Research On Energy Method Of Structures Subjected To Earthquake Based On Random Vibration

As we know,the earthquake frequently takes place in China.In Chinese history there were huge casualties and economic losses due to the earthquake disaster.So it is the main work of structural design that guaranteeing the security of the building structure when the earthquake occurrences.As the structural anti-seismic theory based on energy method fully reflects the nature of the seismic force,we can create many methods of structural anti-seismic design mainly according to the mechanism of energy principle.However,the ground motion is a stochastic process when there is an earthquake,and the energy response of the structure is also random.Therefore,in this paper,the ground motion is treated as a stationary random process,and the statistical characteristics of structural energy response under random earthquakes are studied by random vibration theory.According to the redefinition of seismic instantaneous input energy,focus on the analysis of statistical features of the seismic instantaneous input energy and seismic total input energy of the single degree of freedom and multiple degree of freedom linear system.The main research contents and results are as follows:1.The seismic motion is regarded as stationary random process.According to random vibration theory,the theoretical formulas of mean and variance of the seismic instantaneous energy and mean of the seismic total energy of single degree of freedom in linear system are derived in the frequency domain.The mean and variance of seismic instantaneous input energy are independent of time.Compared with the statistical result of much seismic energy reaction calculated by the time history analysis under random earthquakes,the accuracy and statistical properties of this theoretical formula has been proved.2.According to the theoretical formula derived from the previous paper,mean spectrum and variance spectrum of seismic instantaneous input energy of single degree of freedom in linear system has been studied and the main effects has been analysed.It turned out that damping ratio and self-vibration period in single degree of freedom have influence to mean spectrum and variance spectrum of seismic instantaneous input energy.In the same engineering situation,damping ratio will influence the peak value of the mean spectrum and variance spectrum heavily.When the self-vibration period of the structure is near the characteristic period of the site,the mean value of the seismic instantaneous input energy is maximum.The smaller the damping ratio of single degree of freedom linear system is,the greater the variance of the seismic instantaneous input energy is.3.The seismic motion is regarded as stationary random process.According to random vibration theory,the theoretical formulas of mean and variance of the seismic instantaneous input energy and mean of the seismic total input energy of multiple degree of freedom in linear system are derived in the frequency domain,using the mode decomposition method.The study finds that the linear multiple degree system can be decomposed into linear single degree system.The mean and variance of the seismic instantaneous input energy and mean of the seismic total input energy can be computed using the modal participation factor and seismic energy of various modes.The mean and variance of seismic instantaneous input energy are independent of time.Compared with the statistical result of much seismic energy reaction calculated by the time history analysis under random earthquakes,the accuracy and statistical properties of this theoretical formula has been proved.