Vibrations of a Timoshenko beam on an inertial foundation under a moving load

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.

Use of the Finite Element Method in Predicting Vibrations of Sandwich Beams and Plates Resting on Deformable Foundations Subjected to Moving Loads

“…Vibrations of sandwich structures (such as two beams or plates bonded by an elastic layer) excited by moving loads were also investigated. This subject was studied by Oniszczuk [48], Szcześniak [55][56], Ataman [4], Ataman and Szcześniak [5] and many others while beams of transversely nonuniform stiffness subjected to the action of a moving load are studied in [6] and [7].…”