The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Metin O. Kaya - One of the best experts on this subject based on the ideXlab platform.
-
flapwise bending vibration analysis of double tapered rotating euler bernoulli beam by using the differential Transform Method
Meccanica, 2006Co-Authors: Ozge Ozdemir Ozgumus, Metin O. KayaAbstract:In this study, the out-of-plane free vibration analysis of a double tapered Euler–Bernoulli beam, mounted on the periphery of a rotating rigid hub is performed. An efficient and easy mathematical technique called the Differential Transform Method (DTM) is used to solve the governing differential equation of motion. Parameters for the hub radius, rotational speed and taper ratios are incorporated into the equation of motion in order to investigate their effects on the natural frequencies. Calculated results are tabulated in several tables and figures and are compared with the results of the studies in open literature where a very good agreement is observed.
-
free vibration analysis of a rotating timoshenko beam by differential Transform Method
Aircraft Engineering and Aerospace Technology, 2006Co-Authors: Metin O. KayaAbstract:Purpose – To perform the flapwise bending vibration analysis of a rotating cantilever Timoshenko beam.Design/Methodology/approach – Kinetic and potential energy expressions are derived step by step. Hamiltonian approach is used to obtain the governing equations of motion. Differential Transform Method (DTM) is applied to solve these equations.Findings – It is observed that the ρIΩ2θ term which is ignored by many researchers and which becomes more important as the rotational speed parameter increases must be included in the formulation.Originality/value – Kinetic and potential energy expressions for rotating Timoshenko beams are derived clearly step by step. It is the first time, for the best of author's knowledge, that DTM has been applied to the blade type rotating Timoshenko beams.
-
flapwise bending vibration analysis of a rotating tapered cantilever bernoulli euler beam by differential Transform Method
Journal of Sound and Vibration, 2006Co-Authors: Ö. Özdemir, Metin O. KayaAbstract:Abstract This paper studies the vibration characteristics of a rotating tapered cantilever Bernoulli–Euler beam with linearly varying rectangular cross-section of area proportional to xn, where n equals to 1 or 2 covers the most practical cases. In this work, the differential Transform Method (DTM) is used to find the nondimensional natural frequencies of the tapered beam. Numerical results are tabulated for different taper ratios, nondimensional angular velocities and nondimensional hub radius. The effects of the taper ratio, nondimensional angular velocity and nondimensional hub radius are discussed. The accuracy is assured from the convergence of the natural frequencies and from the comparisons made with the studies in the open literature. It is shown that the natural frequencies of a rotating tapered cantilever Bernoulli–Euler beam can be obtained with high accuracy by using DTM.
-
flapwise bending vibration analysis of a rotating tapered cantilever bernoulli euler beam by differential Transform Method
Journal of Sound and Vibration, 2006Co-Authors: Ö. Özdemir, Metin O. KayaAbstract:Abstract This paper studies the vibration characteristics of a rotating tapered cantilever Bernoulli–Euler beam with linearly varying rectangular cross-section of area proportional to xn, where n equals to 1 or 2 covers the most practical cases. In this work, the differential Transform Method (DTM) is used to find the nondimensional natural frequencies of the tapered beam. Numerical results are tabulated for different taper ratios, nondimensional angular velocities and nondimensional hub radius. The effects of the taper ratio, nondimensional angular velocity and nondimensional hub radius are discussed. The accuracy is assured from the convergence of the natural frequencies and from the comparisons made with the studies in the open literature. It is shown that the natural frequencies of a rotating tapered cantilever Bernoulli–Euler beam can be obtained with high accuracy by using DTM.
-
flexural torsional coupled vibration analysis of a thin walled closed section composite timoshenko beam by using the differential Transform Method
icov, 2006Co-Authors: Metin O. Kaya, Ozge OzdemirAbstract:In this study, a new mathematical technique called the Differential Transform Method (DTM) is introduced to analyse the free undamped vibration of an axially loaded, thin-walled closed section composite Timoshenko beam including material coupling between the bending and torsional modes of deformation, which is usually present in laminated composite beams due to ply orientation. The partial differential equations of motion are derived applying the Hamilton's principle and solved using DTM. Natural frequencies are calculated, related graphics and the mode shapes are plotted.
Liuqing Hua - One of the best experts on this subject based on the ideXlab platform.
-
variational iteration Transform Method for fractional differential equations with local fractional derivative
Abstract and Applied Analysis, 2014Co-Authors: Yongju Yang, Liuqing HuaAbstract:We propose the variational iteration Transform Method in the sense of local fractional derivative, which is derived from the coupling Method of local fractional variational iteration Method and differential Transform Method. The Method reduces the integral calculation of the usual variational iteration computations to more easily handled differential operation. And the technique is more orderly and easier to analyze computing result as compared with the local fractional variational iteration Method. Some examples are illustrated to show the feature of the presented technique.
Shaher Momani - One of the best experts on this subject based on the ideXlab platform.
-
solving the fractional nonlinear bloch system using the multi step generalized differential Transform Method
Computers & Mathematics With Applications, 2014Co-Authors: Eman Abuteen, Shaher Momani, Ahmad AlawnehAbstract:In this paper, the multi-step differential Transform Method is employed for the first time to solve a time-fractional nonlinear Bloch system. The nonlinear Bloch equation is known to govern the dynamics of an ensemble of spins, controlling the basic process of nuclear magnetic resonance (NMR). This nonlinear Bloch equation is formed from a system of nonlinear ordinary differential equations of fractional order. The fractional derivatives are described in the Caputo sense. The results obtained are in good agreement with the ones in the open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.
-
adaptation of differential Transform Method for the numeric analytic solution of fractional order rossler chaotic and hyperchaotic systems
Abstract and Applied Analysis, 2012Co-Authors: Asad Freihat, Shaher MomaniAbstract:A new reliable algorithm based on an adaptation of the standard generalized differential Transform Method (GDTM) is presented. The GDTM is treated as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of fractional-order Rossler chaotic and hyperchaotic systems. A comparative study between the new algorithm and the classical Runge-Kutta Method is presented in the case of integer-order derivatives. The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.
-
application of generalized differential Transform Method to multi order fractional differential equations
Communications in Nonlinear Science and Numerical Simulation, 2008Co-Authors: Vedat Suat Erturk, Shaher Momani, Zaid OdibatAbstract:Abstract In a recent paper [Odibat Z, Momani S, Erturk VS. Generalized differential Transform Method: application to differential equations of fractional order, Appl Math Comput. submitted for publication] the authors presented a new generalization of the differential Transform Method that would extended the application of the Method to differential equations of fractional order. In this paper, an application of the new technique is applied to solve fractional differential equations of the form y ( μ ) ( t ) = f ( t , y ( t ) , y ( β 1 ) ( t ) , y ( β 2 ) ( t ) , … , y ( β n ) ( t ) ) with μ > β n > β n - 1 > … > β 1 > 0 , combined with suitable initial conditions. The fractional derivatives are understood in the Caputo sense. The Method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the new generalization.
-
generalized differential Transform Method application to differential equations of fractional order
Applied Mathematics and Computation, 2008Co-Authors: Zaid Odibat, Shaher Momani, Vedat Suat ErturkAbstract:Abstract In this paper we propose a new generalization of the one-dimensional differential Transform Method that will extend the application of the Method to differential equations of fractional order. The new generalization is based on generalized Taylor’s formula and Caputo fractional derivative. Several illustrative examples are given to demonstrate the effectiveness of the obtained results. The new generalization introduces a promising tool for many linear and nonlinear models containing fractional derivatives.
-
solutions of non linear oscillators by the modified differential Transform Method
Computers & Mathematics With Applications, 2008Co-Authors: Shaher Momani, Vedat Suat ErturkAbstract:A numerical Method for solving nonlinear oscillators is proposed. The proposed scheme is based on the differential Transform Method (DTM), Laplace Transform and Pade approximants. The modified differential Transform Method (MDTM) technique introduces an alternative framework designed to overcome the difficulty of capturing the periodic behavior of the solution, which is characteristic of oscillator equations, and give a good approximation to the true solution in a very large region. The numerical results demonstrate the validity and applicability of the new technique and a comparison is made with existing results.
Zaid Odibat - One of the best experts on this subject based on the ideXlab platform.
-
a multi step differential Transform Method and application to non chaotic or chaotic systems
Computers & Mathematics With Applications, 2010Co-Authors: Zaid Odibat, Cyrille Bertelle, M A Azizalaoui, Gerard DuchampAbstract:The differential Transform Method (DTM) is an analytical and numerical Method for solving a wide variety of differential equations and usually gets the solution in a series form. In this paper, we propose a reliable new algorithm of DTM, namely multi-step DTM, which will increase the interval of convergence for the series solution. The multi-step DTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. This new algorithm is applied to Lotka-Volterra, Chen and Lorenz systems. Then, a comparative study between the new algorithm, multi-step DTM, classical DTM and the classical Runge-Kutta Method is presented. The results demonstrate reliability and efficiency of the algorithm developed.
-
differential Transform Method for solving volterra integral equation with separable kernels
Mathematical and Computer Modelling, 2008Co-Authors: Zaid OdibatAbstract:In this paper, Volterra integral equations with separable kerenels are solved using the differential Transform Method. The approximate solution of this equation is calculated in the form of a series with easily computable terms. Exact solutions of linear and nonlinear integral equations have been investigated and the results illustrate the reliability and the performance of the differential Transform Method.
-
application of generalized differential Transform Method to multi order fractional differential equations
Communications in Nonlinear Science and Numerical Simulation, 2008Co-Authors: Vedat Suat Erturk, Shaher Momani, Zaid OdibatAbstract:Abstract In a recent paper [Odibat Z, Momani S, Erturk VS. Generalized differential Transform Method: application to differential equations of fractional order, Appl Math Comput. submitted for publication] the authors presented a new generalization of the differential Transform Method that would extended the application of the Method to differential equations of fractional order. In this paper, an application of the new technique is applied to solve fractional differential equations of the form y ( μ ) ( t ) = f ( t , y ( t ) , y ( β 1 ) ( t ) , y ( β 2 ) ( t ) , … , y ( β n ) ( t ) ) with μ > β n > β n - 1 > … > β 1 > 0 , combined with suitable initial conditions. The fractional derivatives are understood in the Caputo sense. The Method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the new generalization.
-
generalized differential Transform Method application to differential equations of fractional order
Applied Mathematics and Computation, 2008Co-Authors: Zaid Odibat, Shaher Momani, Vedat Suat ErturkAbstract:Abstract In this paper we propose a new generalization of the one-dimensional differential Transform Method that will extend the application of the Method to differential equations of fractional order. The new generalization is based on generalized Taylor’s formula and Caputo fractional derivative. Several illustrative examples are given to demonstrate the effectiveness of the obtained results. The new generalization introduces a promising tool for many linear and nonlinear models containing fractional derivatives.
-
a generalized differential Transform Method for linear partial differential equations of fractional order
Applied Mathematics Letters, 2008Co-Authors: Zaid Odibat, Shaher MomaniAbstract:Abstract In this letter we develop a new generalization of the two-dimensional differential Transform Method that will extend the application of the Method to linear partial differential equations with space- and time-fractional derivatives. The new generalization is based on the two-dimensional differential Transform Method, generalized Taylor’s formula and Caputo fractional derivative. Several illustrative examples are given to demonstrate the effectiveness of the present Method. The results reveal that the technique introduced here is very effective and convenient for solving linear partial differential equations of fractional order.
A S Fokas - One of the best experts on this subject based on the ideXlab platform.
-
a unified Transform Method for solving linear and certain nonlinear pdes
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1997Co-Authors: A S FokasAbstract:A new Transform Method for solving initial boundary value problems for linear and for integrable nonlinear PDEs in two independent variables is introduced. This unified Method is based on the fact that linear and integrable nonlinear equations have the distinguished property that they possess a Lax pair formulation. The implementation of this Method involves performing a simultaneous spectral analysis of both parts of the Lax pair and solving a Riemann–Hilbert problem. In addition to a unification in the Method of solution, there also exists a unification in the representation of the solution. The sine–Gordon equation in light–cone coordinates, the nonlinear Schrodinger equation and their linearized versions are used as illustrative examples. It is also shown that appropriate deformations of the Lax pairs of linear equations can be used to construct Lax pairs for integrable nonlinear equations. As an example, a new Lax pair of the nonlinear Schrodinger equation is derived.
