A Mathematical Model Of a Vibrating Soil-Foundation System
01 January 1966
Numerous attempts have been made to develop a mathematical model capable of representing the steady-state vibrations of a soilfoundation system. E. Reissner 1 solved the problem of vertical vibrations of a rigid circular plate on a semi-infinite elastic solid. A sign error in his work was discovered by O. J. Sechter 2 who presented also a corrected analytical solution for this case. T. Y. Sung 3 continued this work for different pressure distributions between the plate and the solid. G. N. Bycroft 4 presented approximate solutions of the steady-state vibrations for the degrees of freedom of a rigid circular plate on an elastic isotropic half-space and on an elastic stratum. Since the mathematical solutions become rather difficult, this approach has been used only for a strongly idealized soil, namely the semi-infinite elastic isotropic solid. Another approach to this problem is the determination of a simplified mathematical model capable of describing the vibrations of a soil-foundation system. O. J. Sechter 2 showed that the amplitude-frequency response curve of a vibrating system consisting of constant mass, viscous damping force, and linear spring constant differs only slightly from that 177