Vibration of Multi-Span Non-Uniform Beams Under Moving Loads by Using Modified Beam Vibration Functions

Zheng, D.Y.; Cheung, Y.K.; Au, Ftk; Cheng, Yao

doi:10.1006/jsvi.1997.1435

Cited by 122 publications

(49 citation statements)

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“…Zheng et. al [1] gave a general solution dynamical problem of an infinite beam on an elastic foundation. Lee [2] investigated the dynamic response of a Timoshenko beam on a Winkler foundation subjected to a moving mass.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force

et al. 2010

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In this paper the dynamic response of a simply-supported, finite length Euler-Bernoulli beam with uniform cross-section resting on a linear and nonlinear viscoelastic foundation acted upon by a moving concentrated force is studied. The Galerkin method is utilized in order to solve the governing equations of motion. Results are compared with the finite element solution for the linear foundation model in order to validate the accuracy of the solution technique. A good agreement between the two solution techniques is observed. The effect of the nonlinearity of foundation stiffness on beam displacement is analyzed for different damping ratios and different speeds of the moving load. The results for the time response of the midpoint of the beam are presented graphically.

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Section: Introductionmentioning

confidence: 99%

Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force

et al. 2010

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“…Due to the importance of this problem, many papers have appeared in the literature. Compared with the problem of beams subjected to moving loads (see [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68]), the number of studies related to the vibration of plates due to moving loads is rather limited. Gbadeyan and Oni [69] developed a theory related to the response of Rayleigh beams and plates under an arbitrary number of moving masses.…”

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confidence: 99%

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

et al. 2015

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This study deals with forced vibration analysis of a microplate subjected to a moving load. The formulation is developed based on the modified couple stress theory in conjunction with Kirchhoff-Love plate theory. The equations of motion of the problem are derived using Lagrange's equations. In order to obtain the response of the microplate, the trial function for the dynamic deflection is expressed in the polynomial form. The equations of motion are solved by using the implicit time integration Newmark-β method, and then displacements, velocities and accelerations of the microplate at the considered point and time are determined. Five different sets of boundary condition are considered. For this purpose, boundary conditions are satisfied by adding some auxiliary functions to the trial functions. A parametric study is conducted to study the effects of the material length scale parameter, plate aspect ratio, boundary conditions and the moving load velocity on the dynamic response of the microplate. Also, in order to validate the present formulation and solution method, some comparisons with those available in the literature are performed. Good agreement is found. The results show that the dynamic deflections are significantly affected by the scale parameter and the load velocity.

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“…In passing, we observe that (17) has the 'wavenumber harmonic series' form adopted by Cheng et al [32,33], i.e.…”

Section: Steadily Moving Concentrated Loadmentioning

confidence: 97%

Floating ladder track response to a steadily moving load

Hosking

Milinazzo

2007

Math Methods in App Sciences

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SUMMARYFloating ladder rail tracks, which can significantly reduce traffic vibration and noise, have already been installed at several railway sites in and around Tokyo. The steel rails are fixed onto successive ladder-like sections with two parallel longitudinal reinforced concrete sleepers, which are then mounted upon discrete resilient supports on a concrete bed. A simple mathematical model in which a continuous horizontal Bernoulli-Euler beam on periodic discrete elastic supports represents each floating 'combined rail' (i.e. rail and longitudinal sleeper), used earlier to discuss the low-frequency free vibrations in the system, is again adopted to investigate the response due to a steadily moving load. We demonstrate that Fourier transforms can be invoked to obtain the forced deflexion, which depends upon the load speed. A contribution from the periodic supports determines the steady component of the deflexion moving with the load, and the other contributions from the supports produce oscillations. As is the case for a load moving over a beam or plate with continuous support, the response may be characterized using the free flexural wave dispersion relation-although there is now a countably infinite number of dispersion curves, corresponding to the existence of propagation bands in the periodic structure. The lowest wavenumber local minimum in the phase speed (coincident with the group speed) defines the primary critical load speed of most interest, at which the magnitude of the steady component accompanying the moving load becomes large. This primary critical load speed depends upon the relative elasticity of the discrete supports, which must not be too low if the floating ladder track is to be safe for fast rail systems.

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Vibration of Multi-Span Non-Uniform Beams Under Moving Loads by Using Modified Beam Vibration Functions

Cited by 122 publications

References 0 publications

Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force

Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

Floating ladder track response to a steadily moving load

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