Analytical investigation of forced oscillations of bench foundations

Abstract

An analytical calculation is presented for the forced oscillations of bench foundations; results of comparison between experimental and computed data are described for Series K-lOOO foundations of IO00-MW turbinedriven sets, which suggest the possibility of practical use of the proposed method.The vibrational state of a turbine-driven-set/foundation/bed system is one of the basic factors determining the reliability of thermal and nuclear power plants. As the unit power of generating units increases, solution of the problem requires the development of methods for prediction of dynamic phenomena, especially for bench foundations. In that case, numerical methods encounter difficulties due to the large number of components and sudden changes in the parameters sought; analytical methods may, however, be found more preferable.Let us examine the forced oscillations of bench foundations in the vertical direction (Fig. 1). For the calculation, these foundations can, in first approximation, be represented in the form of a rectangular slab with walls-stiffeners (hereinafter called stiffeners), which are arranged at equal distances apart (Fig. 2). The stiffeners are calculated within the framework of the plane problem of the theory of elasticity, since their thickness is small in comparison to the length of the slab, which is sufficient for the stiffener to retain its stability. The effect of stiffener eccentricity relative to the median surface of the slab can be neglected, since this is essential only for a more precise definition of stresses in the plane of the slab. The slab is isotropic, and lies on a viscoelastic bed. The boundary conditions consist of a fixity, which permits vertical displacement, i.e., r-Ox=Wxxx =0 for x = +0,5LI; Wy=r~yyy=O for y = -+0,5L2.(1) A vertical concentrated dynamic load is applied at the center of the stiffeners along the longitudinal axis of the slab. Imagine the stiffeners to be separated from the slab, and the effect of the i-th stiffener on the slab replaced by the contact force u(x, z, t). The simplified homogeneous differential equation of the plane theory of elasticity [1] ~u a~u . ~u s--Z+o-AT-; = 0,