دانلود رایگان مقاله انگلیسی تحلیل ارتعاش تصادفی ساختمان های چند طبقه با استفاده از یک مدل پارامتر توزیع شده - الزویر 2018

ABSTRACT

The objective of the current paper is to provide an accurate distributed parameter model for random vibration analysis of multi-floor buildings. The Hamilton's principle is employed to derive the equations governing the dynamic behavior of the system as well as the related kinematic and natural boundary conditions. The natural frequency and mode shapes of the developed model are then extracted analytically and validated using finite element simulations. It is also observed that the predictions of the proposed model for the natural frequencies of the system is far more accurate than those of that of the discrete model available in the literature. Using a single mode approximation in the Lagrange equation, the partial differential equations of the motion are reduced to a single ordinary differential equation. Assuming a band limited white noise for the acceleration of the support, the random response specifications (such as expected value, autocorrelation, spectral density and mean square) of the system is calculated by making use of the random vibration theory. The qualitative and quantitative nature of the response characteristic are also analyzed to reveal the effects of different design parameters on the system's response. The suggested modeling approach in this paper may be employed for prediction of the dynamic behavior of more complex structures to different types of deterministic or random excitations. Also the provided analytical method for the random response calculation of the system can be utilized to make more informed decisions in the design process.

 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.