Special dynamic soilstructure analysis procedures demonstrated for two tower-like structures

Many problems in Earthquake Engineering require the modeling of the structure as a dynamic system including the sub-grade. A structural engineer is usually familiar with the Finite Element Method but has a problem modeling the sub-grade when its infinite extension and wave propagation are the essential features. If the dynamic equation of a soil-structure system is written in a frequency domain and the variables of the system are total displacements, then the governing equations are given as in statics. The dynamic stiffness matrix of the system is obtained as the sum of the stiffnesses of the structure and sub-grade sub-structures. To illustrate the influence of the sub-grade on the dynamic behavior of the structure, the frequency response of two tower-like structures excited by a seismic harmonic wave field is shown. The sub-grade is modeled as an elastic homogeneous half-space. The structure is modeled as a finite beam element with lumped masses