On the Linear and Nonlinear Vibration Responses of Elastically End Restrained Beams Using DTM

Wattanasakulpong, Nuttawit; Chaikittiratana, Arisara

doi:10.1080/15397734.2013.847778

Cited by 25 publications

(8 citation statements)

References 18 publications

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“…In their studies, the translational and rotational springs are used to simulate damaged boundary conditions of beams, for buckling and vibration analyses. Other studies dealing with mechanical problems of structures with elastic supports were reported in Refs (Rao and Rao 2011;Wattanasakulpong and Chaikittiratana 2014).…”

Section: Introductionmentioning

confidence: 96%

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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Section: Introductionmentioning

confidence: 96%

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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“…He used an iterative procedure to solve the equation. Wattanasakulpong and http://Chaikittiratana [41] applied the differential transformation method to solve the linear and nonlinear vibration problems of elastically end‐restrained beams. Tari [38] studied the problem of determining the parametric large deflection components of E–B beams subjected to a point load.…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear vibrations of variable cross‐section beams using shear deformation theory

Sohani

Eipakchi

2021

Z Angew Math Mech

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In the present paper, the governing equations of a vibratory beam with moderately large deflection and arbitrary cross‐section are derived by using the first‐order shear deformation theory. The beam is homogenous, isotropic and it is subjected to the axial loads. The kinematic of the problem is according to the von‐Kármán strain‐displacement relations and the Hooke law is used as the constitutive equations. The partial differential governing equations describing the axial and transverse vibrations of homogeneous beams contain four coupled nonlinear equations with variable coefficients which are derived employing Hamilton's principle. The Galerkin method in conjunction with the perturbation technique is applied to obtain the linear natural frequencies. A parametric study is performed and the effects of different thickness functions such as linear, polynomial and trigonometric on the results are investigated. The non‐linear frequencies which contain the corrections on the linear frequencies are calculated. The corrected parts of the non‐linear frequencies are functions of the axial as well as the transverse amplitudes of the vibrations. The influences of the axial load and aspect ratio on the linear and non‐linear frequencies are studied too. To confirm the reliability of the vibration analysis carried out in the present paper, the analytical results are checked with the corresponding numerical results obtained from the finite element analysis. The numerical and analytical results are in a good agreement.

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“…Saito and Otomi 19 also analysed the stability of a viscoelastic beam with viscoelastic end supports and an attached mass, exposed to tangential and axial periodic loads. Wattanasakulpong and Chaikittiratana 20 used the differential transform method to examine the aspects of non-linear and linear vibration of a beam with elastic restraints. Yayli 21 investigated the buckling load of an Euler column with elastic restraints to analyse the stability for several boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Analysis of parametric instability of a spring-attached pre-twisted beam with viscoelastic end support

Nayak

Pradhan

Jena

et al. 2021

Noise & Vibration Worldwide

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This study investigated the parametric instability of a single elastic beam with spring attachment on the top and viscoelastic springs as end supports. The beam considered is pre-twisted with a pin connection at both ends that supports the beam. The analytical solution of the problem is expressed in the matrix form achieved from the implementation of Hamilton’s principle and General Galerkin’s method, from which both static and dynamic stability of the beam can be investigated. The results of various influential dimensionless parameters such as stiffness, mass, length, position of the spring attachment, and stiffness of the viscoelastic springs on both the stabilities are studied. This analysis concluded that the spring attachment on the system leads to substantial contribution in improving the stability. The viscoelastic springs also contribute in upsurging the beam’s stability. Three different profiles of the beam have been considered, and for each profile, three different types of springs have been examined. The results revealed that the beam with parabolic profile and stiffness of the spring attachment with parabolic variation is most effective towards strength-to-weight ratio.

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On the Linear and Nonlinear Vibration Responses of Elastically End Restrained Beams Using DTM

Cited by 25 publications

References 18 publications

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

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

Linear and nonlinear vibrations of variable cross‐section beams using shear deformation theory

Analysis of parametric instability of a spring-attached pre-twisted beam with viscoelastic end support

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