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In recent years, seismic evaluation and design techniques which are able to evaluate cumulative damage have been required. Authors have dealt with this issue from the viewpoint of the energy balance equation. The energy balance equation expresses cumulative information of response, so that the energy balance equation is adequate for the evaluation of the influence of cumulative load such as seismic response. Authors have already clarified qualitative relationships between input energy and fatigue failure of simple single degree of freedom system. However, in order to apply energy balance equation on actual structure for seismic evaluation, expansion of it to multiple degree of freedom systems is required. Therefore this paper proposes three types of energy balance equation for multiple degree of freedom systems, that is a matrix method, an each mass method and a modal method. Energy balance equation by the matrix method indicates energy of a whole system. The equation by the each mass method indicates energy of each mass. The equation by the modal method indicates energy of each mode. In this paper, behaviors and features are investigated by numerical simulation and vibration experiment.

Structural strengths of the piping and components in NPPs have been designed with seismic margin. They are classified seismically S, B and C class in terms of the influence rate to nuclear safety. For the highest seismic class (Class S) equipment, it is clarified that they have enough seismic margins against design seismic conditions by shaking table tests or numerical simulations. However, for the lower seismic class (Class B and C) equipment, their seismic margins have not been clarified quantitatively. In this paper, in order to evaluate seismic robustness of the lower seismic class equipment with no clarification of seismic margin, seismic influences of the lower seismic class equipment in NPPs damaged by actual large earthquakes have been surveyed and sorted as a database, and the integrity of the lower class equipment have been discussed. Seismic effects on 24 plants damaged by the recent large 6-earthquakes are surveyed, sorted as a database, and investigated. As a result, a total of 29 cases of function deterioration or loss were observed. Considering the total number of components and piping, the frequency of those cases in class B and C components and piping was low. And also, as it is found there are a few cases of degradation or loss of function in the equipment installed on the bedrock or in the buildings.