On the Transverse motions under heavy loads of thin beams with variable prestress
In this paper, the effect of variable axial force on the dynamic response of elastic beam resting on elastic foundation and subjected to concentrated moving loads is investigated. The fourth order partial differential equation with variable and singular coefficients governing the motion of the elastic thin beam is solved using the Generalized Galerkin's Method and the Modified Asymptotic Method of Struble. It is established by both Analytical solution and Numerical analysis that, the higher the values of axial force N and the foundation rigidity K, the lower the response amplitudes of the elastic thin beam with variable prestress when it is under the action of the concentrated moving loads. Furthermore, it is found that the critical velocity for the system under the influence of the moving force is greater than that under the influence of the moving mass first approximation and moving mass entire beam model. Hence, resonance is reached earlier in the latter.
Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 127-142