Abstract
In the paper vibrations of the Timoshenko beam on an inertial foundation subjected to a moving force are discussed. Considered model of the inertial foundation is described by three parameters. They take into account elasticity, shear and inertia of the subgrade. In the literature such model of the subgrade is called Vlasov or Vlasov-Leontiev model. The Timoshenko beam is traversed by a concentrated load, moving with uniform speed. Response of the beam is found from the governing equations of motion of the problem. Problem of forced vibrations and problem of free vibrations of the beam are solved. Damping of the system is taken into consideration. Solution of the problem is illustrated by numerical example.
Highlights
IntroductionThe problem of vibration of beams and plates, resting on foundations and subjected to moving loads is closely related to the dynamics of bridges, roads, airfield and railway pavements [1, 2, 3]
The problem of vibration of beams and plates, resting on foundations and subjected to moving loads is closely related to the dynamics of bridges, roads, airfield and railway pavements [1, 2, 3].A mathematical model describing transverse vibrations of a beam, including the effects of rotatory inertia and shear deformations, was presented by Timoshenko [4, 5]
The model is described by two coupled partial, differential equations of motion with two independent variables: transverse displacement w w x,t and rotation of the beam cross section x,t
Summary
The problem of vibration of beams and plates, resting on foundations and subjected to moving loads is closely related to the dynamics of bridges, roads, airfield and railway pavements [1, 2, 3]. A mathematical model describing transverse vibrations of a beam, including the effects of rotatory inertia and shear deformations, was presented by Timoshenko [4, 5]. Most often the subgrade is modelled as an elastic foundation and the analyses are based on the model of subgrade presented by Winkler [12], e.g. The Pasternak model consists of the Winkler foundation and includes shear interaction but does not take into account inertia of subsoil. In the paper we consider the soil model which is defined by three parameters. They take into account elasticity, shear and inertia of subgrade. The Timoshenko beam resting on a such inertial foundation and subjected to a moving force is analysed. Solution of forced vibrations and free vibrations along with numerical example are presented
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