Mathematical modelling of earthquake induced vibrations on multistory buildings

Abstract

Logically, the taller building will be collapsed with a small period. We will give the reason in mathematical ways according to our study. The ability to make predictions about the vibrations from the earthquake could enable scientist to evaluate or plans and may have a significant effect on the period of time for the building collapsed. The modelling of unforced and forced vibrations on multistory buildings are used as a tool to study the mechanisms of vibration that caused by an earthquake. Both models are used to calculate the natural frequencies,w and period, P of the building vibrations. Furthermore, the maximal amplitude of the building vibrations also can be analysed. For this research, eight, eleven and fifteen floors building have been applied. In our analysis, eigenvalues method is used via Maple 13 package. The graph of forced frequency versus amplitude and period versus maximal amplitude are plotted and discussed.