Adomian Decomposition Method for Solving a Cantilever Beam of Varying Orientation with Tip Mass

Abstract

A uniform cantilever beam of varying orientation with a tip mass at the free end can be used as a basic model of many practical structures such as flexible robot arm or antenna mast. The aim of the study described here is to investigate the influence of the orientation effect on the natural frequency of the cantilever beam carrying a tip mass. An analytic solution is obtained by using the Adomian decomposition method. The accuracy of the Adomian decomposition method with a varying number of terms in the series is investigated by comparing its results with those generated by the finite element method.

The first frequency of cantilevered bars with geometric effect: a mathematical and experimental evaluation

“…The recent work of Yaman [31], the Adomian decomposition method is used to determine the vibrations of the beam/column with a variable rotation relative to the initial straight axis, obtaining results that are compatible with the finite elements method. Using Eq.…”

Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

“…The method of solution chosen here is the Adomian modified decomposition method [13] which is a wide-ranging method of solution for problems involving algebraic [14], differential [15], integro-differential [16], and partial differential equations [17]. Specific to this work, the Adomian decomposition and Adomian modified decomposition method have been used by several groups [18][19][20][21][22][23] for uniform and nonuniform beams, starting with either the Euler-Bernoulli or Timoshenko formulations. Mao [18] applied the Adomian modified decomposition method (AMDM) to rotating uniform beams and included a centrifugal stiffening term, Adair and Jaeger [19] applied the AMDM to rotating nonuniform beams which also included a centrifugal stiffening term, whereas Hsu et al [20] applied the AMDM to Timoshenko beams.…”

Flexural response of thermoelastic thin beam resonators due to thermal and mechanical loads

“…Mao [24] employed ADM to investigate the free vibrations of the Euler-Bernoulli beams with multiple cross-section steps. Yaman [25] investigated the influence of orientation effect on the natural frequency of a cantilever beam carrying a tip mass by using ADM. Mao and Pietrzko [26] analyzed free vibrations of stepped and tapered beams by using ADM. Tapaswini and Chakraverty [27] studied the dynamic response of a beam subjected to unit step and impulse loads by employing ADM. Kuang and Chen [28] employed ADM to study the nonlinear pull-in behaviour in electrostatic fixed-fixed beam and cantilever micro-beam actuators.…”