Conclusion
Investigation of the dynamic response of the buildings under earthquake loads is an important step in the design of these constructions. Such a study can be complicated in different ways. First, the nature of the earthquake excitations is random which intricates the simulations. Also, buildings are multi-body systems consisting of rigid masses (representing the floors) interconnected to some flexible beams (representing the walls). As far as the authors knew, the researchers had not yet provided an accurate multi-body distributed parameter model for the vibratory behavior of such structures, but they usually considered a simple lumped parameter model for the system. So, the objective of the current paper was to provide a more comprehensive and accurate model for dynamic analysis of buildings under the effect of random loads. The equations of motion and the corresponding boundary conditions were derived based on Hamilton's principle. The exact eigen value problem were solved and analytical expressions were derived for mode shapes of the system which were validated via FEA. Then utilizing a single mode assumption, the response of the building to stochastic motion of the support were also simulated based on the random vibration theory and closed-form expressions were provided for different statistical parameters of the response in terms of those of the excitation. Specifically, the mean, autocorrelation, spectral density and the mean square of the relative deflection of the floors were obtained and the effect of different design parameters on the random response of the structure were discussed.
