Free vibration analysis of multiple-stepped beams by using Adomian decomposition method

Abstract

a b s t r a c tThe Adomian decomposition method (ADM) is employed in this paper to investigate the free vibrations of the Euler-Bernoulli beams with multiple cross-section steps. The proposed ADM method can be used to analyze the vibration of beams consisting of an arbitrary number of steps through a recursive way. The solution can be obtained by solving a set of algebraic equations with only three unknown parameters. Furthermore, the method can be extended to obtain an approximate solution to vibration problems of any type of non-uniform beams. Several numerical examples are presented and compared to those given in the paper. It is shown that the ADM offers an accurate and effective method of free vibration analysis of multiple-stepped beams with arbitrary boundary conditions.

A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods

“…The lowest three natural frequencies of a multistep up and down cantilever beam using a global Rayleigh-Ritz formulation, component modal analyses (CMA), ANSYS5, and experimental are evaluated [24]. Adomian decomposition method (ADM) was used to obtain the effect of step ratio and step location on the beam natural frequencies [25,26]. The free and forced vibrations of beams with either single-or multiple-step changes using the composite element method (CEM) were introduced by Lu et al [27].…”

Analiza Drgań Poprzecznych Smukłej Kolumny O Zmiennym Przekroju Poprzecznym Przy Obciążeniu Uogólnionym Z Siłą Skierowaną Do Bieguna Dodatniego

“…Rozwiązanie nieliniowych różniczkowych równań ruchu o zmiennych współ-czynnikach opisujących dynamikę układu rozwiązano stosując metodę równań równoważnych (AEM) Katsikadelisa. Analiza drgań swobodnych wielosegmentowej belki Bernoullego -Eulera podpartej sprężyście na obu końcach była tematem pracy [8]. Wykazano, że zaproponowana metoda rozwiązania zagadnienia brzegowego -metoda rozkładu Adomiana -może być użyta do analizy drgań różnego typu belek niepryzmatycznych zbudowanych z dowolnej liczby członów.…”

The Transfer Matrix Method for Modal Analysis of Cracked Multistep Beam

“…The findings are important to show the dynamic property of stepped beam and which method could be useful for vibration analysis of the beam. Other methods such as Adomian Decomposition Method (ADM) and Differential Quadrature Element Method (DEM) have been developed in [4] and [5], respectively, for free vibration analysis of multi-step beams. Cunha and Junior [6] investigated effect of elastic boundary supports on natural frequencies and mode shapes of multiple stepped beam.…”