Free vibrations of rigid massive rectangular foundations embedded in a viscoelastic half-space

A method is presented to analyse the free vibration of a rigid massive rectangular foundation buried to some extent beneath the surface of the ground. The response is evaluated using the complex eigenvalue analysis which is mathematically accurate and employs complex, nonclassical vibration modes. Taking the frequency dependence of dynamic impedance functions for the embedded foundation into account, the dimension less damped natural frequency for each mode is obtained as a single real root of transcendental real frequency equation. The numerical results including the dynamic interaction effects are compared with those obtained at neglected radiation damping in the supporting medium and based on static data. It is shown that the embedment of the foundation and the state of backfill considerably affect its complex eigenvalues.