Erratum to: “Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load”

The aim of the present study is to analyze and find a solution for the model of nonlinear ordinary differential equations (ODEs) describing the so-called coronavirus (COVID-19), a deadly and most parlous virus. The mathematical model based on four nonlinear ODEs is presented, and the corresponding numerical results are studied by applying the variational iteration method (VIM) and differential transformation method (DTM).

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Explicit solution to the large deformation of a cantilever beam under point load at the free tip using the variational iteration method-II

Journal of Mechanical Science and Technology ◽

10.1007/s12206-013-0866-4 ◽

2013 ◽

Vol 27 (11) ◽

pp. 3433-3438 ◽

Cited By ~ 17

Author(s):

Hosein Ghaffarzadeh ◽

Ali Nikkar

Keyword(s):

Large Deformation ◽

Cantilever Beam ◽

Iteration Method ◽

Explicit Solution ◽

Variational Iteration Method ◽

Point Load ◽

Variational Iteration

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Differential Transformation Method And Variation Iteration Method For Cauchy Reaction-diffusion Problems

Journal of Mathematics and Computer Science ◽

10.22436/jmcs.001.02.01 ◽

2010 ◽

Vol 01 (02) ◽

pp. 61-75 ◽

Cited By ~ 5

Author(s):

Mohamed I. A. Othman ◽

A. M. S. Mahdy

Keyword(s):

Iteration Method ◽

Reaction Diffusion ◽

Transformation Method ◽

Differential Transformation Method ◽

Differential Transformation ◽

Variation Iteration Method ◽

Diffusion Problems

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Analysis of Coupled Dynamic and Voltage Models of Piezoelectric Cantilever Energy Harvester using Differential Transformation Method

Journal of Applied Material Science & Engineering Research ◽

10.33140/jamser.04.03.04 ◽

2020 ◽

Vol 4 (3) ◽

Keyword(s):

Output Voltage ◽

Energy Harvester ◽

Electrical Energy ◽

Transformation Method ◽

Analytical Models ◽

Differential Transformation Method ◽

Treatment Technique ◽

Cantilever Beams ◽

Differential Transformation ◽

Piezoelectric Energy

In this work, differential transformation method with after treatment technique is applied to develop analytical models for the prediction of the behavior and output voltage of cantilever piezoelectric energy harvesters. The analytical results are in a good agreement with the experimental results in literature. The first mode of vibration has the lowest resonant frequency, and typically provides the most deflection and therefore electrical energy. The output voltage increases with the length of the beam but increase in the thickness of the beam decreases the output voltage. The results depict that the shape of the cantilever energy harvester plays an important role in improving the harvester’s efficiency. It is established that under the same loading, material and geometrical conditions, triangular cantilever beams are more efficient than rectangular ones. From the results, it is also established that that among all the cantilever beams with uniform thickness, the triangular cantilever, can lead to highest resonance frequency. Therefore, in order to obtain more wideband piezoelectric energy harvester, the geometrical and material designs of piezoelectric resonant cantilevers must be properly analyzed.

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Design of shaped piezoelectric modal sensors for cantilever beams with intermediate support by using differential transformation method

Applied Acoustics ◽

10.1016/j.apacoust.2011.07.010 ◽

2012 ◽

Vol 73 (2) ◽

pp. 144-149 ◽

Cited By ~ 9

Author(s):

Qibo Mao

Keyword(s):

Transformation Method ◽

Differential Transformation Method ◽

Cantilever Beams ◽

Differential Transformation ◽

Intermediate Support

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Lateral-Torsional Stability of Rectangular Prismatic Beams Using Some Analytical Approximation Techniques

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455420500273 ◽

2020 ◽

Vol 20 (02) ◽

pp. 2050027

Author(s):

Ahmet Yücesoy ◽

Safa Bozkurt Coşkun

Keyword(s):

Iteration Method ◽

Adomian Decomposition Method ◽

Variational Iteration Method ◽

Transformation Method ◽

Single Equation ◽

Analytical Approximation ◽

Governing Equations ◽

Approximation Techniques ◽

Variational Iteration ◽

Adomian Decomposition

The paper presents simple computational algorithms for analyzing the lateral-torsional buckling of prismatic beams with rectangular cross-sections under bending action due to uniform and nonuniform loads by the Adomian decomposition method (ADM) and variational iteration method (VIM). Unlike the numerical techniques that lead to a discretization process, the proposed method allows us to derive the solution in terms of an analytical function for the problem considered. Although the governing equations of the problem appear as a system of two coupled variable coefficient ordinary differential equations, they reduce to a single equation for rectangular beams. The buckling loads for different loading conditions are computed, with the results for the simple beam compared with previous available results by the differential transformation method (DTM), variational iteration method (VIM) and finite element method (FEM) based on coupled governing equations. The results clearly show the efficiency and advantage of the present technique over those based on the coupled governing equations using the DTM and VIM in view of the number of terms required to obtain the convergent solution.

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