Investigation of auto-correlation function and mathematic expected value to determine the maximum response of the structure due to random earthquake loading

Abstract eng:
Structures experiment different kinds of static and dynamic loads. Most of the time, they are random loads such as dynamic instrumental loads, explosion and the future earthquake loads do not have a deterministic distribution and occurs randomly. The most important property of random loading is being non periodic which makes the determination of the exact analytical amount impossible unless by investigation of probabilistic theory and random vibration theory, one can guess the probabilistic and maximum amount of it. At this paper, the dynamic equilibrium equation on an assumed area has been determined. Then, by calculating the response function in terms of time, applying response mean value, Auto-Correlation Functions, distribution functions and mathematic expected value and also by using the amount of density, the response of structure due to unique impulse in the frequency domain has been determined. Then the total response of the structure or mean square response of the system has been determined by defining input spectrum density and response spectrum density and finally an example has been solved.

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