Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation

Yang, Young-Soo; Ding, Hu; Chen, Liqun

doi:10.1007/s10409-013-0069-3

Cited by 46 publications

(18 citation statements)

References 23 publications

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“…The present expression of general solutions given by (18) and (19) is equivalent to the expression for three frequency ranges, 0 < < , = , and > , by van Rensburg and van der Merwe [28].…”

Section: Mathematical Model Of a Timoshenko Beam The Governing Equatmentioning

confidence: 93%

“…where The general solution at = can be readily obtained from either (18) or (19), by allowing to approach , as follows: (47)…”

Section: Natural Frequencies and Mode Shapesmentioning

confidence: 99%

“…To examine the transverse vibrations of a 1D beam structure, the Timoshenko beam model has been widely adopted to take into account the effects of shear deformation and rotatory inertia on the dynamic responses. In transverse vibration analysis, various solution techniques have been described in the literature including MAM or eigenfunction expansion methods [1,2], mode summation methods or assumed mode methods [3][4][5], semianalytical methods [6][7][8][9][10][11], integral transform methods (Laplace-Carson transform and Fourier transform) [12][13][14], transfer matrix method [15], Lagrange multiplier methods [16,17], Galerkin methods [18,19], finite element methods [20,21], finite difference method [22], time-domain spectral element method [23], and frequency-domain spectral element method [24].…”

Section: Introductionmentioning

confidence: 99%

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Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

Kim

Park

Lee

2017

Shock and Vibration

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The modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey reveals that the necessary information reported in the existing literature is sometimes very limited or incomplete, even for simple beam models such as Timoshenko beams. Thus, we present complete information on the natural frequencies, three types of mode shapes, and the orthogonality of the mode shapes for simply supported Timoshenko beams. Based on this information, we use the MAM to derive the forced vibration responses of a simply supported Timoshenko beam subjected to arbitrary initial conditions and to stationary or moving loads (a point transverse force and a point bending moment) in analytical closed form. We then conduct numerical studies to investigate the effects of each type of mode shape on the long-term dynamic responses (vibrations), the short-term dynamic responses (waves), and the deformed shapes of an example Timoshenko beam subjected to stationary or moving point loads.

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“…The present expression of general solutions given by (18) and (19) is equivalent to the expression for three frequency ranges, 0 < < , = , and > , by van Rensburg and van der Merwe [28].…”

Section: Mathematical Model Of a Timoshenko Beam The Governing Equatmentioning

confidence: 93%

“…where The general solution at = can be readily obtained from either (18) or (19), by allowing to approach , as follows: (47)…”

Section: Natural Frequencies and Mode Shapesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

Kim

Park

Lee

2017

Shock and Vibration

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“…The Galerkin method is a common tool for dealing with dynamical problems for such cases. Convergences of Galerkin truncation for dynamical response of beams on nonlinear foundations [58] and Timoshenko beams resting on a six-parameter foundation [59] under a moving load were studied based on the asphalt pavement resting on soft soil foundation moving the vehicle. In Figure 5, l is the length of the elastic beam resting on foundations, n is the truncation term.…”

Section: Convergence Studies On the Continua On The Nonlinear Foundationmentioning

confidence: 99%

Convergence of the Galerkin Method for Nonlinear Dynamics of the Continuous Structure

Ding

2015

J. Adv. App. Comput. Math.

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The Galerkin truncation method is a powerful method for nonlinear dynamics analysis, and has been widely used to discretize the spatial differential operator. Due to more and more new fields of application, the research interest on the Galerkin method is still high today. In this paper, research on the convergence of Galerkin method for nonlinear dynamics of the continuous structure is thoroughly reviewed. At the beginning, the Galerkin method is briefly introduced. Then, the paper reviews the application of the truncation method. This paper also sums up the comparative study on the Galerkin method with other methods, such as the finite difference method (FDM), the finite element method (FEM), and the multiple time scales method. In the investigations concerning the convergence of the Galerkin method, this paper summarizes recent studies on nonlinear dynamics of the axially moving systems, the continua on the nonlinear foundation, and the belt-pulley systems. Finally, the truncation terms of Galerkin method for the continuous structure's nonlinear dynamics analysis is suggested for the future research applications.

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“…The differential equations were obtained byemploying the Timoshenko beam theory and were solved based on the Adomian decomposition methodand a perturbation method in conjunction with complex Fourier transformation. The dynamic response of finite Timoshenko beamsresting on a six parameter foundation was studied by Yang et al (2013).…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic Substrates Effects on the Elimination or Reduction of the Sandwich Structures Oscillations Based on the Kelvin-Voigt Model

Molla-Alipur

Rajabi

2017

Lat. Am. j. solids struct.

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Effects of viscoelastic substrates on the sandwich structures oscillations are examined in this paper. In this regard, dynamic response of sandwich annular panels with FG polar orthotropic face sheets resting on viscoelastic substrate is presented. Young's modulus in the radial and circumferential direction, shear modulus and density of each face sheet may be varied continuously in the radial direction. The viscoelastic substrate is modeled as Kelvin-Voigt foundation. To describe more accurately response of sandwich structures, the governing dynamical equations are derived based on the layerwise theory and five systems of second order coupled partial differential equations are obtained. The effects of the stiffness and damping coefficients of the foundation on the dynamic behavior of sandwich plate are investigated for various transient loads and boundary condition. Since no available results may be found in literature to demonstrate the efficiency and accuracy of the obtained results, the obtained results are verified by comparison with finite element results based on the three dimensional theory of elasticity for some special cases.

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Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation

Cited by 46 publications

References 23 publications

Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

Convergence of the Galerkin Method for Nonlinear Dynamics of the Continuous Structure

Viscoelastic Substrates Effects on the Elimination or Reduction of the Sandwich Structures Oscillations Based on the Kelvin-Voigt Model

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