Moving load

[4] Inertial load in numerical models is described in [5] 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.

[citation needed] The critical velocity, at which the growth of displacements is the maximum, must be taken into account in engineering projects.

[citation needed] Structures that carry moving loads can have finite dimensions or can be infinite and supported periodically or placed on the elastic foundation.

[citation needed] Consider simply supported string of the length l, cross-sectional area A, mass density ρ, tensile force N, subjected to a constant force P moving with constant velocity v. The motion equation of the string under the moving force has a form[citation needed] Displacements of any point of the simply supported string is given by the sinus series[citation needed] where and the natural circular frequency of the string In the case of inertial moving load, the analytical solutions are unknown.

[citation needed] The equation of motion is increased by the term related to the inertia of the moving load.

A concentrated mass m accompanied by a point force P:[citation needed] The last term, because of complexity of computations, is often neglected by engineers.

[citation needed] In higher ranges both the amplitude and the frequency of vibrations differ significantly in the case of both types of a load.

[citation needed] Consider a massless string, which is a particular case of moving inertial load problem.