Mathematical modelling of tall buildings and its foundation under randomly fluctuating wind and earthquake ground motions

In the present paper, a non-dimensional mathematical model for high tower buildings and its foundation under randomly fluctuating wind loads and earthquake ground motions excitations is developed as a nonlinear model to study the system more extensively. The system main equations could be derived using two different derivation methods and linearized in minimal symbolic forms; which facilitate a subsequent numerical simulation in order to investigate the vibration characteristics of whole system. The analysis enables designers to have more insight into the characteristics of high tower buildings of similar configuration but with different geometry and material. The complexity of wind loading with its variations in space and time has been considered. A comprehensive mathematical model of six degrees of freedom is presented and solved for free and forced vibrations.

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