Influence of foundation and axial force on the vibration of thin beam under variable harmonic moving load

Awodola, T. O.

doi:10.4314/jonamp.v9i1.40040

Cited by 2 publications

(3 citation statements)

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“…We shall adopt the example in [5] and take the moving load to be of the form; P(x, t) = P(t) [ x -( x 0 + sin t ) ] (2.5a) for load moving with variable velocity. and P(x, t) = P(t) [ x -ct] (2.5b) for load moving with constant velocity where P(t) is the variable magnitude of the load, sin t is the distance function which makes the velocity of the moving load a variable, c is the constant velocity and x 0 , and are constants.…”

Section: The Governing Equationmentioning

confidence: 99%

“…Kenny [4] investigated the dynamic response of finite elastic beam under the influence of a dynamic load moving with constant speed. Awodola [5] analyzed the influence of foundation and axial force on the vibration of thin beam under variable harmonic moving load. However, the above studies failed to give the effect of variable velocity on the transverse displacement of a thin beam subjected to moving loads.…”

Section: Introductionmentioning

confidence: 99%

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Variable Velocity Influence on the Vibration of Simply Supported Bernoulli - Euler Beam Under Exponentially Varying Magnitude Moving Load

Awodola¹

2007

J. of Mathematics and Statistics

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Abstract:The variable velocity influence on the vibration of a simply supported Bernoulli-Euler beam, resting on a uniform foundation, under the action of an exponentially varying magnitude load moving with variable velocity is investigated in this work. The technique is based on the Finite Fourier Sine transformation and the Finite Difference method. Numerical results in plotted curves are presented. It is observed from the plotted curves that, when the foundation modulli 'K' and the axial force 'N' are fixed, the transverse deflections of the beam under load moving with variable velocity are higher than the deflections when the load moves with constant velocity. It is also observed that the response amplitudes in both cases of variable velocity and constant velocity decrease both with increasing 'K' and with increasing 'N'. Also, the analysis shows that the effects of the foundation modulli 'K' and the axial force 'N' are more pronounced in the vibration of the beam under load moving with variable velocity than in the case when the load moves with constant velocity, hence more reinforcement is needed when the load moves with variable velocity.

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Section: The Governing Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Variable Velocity Influence on the Vibration of Simply Supported Bernoulli - Euler Beam Under Exponentially Varying Magnitude Moving Load

Awodola¹

2007

J. of Mathematics and Statistics

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“…The effect of the moving load velocity on the dynamic displacement response of the beam is discussed. Recently, Awodola [9] considered the influence of foundation and axial force on the vibration of thin beam under variable harmonic moving load. The technique is based on the finite Fourier sine transformation.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response to Variable-magnitude Moving Distributed Masses of Bernoulli-Euler Beam Resting on Bi-parametric Elastic Foundation

Adeniyi¹,

Olubunmi²

2017

ARJOM

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This work investigates the problem of dynamic response to variable-magnitude moving distributed masses of Bernoulli-Euler beam resting on bi-parametric elastic foundation. The governing equation is a fourth order partial differential equation with variable and singular co-efficients. This equation is reduced to a set of coupled second order ordinary differential equation by the method of Garlerkin. For the solutions of these equations, two cases are considered; (1) the moving force case -when the inertia is neglected and (2) the moving mass case -when the inertia term is retained. To solve the moving force problem, the Laplace transformation and convolution theory are used to obtain the transversedisplacement response to a moving variable-magnitude distributed force of the Bernoulli-Euler beam resting on a bi-parametric elastic foundation. For the solution of the moving mass problem, the celebrated struble's technique could not simplify the coupled second order ordinary differential equation with singular and variable co-efficient because of the variability of the load magnitude; hence use is made of a numerical technique, precisely the Runge-Kutta of fourth order is used to solve the moving mass problem of the response to variable-magnitude moving distributed masses of Bernoulli-Euler beam resting on Pasternak elastic foundation. The analytical and the numerical solutions of the moving force problem are

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Influence of foundation and axial force on the vibration of thin beam under variable harmonic moving load

Cited by 2 publications

References 0 publications

Variable Velocity Influence on the Vibration of Simply Supported Bernoulli - Euler Beam Under Exponentially Varying Magnitude Moving Load

Variable Velocity Influence on the Vibration of Simply Supported Bernoulli - Euler Beam Under Exponentially Varying Magnitude Moving Load

Dynamic Response to Variable-magnitude Moving Distributed Masses of Bernoulli-Euler Beam Resting on Bi-parametric Elastic Foundation

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