C Dynamics Respo Euler-Bernoulli Be F.O. Akinpelu Department of Pure and Applied Mathema University of Technology, Ogbom email: foakinpelu@yahoo. Abstract: The dynamic response of sim force Euler-Bernoulli beam subjected t distributed moving loads was examin fourth order partial differential equatio was first reduced to second order diffe assume a solution in form of series solut using maple software in order to determ the system under consideration. The ef beam on both the moving force and th examined. It was observed that as the increases, the transverse displacement (d increases for both the moving force an with respect to the tensile force and the c was also observed that as the axial displacement decreases under the action and the moving mass for the tensile force the compressive force, as the axial displacement is equally increases. Keywords: Axial Force, Beam, Pa Simply Supported I. INTRODUCTION Bridges and viaducts for high speed demanding dynamic loads and much la dangerous effects arise from dynamic re above 220 km/h. The basic dynam moving load on a simply supported be classical solutions among others by response of dynamic effect of movi known until mid-nineteenth century as bridge disaster which was a rail accid occurred on 24th May, 1847 precisel terrible incident caused tremendous created a lot of excitement in the field and this is what makes the study of with moving loads to be an inte discussion to the engineers and tho physics and applied mathematics. Akinpelu [1] examined the respo damped Euler-Bernoulli beam to distributed moving loads. The author beam has more than one mode of v mode having a different natural f discovered that as the mass of the amplitude is also increases and t magnification factor occurs for a value ε = 0.1. Copyright © 2015 IJISM, All right reserved 91 International Journal of Innovation in Sc Volume 3, Issue 2, ISS onse of Simply Supported A eam Subjected to Partially Moving Load atics, Ladoke Akintola moso, Nigeria. .co.uk S.O. Sangon Department of Mathematics, Emma Education, Oyo, N email: sangoniyisunday mply supported axial to uniform partially ned. The governing on for moving loads erential equation by tion and numerically mine the behaviour of ffect of mass of the he moving mass was e mass of the beam deflection) is equally nd the moving mass compressive force. It force increases the n of the moving force e while in the case of force increases the artially Distributed, N trains are subject to arger and potentially esonance for speeds mic response for a eam is known from Timoshenko. The ing loads was not s a result of the Dee dent in England that ly in Chester. This s human loss and of civil engineering dynamic structures eresting subject of ose in the field of onse of viscously uniform partially r observed that the vibration with each frequency. It was load increases the the value of the e ω less than one for The dynamic analysis of pre- beam was considered by I.A. A difference method was used to s boundary value problem numeri that the deflection of the moving Bernoulli beam was greater tha force. Dynamic response of loads on force Rayleigh beam was studied Baba Seidu [3]. The theory i functions and the results indica differential equation can be tran couple ordinary differential equati for the corresponding moving resulting governing differentia numerically by finite central diff concluded that the deflection d greater than that due to moving fo The response of initially stress with an attached mass to unifo moving loads was carried out by Gbadeyan [4]. The resulting cou equation is solved using finite d found that the response amplitude as mass of the load increases problem and also that the respo with an increase in the mass of th of time t and ε. Axial loaded beams on elastic f harmonic loads was investigated The work was based on the vibr infinite Euler-Bernoulli beam on applying a static axial force and a constant or harmonic amplitude system and some important result process of changing relative param Jaiswal and Iyengar [6] examin a beam on elastic foundation o moving force. The dynamics of finite elastic foundation base sub was studied. Again, the effects of as foundation mass, velocity of th and axial force on the beam were Response of beam on visc moving distributed load was exam and Wlodzimierz Czyczula [7] problems caused by a distributed l cience and Mathematics SN (Online): 2347–9051 Axial Force Distributed niyi anuel Alayande College of Nigeria. [email protected]m -stressed Euler-Bernoulli Adetunde [2]. The finite solve the pertinent initial ically and he concluded mass pre-stressed Euller- an those of the moving n viscously damped axial d by I. A. Adetunde and is based on orthogonal ates that the governing nsformed into a series of ions which is the solution distributed force. The al equation is solved ference method where he due to moving mass is orce. sed Euler-Bernoulli beam orm partially distributed Adetunde, Akinpelu and upled partial differential difference method. It was e increases s under a moving force onse amplitude increases he load for various values foundation under moving by Kim Seong-Min [5]. ration and stability of an a Winkler foundation by a moving load with either variations to excite the ts were obtained from the meters. ned dynamic response of of finite depth under a f the infinite beam on a bjected to a moving load f various parameters such he moving load, damping investigated. co-elastic foundation to mined by Roman Bogacz ] where the dynamical load which was acting on
Dynamics Response of Simply Supported Axial Force Euler-Bernoulli Beam Subjected to Partially Distributed Moving Load
May 17, 2023
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