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A review: differential transform method for semi-analytical solution of differential equations

Rashidi M. M., Rabiei F., Naser Nia S., Abbasbandy S.

International Journal of Applied Mechanics and Engineering

2020

Vol. 25, no. 2

122--129

In this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.

Transient forced vibration response analysis of heterogeneous sandwich circular plates under viscoelastic boundary support

Alipour M. M.

Archives of Civil and Mechanical Engineering

2018

Vol. 18, no. 1

12--31

For the first time the transient bending analysis of a sandwich plate with viscoelastic boundary support is investigated in this study. Viscoelastic support consists of two sets of translational springs and dashpots connected in parallel along the in-plane and transverse directions. The sandwich plate is fabricated from heterogeneous face sheets where the material properties of each face sheets are assumed to be varied continuously in the radial direction according to a power-law function. Variations of the material properties of each face sheets are monitored by eight distinct inhomogeneity parameters. Therefore, the solution procedure may be used for a wide range of the practical problems. In order to investigate the effects of viscoelastic edge supports on the transient response of sandwich plate a wide range of the stiffness and damping coefficients of the edge supports in the in-plane and transverse directions are applied. Results of sandwich plates with the classical edge conditions as some special cases of the elastic/viscoelastic supports are compared with those extracted from the ABAQUS software based on the 3D theory of elasticity. The comparisons show that even for relatively complicated cases, there is a good agreement between the results.

Semi-analytical method for the dynamic analysis

Alecu A. M., Boiangiu M. I., Anghel V. I.

Computer Assisted Mechanics and Engineering Sciences

2002

Vol. 9, No. 4

424-439

The paper presents a semi-analytical method for the study of a linear differential system with variable coefficients. The solution is given in terms of real positive integer powers; it is obtained in terms of independent functions which are computed numerically. The paper extended the semi-analytical method from [1] (for one differential equation only), to the study of a linear differential system. The differential system became a system with recurrent expressions between the coefficients of the power series in a matrix form. The strength of this method is shown by application to the dynamic analysis of typical rotor blades. The frequencies and mode shapes are calculated. The results are compared with theoretical results for the degenerate cases and with results obtained through other methods.