Mathematical modelling of earthquake induce vibrations on multistory buildings

Logically, the taller building will collapse within a short 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 scientists to evaluate our plans and may have a significant effect on the period of time for the building to collapse. The modelling of unforced and forced vibrations on multistory buildings is used as a tool to study the mechanisms of vibration that are caused by an earthquake. Both models are used to calculate the natural frequencies, {J} 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-floor buildings have been applied. In our analysis, the eigenvalues method is used via Maple 13 package. The graph of forced frequency versus amplitude and period versus maximal amplitude are plotted and discussed