Free vibration analysis of stepped beams by using Adomian decomposition method

Mao, Qibo; Pietrzko, Stanislaw

doi:10.1016/j.amc.2010.09.010

Cited by 42 publications

(38 citation statements)

References 14 publications

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“…Thus, the accuracy of the model of the non-uniform beam is proved by little difference between the results derived from the proposed method in this paper and those in reference [24].…”

Section: Non-uniform Beam On Pasternak Soilmentioning

confidence: 59%

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

Xiao

Sheng

Liu

et al. 2013

Shock and Vibration

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Abstract. The flexible beams carrying attachments often appear in engineering structures, modal analysis of those structures is important and necessary in structural design. This manuscript develops a proposed analytical method as a general tool for solving the free vibration of varying cross-section beams carrying various types of attachments with different distributions and arbitrary boundary conditions. In current practice, the natural frequencies of beam carrying lumped and uniform sprung mass and resting on Pasternak soil are calculated and compared with those in references to verify the methodology firstly. Then, the natural frequencies of beam carrying non-uniform spring-mass systems and stepped beam on Pasternak soil are calculated by the proposed method to study free vibration of beam carrying attachments with non-uniform cross section or distribution. Finally, some important conclusions are derived from results, which reveal that distribution density of spring-mass system at peaks of the mode shape makes dominate effects on the change of the natural frequencies at that mode and the natural frequencies of the stepped beam resting on elastic foundation are more sensitive to the increase of soil parameters.

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“…Thus, the accuracy of the model of the non-uniform beam is proved by little difference between the results derived from the proposed method in this paper and those in reference [24].…”

Section: Non-uniform Beam On Pasternak Soilmentioning

confidence: 59%

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

Xiao

Sheng

Liu

et al. 2013

Shock and Vibration

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“…(28) and (29), which in fact, provides us with the critical flow velocity for divergence of the system. ADM and its variants have widely been used in physics, applied mathematics and engineering to solve linear/ nonlinear, ordinary/partial differential equations subjected to initial/boundary conditions; for some examples of application of ADM to problems in vibration, see Haddadpour (2006), Hsu et al (2008), Mao and Pietrzko (2010) and Das (2009).…”

Section: Divergence Of a Pinned-free Cylindermentioning

confidence: 99%

Dynamics and stability of a flexible pinned-free cylinder in axial flow

Kheiri

Paı̈doussis

2015

Journal of Fluids and Structures

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“…A stepped beam made from composite materials was chosen to investigate its vibration characteristic in the study of Dong et al (2005) by means of a Timoshenko beam theory. The Adomain decomposition method (ADM) with standard version was implemented to solve vibration analysis of stepped beams with elastically constrained ends in Refs (Mao and Pietrzko 2010;Mao 2011). An application of differential transformation method (DTM) to free vibration of stepped beams with various elastic boundary conditions was presented by Wattanasakulpong (2013, 2014).…”

Section: Introductionmentioning

confidence: 99%

Adomian-modified decomposition method for large-amplitude vibration analysis of stepped beams with elastic boundary conditions

Wattanasakulpong

Chaikittiratana

2015

Mechanics Based Design of Structures and Machines

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The main objective of this paper is to apply an Adomian modified decomposition method for solving large amplitude vibration analysis of stepped beams with various general and elastic boundary conditions. Damaged or imperfect supports of beams can be modelled by using elastic boundary conditions composing of translational and rotational springs. For the beams subjected to dynamic severe loading, it is important to include the nonlinear term of axial stretching force Downloaded by [New York University] at 04:16 21 June 2015 2 developed by the large vibration amplitude in the governing equation for more accurate design. By using the method, the convergence studies for linear and nonlinear vibration analyses of stepped beams are shown for determining an appropriate number of terms in the solutions. The accuracy of the present results is validated numerically by comparing with some available results in the literature. New results of nonlinear frequency ratios of stepped beams with different boundary conditions are presented and discussed in detail. Aspects of step ratio, step location, boundary conditions, vibration amplitudes, etc. which have significant impact on linear and nonlinear frequencies of such beams are taken under investigation.

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Free vibration analysis of stepped beams by using Adomian decomposition method

Cited by 42 publications

References 14 publications

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

Dynamics and stability of a flexible pinned-free cylinder in axial flow

Adomian-modified decomposition method for large-amplitude vibration analysis of stepped beams with elastic boundary conditions

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