۱- Introduction

۲- Mathematical modeling

۳- Eigen value analysis

۴- Random vibration modeling

۵- Conclusion

References

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.

Introduction

Protection of engineering structures against un-wanted vibrations have always been a challenge for civil and mechanical engineers. In building constructions, an earthquake can bring about severe unwelcomed vibrations of the system and produce large stresses which ultimately can lead to catastrophic collapse of the structure. So researchers have been trying to innovate new techniques to study the vibrational phenomena in such structures and also to develop new vibration suppression techniques to minimize their vibration level. In some studies, the earthquakes have been modeled as harmonic support motion. For example Farshidianfar and Soheili [1] investigated the optimized parameters of tuned mass dampers for high rise structures considering soil structure interaction effects under harmonic base excitations. Park and Reed [2] examined the performance of uniformly and linearly distributed multiple mass dampers in suppressing the vibrations resulted from harmonic and earthquake excitations. In practice, the nature of earthquake is not deterministic. So in many other studies, the vibrational response of buildings and other mechanical systems has been analyzed based on the hypothesis of random excitations. For example, Kiureghian and Neuenhofer [3] developed a new response spectrum method for seismic analysis of linear multi-degree-of-freedom, multiply supported structures subjected to spatially varying ground motions. Heredia-Zavoni and Vanmarcke [4] employed the random-vibration methodology to study the seismic random response analysis of linear multi support structural systems. While respecting the stationarity assumption, their method, simplified the random analysis by equalizing the response evaluation of the system to that of a series of linear one-degree systems. Wen [5] provided an overview of the major developments in modeling and response analysis of inelastic structures under random excitations. Kiureghian [6] developed a response spectrum method for stationary random vibration analysis of linear, multi-degree-of-freedom systems.