free vibration of tall buildings using energy method and hamilton’s principle

free vibration of tall buildings using energy method and hamilton’s principle

in a framed-tube tall building, shear wall systems are the most efficient structural systems for increasing the lateral load resistance. a novel and simple mathematical model is developed herein which calculates the natural frequencies of such tall buildings. the analyses are based on a continuous model, in which a tall building structure is replaced by an idealized cantilever beam that embodies all relevant structural characteristics.

governing equations and the corresponding eigen-problem are derived based on the energy method and hamilton’s principle. solutions are obtained for three examples; using the separation of variables technique implemented in matlab. the results are compared to sap2000 full model analysis; and they indicate reasonable accuracy. the computed natural frequencies for structures 50, 60 and 70 storey buildings were over-estimate 7, 11 and 14 percent respectively. the computed errors indicate that the proposed method has acceptable accuracy; and can be used during the initial stages of designing of tall buildings; it is fast and low cost computational process.