Free vibration of non-uniform Euler–Bernoulli beams with general elastically end constraints using Adomian modified decomposition method

Hsu, Jung-Chang; Lai, Hsin Yi; Chen, C.K.

doi:10.1016/j.jsv.2008.05.010

Cited by 98 publications

(60 citation statements)

References 18 publications

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“…3 By applying the Adomian modified decomposition method, Hsu et al converted the governing differential equation to a recursive algebraic equation and kept the boundary conditions within simple algebraic frequency equations which were suitable for symbolic computation. 4 Based on the fact that a nonuniform beam can be partitioned into multi homogeneous uniform sub-beams, Singh et al 5 developed a numerical method for determining the natural frequencies of a nonuniform beam. By assuming the material constituents are varied throughout the thickness or longitudinal directions according to a simple power law, Alshorbagy et al used the numerical finite element method to investigate the dynamic behaviors of functionally graded beams.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Axially Inhomogeneous Beams that are Made of Functionally Graded Materials

Huang¹,

Rong²

2017

IJAV

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A simple approach to deal with an engineering problem of free vibration of functionally graded beams with nonuniform cross-sections where the material properties arbitrarily vary along the axial direction is presented. Instead of directly solving the fourth-order governing differential equation with variable coefficients, we transform the governing equation to a system of linear algebraic equations based on the polynomial expansion and integral technique. Then, a characteristic equation in natural frequencies will be obtained. Several examples of estimating natural frequencies for axially graded beams and non-uniform beams are presented, which show that our method has a fast convergence and the obtained numerical results are accurate. The proposed method is important to investigate because of the dynamic behavior of axially non-uniform beams in engineering applications.

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Section: Introductionmentioning

confidence: 99%

Free Vibration of Axially Inhomogeneous Beams that are Made of Functionally Graded Materials

Huang¹,

Rong²

2017

IJAV

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“…The problem of assessing the dynamic response of a structural elements (beam or plate) which supports moving loads is fundamental in the analysis and design of high way and railway bridges and as such this problem continues to attract the attention of research engineers in the field of civil, mechanical, aerospace, transport engineering and related fields [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Response characteristics of non-uniform beam with time-dependent boundary conditions and under the actions of travelling distributed masses

Omolofe

Adedowole

2017

J. Appl. Math. Comput. Mech.

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Abstract. In this paper, dynamic response of non-prismatic elastic beam resting on elastic foundation and subjected to moving distributed masses is investigated. To obtain the solution of the fourth order partial differential equations with singular and variable coefficients governing the motion of the structural member, an elegant mathematical procedure involving the Mindlin and Goodman's technique, the generalized Galerkin method and the asymptotic Struble's technique with the series representation of the Heaviside function. Various results obtained from the analysis of the closed form solutions are presented in plotted curves and fully discussed.

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“…Studies concerning vibrating bodies resting on an elastic foundation carrying moving loads are of considerable practical importance and have been a subject of numerous scientific investigations by different authors in past few years [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. In most of the studies available in literature, such as the work of Sadiku and Leipolz [21], Oni and Awodola [22], the scope of the problem of assessing the dynamic response of a structural member under the passage of moving load has been limited to that of thin beam or thick beam.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Characteristics of a Rotating Timoshenko Beam Subjected to a Variable Magnitude Load Travelling at Varying Speed

Omolofe¹,

Ogunyebi²

2016

Journal of the Korea Society for Industrial and Applied Mathema

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ABSTRACT. In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin's Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.

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Free vibration of non-uniform Euler–Bernoulli beams with general elastically end constraints using Adomian modified decomposition method

Cited by 98 publications

References 18 publications

Free Vibration of Axially Inhomogeneous Beams that are Made of Functionally Graded Materials

Free Vibration of Axially Inhomogeneous Beams that are Made of Functionally Graded Materials

Response characteristics of non-uniform beam with time-dependent boundary conditions and under the actions of travelling distributed masses

Dynamic Characteristics of a Rotating Timoshenko Beam Subjected to a Variable Magnitude Load Travelling at Varying Speed

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