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Coupled Systems Mechanics
  Volume 3, Number 3, September 2014, pages 247-265
DOI: http://dx.doi.org/10.12989/csm.2014.3.3.247
 


A new approach to modeling the dynamic response of Bernoulli-Euler beam under moving load
J.T. Maximov

 
Abstract
    This article discusses the dynamic response of Bernoulli-Euler straight beam with angular elastic supports subjected to moving load with variable velocity. A new engineering approach for determination of the dynamic effect from the moving load on the stressed and strained state of the beam has been developed. A dynamic coefficient, a ratio of the dynamic to the static deflection of the beam, has been defined on the base of an infinite geometrical absolutely summable series. Generalization of the R. Willis\' equation has been carried out: generalized boundary conditions have been introduced; the generalized elastic curve\'s equation on the base of infinite trigonometric series method has been obtained; the forces of inertia from normal and Coriolis accelerations and reduced beam mass have been taken into account. The influence of the boundary conditions and kinematic characteristics of the moving load on the dynamic coefficient has been investigated. As a result, the dynamic stressed and strained state has been obtained as a multiplication of the static one with the dynamic coefficient. The developed approach has been compared with a finite element one for a concrete engineering case and thus its authenticity has been proved.
 
Key Words
    Bernoulli-Euler beam; moving load; dynamic stress; dynamic deflection; elastic supports; FE analysis
 
Address
J.T. Maximov: Technical University of Gabrovo, Department of Applied Mechanicas, 5300 Gabrovo, Bulgaria
 

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