A comparison of dynamic responses of three versions of moving load problem involving elastic rectangular plates

Abstract

The dynamic responses of an elastic rectangular plate to some types of moving loads’ distribution are obtained and compared. The partial differential equation describing the force vibration of each system comprising of the elastic rectangular plate and moving load is expressed in terms of each of the three moving loads’ distribution respectively. The three moving loads’ distribution considered are concentrated, uniformly and linearly distributed moving masses. An assumed Series solution in the form of the separation of variables is employed to transform each equation of motion into an ordinary coupled differential equation whose solution is obtained in form of a Duhamel integral. Numerical results are presented for simply supported boundary conditions in graphical and tabular forms. It is found that velocity, moving load’s distribution and mass ratio (Msr) significantly affect the vibration of the elastic rectangular plate.

Keywords

Comparison deflection amplitudes dynamic responses elastic plates moving load’s distribution

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References

Esmailzadeh E. and Ghorashi M. ( 1995) Vibration analysis of beams traversed by uniform partially distributed moving masses. Journal of Sound and Vibration 184(1): 9-17.

Esmailzadeh E. and Ghorashi M. ( 1997) Vibration analysis of Timoshenko beams subjected to a travelling mass. Journal of Sound and Vibration 199(4): 615-628.

Fryba L. ( 1972) Vibration of Solids and Structures under Moving Loads . Groningen, The Netherlands: Research Institute of Transport, Noordhoff International Publishing .

Gbadeyan JA and Dada MS ( 2001) The dynamic response of plates on Pasternak Foundation to distributed moving load. Journal of Nigerian Association of Mathematical Physics 5: 186-200.

Gbadeyan JA and Dada MS ( 2006) Dynamic response of a Mindlun Elastic Rectangular Plate under a distributed moving mass. International Journal of Mechanical Sciences 48: 323-340.

Gbadeyan JA and Dada MS ( 2008) On the dynamic responses of beams subjected to non-uniform distributed moving masses. Far East Journal of Applied Mathematics 33(1): 43-59.

Gbadeyan JA and Oni ST ( 1992) Dynamic response to the moving concentrated masses of elastic plate on a nonwinkler elastic foundation. Journal of Sound and Vibration 154(2): 343-358.

Michaltsos GT and Kounads AN ( 2001) The effect of centripetal and crioloris forces on the dynamic response of light bridges under moving load. Journal of Vibration and Control 7: 315-326.

Pilkey WD and Pilkey OH ( 1974) Mechanics of Solids. New York : Quantum Publishers.

10.

Sadiku S. and Leipholz HHE ( 1987) On the dynamic of elastic system with moving concentrated masses. Ingenieur-Archiv 59: 229-242.

11.

Stanistic MM and Hardin JC ( 1969) On the response of beams to an arbitrary number of moving masses. Journal of Franklin Institute 287: 115-123.

12.

Timoshenko SP ( 1953) History of the Strength of Materials. New York: D. Van Nostrand.