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

Abstract

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.

Closed-form solution for a rectangular stepped fin involving all variable thermal parameters and nonlinear boundary conditions

“…Further based upon equations (34) to (36), individual terms given in equation 37are evaluated. The effect of number of terms on accuracy and computational time is analyzed as given in Table 1.…”

“…In the present work, ADM is used 33 due to its wide application in solving diverse nonlinear problems with very effectual and enhanced accuracy. [34][35][36][37] So far the study of stepped fin is concerned, recently, few studies have been reported using other methods. For example, using linear boundary conditions and by discarding the radiation effect, Arslanturk 38 investigated a stepped fin with variable thermal conductivity using HPM.…”