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- Moving_load abstract "In structural dynamics this is the load that changes in time the place to which is applied. Examples: vehicles that pass bridges, trains on the track, guideways, etc. In computational models the load is usually applied as: a simple massless force, an oscillator, an inertial force (mass and a massless force).Numerous historical reviews concerning the moving load problem exist (for example,).Several publications deal with similar problems.The fundamental monograph is devoted to massless loads. Inertial load in numerical models are described in Unexpected property of differential equations that govern the motion of the mass particle travelling on the string, Timoshenko beam, and Mindlin plate is described in. It is the discontinuity of the mass trajectory near the end of the span (well visible in string at the speed v=0.5c). The moving load significantly increases displacements. The critical velocity, at which the growth of displacements is the maximum, must be taken into account in engineering projects.Structures that carry moving loads can have finite dimensions or can be infinite and supported periodically or placed on the elastic foundation. Let us consider simply supported string of the length l, cross-sectionalarea A, mass density ρ, tensile force N, subjected to a constant force Pmoving with constant velocity v. The motion equation of the string underthe moving force has a form Displacements of any point of the simply supported string is given bythe sinus series where and the natural circular frequency of the string In the case of inertial moving load the analytical solutions areunknown. The equation of motion is increased by the term related to theinertia of the moving load. A concentrated mass m accompanied by a pointforce P: The last term, because of complexity of computations, is often neglected by engineers. The load influence is reduced to the massless load term. Sometimes the oscillator is placed in the contact point. Such approaches are acceptable only in low range of the travelling load velocity. In higher ranges both the amplitude and the frequency of vibrations differ significantly in the case of both types of a load.The differential equation can be solved in a semi-analytical way only for simple problems. The series determining the solution converges well and 2-3 terms are sufficient in practice. More complex problems can be solved by the finite element method or space-time finite element method.The discontinuity of the mass trajectory is also well visible in the Timoshenko beam. High shear stiffness emphasizes the phenomenon.The Renaudot approach vs. the Yakushev approachThe Renaudot approach The Yakushev approach Massless string under moving inertial loadLet us consider a massless string, which is a particular case of movinginertial load problem. The first solve the problem Smith .The analysis will follow the solution of Fryba. Assumingρ=0, the equation of motion of a string under a moving mass canbe put into the following form We impose simply-supported boundary conditions and zero initialconditions. To solve this equation we use the convolution property. Weassume dimensionless displacements of the string y anddimensionless time τ : where wst is the static deflection in the middle ofthe string.The solution is given by a sum where α is the dimensionless parameters : Parameters a, b and c are given below In the case of α=1 the considered problem has a closed solution References".
- Moving_load thumbnail Cb_pant.png?width=300.
- Moving_load wikiPageID "37580917".
- Moving_load wikiPageRevisionID "601302306".
- Moving_load align "right".
- Moving_load alt "Force".
- Moving_load alt "Mass".
- Moving_load alt "Oscillator".
- Moving_load alt "Pantograph".
- Moving_load alt "Rifle".
- Moving_load alt "Train".
- Moving_load backgroundColor "#fffcbf".
- Moving_load caption "Force".
- Moving_load caption "Mass".
- Moving_load caption "Oscillator".
- Moving_load caption "Pantograph".
- Moving_load caption "Rifle".
- Moving_load caption "Train".
- Moving_load direction "vertical".
- Moving_load footer "Examples of a moving load.".
- Moving_load footer "Types of a moving load.".
- Moving_load footerBackground "#fffcbf".
- Moving_load hasPhotoCollection Moving_load.
- Moving_load image "Cb_pant.png".
- Moving_load image "Transrapid.jpg".
- Moving_load image "Winchester 1897.jpg".
- Moving_load image "force_as_a_load.png".
- Moving_load image "mass_as_a_load.png".
- Moving_load image "oscillator_a_s_a_load.png".
- Moving_load width "102".
- Moving_load width "104".
- Moving_load width "180".
- Moving_load width "70".
- Moving_load subject Category:Mechanical_vibrations.
- Moving_load comment "In structural dynamics this is the load that changes in time the place to which is applied. Examples: vehicles that pass bridges, trains on the track, guideways, etc. In computational models the load is usually applied as: a simple massless force, an oscillator, an inertial force (mass and a massless force).Numerous historical reviews concerning the moving load problem exist (for example,).Several publications deal with similar problems.The fundamental monograph is devoted to massless loads.".
- Moving_load label "Moving load".
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- Moving_load sameAs Q6927141.
- Moving_load sameAs Q6927141.
- Moving_load wasDerivedFrom Moving_load?oldid=601302306.
- Moving_load depiction Cb_pant.png.
- Moving_load isPrimaryTopicOf Moving_load.