scholarly journals An Improved Analytical Method for Vibration Analysis of Variable Section Beam

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jingjing Feng ◽  
Zhengneng Chen ◽  
Shuying Hao ◽  
Kunpeng Zhang
Keyword(s):  
Natural Frequency ◽  
Analytical Method ◽  
Adomian Decomposition Method ◽  
Theoretical Method ◽  
Element Simulation ◽  
Adomian Decomposition ◽  
Variable Section ◽  
Vibration Problems ◽  
Section Structure ◽  
Section Function

The variable section structure could be the physical model of many vibration problems, and its analysis becomes more complicated either. It is very important to know how to obtain the exact solution of the modal function and the natural frequency effectively. In this paper, a general analytical method, based on segmentation view and iteration calculation, is proposed to obtain the modal function and natural frequency of the beam with an arbitrary variable section. In the calculation, the section function of the beam is considered as an arbitrary function directly, and then the result is obtained by the proposed method that could have high precision. In addition, the total amount of calculation caused by high-order Taylor expansion is reduced greatly by comparing with the original Adomian decomposition method (ADM). Several examples of the typical beam with different variable sections are calculated to show the excellent calculation accuracy and convergence of the proposed method. The correctness and effectiveness of the proposed method are verified also by comparing the results of the several kinds of the theoretical method, finite element simulation, and experimental method.

Comparison of Adomian Decomposition Method and Differential Transformation Method for Vibration Problems of Euler-Bernoulli Beam

2012 ◽  
Vol 157-158 ◽  
pp. 476-483
Author(s):  
Zhi Feng Liu ◽  
Chun Hua Guo ◽  
Li Gang Cai ◽  
Wen Tong Yang ◽  
Zhi Min Zhang
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Differential Transformation ◽  
Adomian Decomposition ◽  
Vibration Problems ◽  
Euler Bernoulli Beam

In this paper, we compare the Differential transformation method and Adomian decomposition method to solve Euler-Bernoulli Beam vibration problems. The natural frequencies and mode shapes of the clamped-free uniform Euler-Bernoulli equation are calculated using the two methods. The Adomian decomposition method avoids the difficulties and massive computational work inherent in Differential transformation method by determining the very rapidly convergent analytic solutions directly. We found the solution between the two methods to be quite close. According to calculation of eigenvalues, natural frequencies and mode shapes, we compare the convergence of Differential transformation method and Adomian decomposition method. The two methods can be alternative ways to solve linear and nonlinear higher-order initial value problems.

scholarly journals Analytical and semi analytical solutions of the internal waves of deep-stratified fluids

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 227-232
Author(s):  
Mostafa Khater ◽  
Raghda Attia ◽  
Sayed Elagan ◽  
Fatma Bayones
Keyword(s):  
Internal Waves ◽  
Analytical Solutions ◽  
Analytical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Stratified Fluids ◽  
Wave Solutions ◽  
Simplest Equation Method ◽  
Adomian Decomposition ◽  
Soliton Wave Solutions

In this paper, we study the soliton wave of the fractional Benjamin-Ono equation based on the extended simplest equation method. The accuracy of the obtained soliton wave solutions is investigated by comparing the obtained analytical and semi-analytical solutions. The semi-analytical solutions are constructed by applying the Adomian decomposition method. The semi-analytical method is used based on the constructed initial and boundary conditions from the obtained analytical solutions. Both solutions (analytical and semi-analytical) are plotted through different techniques for explaining the internal waves of deep-stratified fluids.

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 182-188
Author(s):  
O. González-Gaxiola ◽  
Anjan Biswas ◽  
Abdullah Kamis Alzahrani
Keyword(s):  
Numerical Simulations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Decomposition Scheme ◽  
Error Analyses ◽  
Adomian Decomposition ◽  
Log Law

AbstractThis paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme. The numerical simulations are presented both in the presence and in the absence of the detuning term. The error analyses of the scheme are also displayed.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

Implementation of fractional optimal control problems in real-world applications

2020 ◽  
Vol 23 (6) ◽  
pp. 1783-1796
Author(s):  
Neelam Singha
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Necessary Optimality Conditions ◽  
Order Model ◽  
Fractional Optimal Control ◽  
Adomian Decomposition ◽  
Real World Applications ◽  
Fractional Optimal Control Problems ◽  
And Control

Abstract In this article, we aim to analyze a mathematical model of tumor growth as a problem of fractional optimal control. The considered fractional-order model describes the interaction of effector-immune cells and tumor cells, including combined chemo-immunotherapy. We deduce the necessary optimality conditions together with implementing the Adomian decomposition method on the suggested fractional-order optimal control problem. The key motive is to perform numerical simulations that shall facilitate us in understanding the behavior of state and control variables. Further, the graphical interpretation of solutions effectively validates the applicability of the present analysis to investigate the growth of cancer cells in the presence of medical treatment.

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