Using the developed element, the natural frequencies of beams having various boundary conditions are computed for different values of the axial force and foundation stiffness. The influence of the axial force and the foundation stiffness on the frequency of the beams is investigated. The effect of partial support by the foundation and the type of mass matrices on the vibration frequency of the beam is also studied and highlighted. | Vietnam Journal of Mecha nics, VAST, Vol. 28, No. 4 (2006), pp. 241 - 251 VIBRATION FREQUENCY OF PRESTRESS SLENDER BEAMS RESTING ON WINKLER ELASTIC FOUNDATION NGUYEN DINH KIEN Institute of Mechanics , VAST Abstract. The present paper investigates the vibration frequency of slender beams prestressing by axial force and resting on an elastic Winkler foundation by the finite element method. A beam element taking the effects of both the prestress and foundation support into account is formulated using t he expression of strain energy. Using the developed element, the natural frequencies of beams having various boundary conditions are computed for different values of the axial force and found ation stiffness. The influence of the axial force and the foundation stiffness on the frequency of the beams is investigated . The effect of partial support by the foundation and the type of mass matrices on the vibration frequency of the beam is also studied and highlighted. 1. INTRODUCTION Prestress beams formed by inducing axial force are common structural elements in civil engineering. With the presence of the axial force , both the static and dynamic characteristics of the structure are altered. The effect of the axial load can be explained by alternation of the bending stiffness of the structure under the load. Thus, buckling occurs when the compressive membrane forces are large enough to reduce the bending stiffness to zero [1] . At the same time, the vibration frequency of the beam is very much affected by the membrane force, and it is rapidly reduced with the compressive membrane force. From practical point of view , the problem of analyzing beams resting on an elastic foundation has many applications. Examples include a rail on a roadbed or a pavement slab on soil. The rail or slab must be analyzed, and the effect of the roadbed or soil support must be modelled. The effect of foundation support on the deflection and buckling of the beam has been studied for different
