Simplified Calculation Method of Seismic Response Energy of Mechanical System

When the mechanical systems are subjected to seismic excitation, the responses are nonstationary random process, since seismic excitation has nonstationary characteristics. Mean square response is a representative value of the statistical properties of the response. Seismic response energy which is integral of mean square response is used to evaluate absorbed energy and cumulative damage of mechanical system. Theoretical method for obtaining nonstationary mean square response of the secondary system is very complicated and time consuming. Thus, some approximate methods are sometimes used. In this paper, an approximate method for calculation method of seismic response energy using statistical properties of stationary response is proposed. As input excitation, nonstationary white noise is used. The input is defined by product of stationary white noise and envelope function. Mean square response of absolute acceleration of the mechanical system, relative velocity of the mechanical system to the ground and relative displacement are obtained. Some numerical results are shown. It is found that the proposed method gives exact values of seismic response energy independent of the damping ratio, mass ratio and the natural period.