - 31 Dec 2010

Cited by 3 | Viewed by 1312

Abstract

The variational iteration method is employed to solve conservative oscillator containing complicated nonlinearities. In order to expand the nonlinear terms into truncated Fourier series, an approach of undetermined coefficient is proposed. Numerical examples shows the feasibility and efficiency of the variational iteration method [...] Read more.

The variational iteration method is employed to solve conservative oscillator containing complicated nonlinearities. In order to expand the nonlinear terms into truncated Fourier series, an approach of undetermined coefficient is proposed. Numerical examples shows the feasibility and efficiency of the variational iteration method as well as the presented technique for Fourier series expansion. Full article

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Math. Comput. Appl., Volume 15, Issue 5 (December 2010) – 36 articles , Pages 762-977

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