Generally seismic design of mechanical structures is based on static force in elastic region. However dynamic cyclic load may causes cumulative damage, and such damage induces fatigue failure on the structures. In addition, evaluation method of soundness after a huge earthquake is also required. Therefore quantitative evaluation of cumulative damage by earthquakes is required. Authors have investigated 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, expansion of it to multi-degree-of-freedom systems is required. This paper proposes extension method of energy balance equation to multi-degree-of-freedom system. This paper investigates 2-degree-of-freedom model as an example of multi-degree-of-freedom model, and relationship between energy and failure is investigated by vibration experiment.

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