Viscous damping is often represented by dashpot in earthquake engineering. However, it is seen that the process of earthquake wave attenuation cannot be fully explained by such representation. The restrictions of dashpot can be substantially relieved by application of the linear theory of fading memory. The theoretical solution to the problem of wave propagation in the ground with fading memory, together with the attenuation property Q (quality) factor, are presented. The memory functions of dashpot system, creep function, and hysteretic model arc discussed. It is concluded that the application of fading memory theory makes it possible to study the real dynamic behavior of ground. For the ground model to be realistic, justifiably pertinent memory function can be selected. The memory function may also be derived suitably from data.

Spatial wave attenuation in elastic material is investigated in light of attenuating neighborhood theory of continuum mechanics. The attenuating part of the constitutive equation is expressed by an integral function of strain over each point of the material. It is shown that the spatial attenuation can be determined independent of the temporal attenuation in the viscoelastic material with fading memory, discussed by the writers in their previous paper, where the nonelastic part of the constitutive equation is determined by a functional of strain rate. However, the functional expressions for constitutive law are similar. The linear theory of attenuating neighborhood is briefly introduced and the solution to plane wave equation is derived. Then the characteristics of spatial wave attenuation are investigated in wavenumber domain. The critical conditions for wave propagation are also discussed. The fading memory is utilized in the previous paper by the writers to express all the temporal characteristics of wave attenuation. The present study shows that the attenuating neighborhood theory can be advantageously utilized to express the characteristics of spatial attenuation, such as the wavenumber dependence of Q-I factor.

A new structural vibration control system called the Intelligent Passive Vibration Control (IPVC) System is presented. Such a system theoretically consists of two parts: a passive part (first) and an intelligent part (second). Generally, under small earthquake excitations, only the first part works as a base. isolation device. In the case of intense earthquake shaking, if the response (e.g the displacement response) of the structure exceeds the determined allowance of the first part, then the intelligent part also works to change the mechanical characteristics of the system. The general constitutive law and the mechanism of the system ale presented. Assuming the passive part and the intelligent part to be viscoelastic material with fading memory, the mechanics of such a new system have been studied, and the theoretical solution to the vibration equation is presented, Also a numerical simulation was done for a real twin structure (one is nonisolated and the Other is base isolated) built at the campus of Tohoku University together with one more structure having the IPVC system. The result clearly shows that the system is effective, especially for reduction of maximum displacement response.