A method is presented for investigating the seismic response of multiple-story shear buildings on flexible elastic foundation media which are represented by an elastic half space. It is shown that the frequency dependent dynamic properties of the foundation medium may be assumed to be constant with respect to the frequency. This assumption leads to equations of motion with constant coefficients which are solved numerically. A study of several structure-foundation systems indicates that the flexibility of the foundation medium can increase or decrease the flexural response of the structure compared to the case of the rigid foundation.

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