Free vibration analysis of tall buildings using a generalized continuous model: simplified approach to soil-structure interaction

Currently, due to the simplifications imposed on continuous models, there is an absence of a generalized approximate solution to investigate all possible dynamic behaviors of a tall building. In an attempt to address this deficiency, this paper proposes a new generalized continuous model and its solution methods to generalize all types of behavior that may be encountered in structural systems and tall buildings. The continuous model results from a composite beam that serially couples the classical sandwich beam and a pure shear beam. Unlike existing continuous models, the serial coupling, inclusion of new kinematic fields, and inclusion of rotational inertia allow for the resolution of complex interaction among different types of bending and shear behaviors. Specifically, it is shown how local shear behavior simultaneously interacts with global bending behavior, global shear, and local bending. Two solutions to the dynamic problem are presented: a closed-form analytical solution method for structures with uniformity along their height, and a numerical method that combines the advantages of the continuous method and the transfer matrix method to resolve structural and geometric variability in height. The transfer matrix is analytically solved by maintaining a fixed 6 × 6 matrix range that is independent of the number of levels of the structure, drastically reducing computational cost by eliminating the classical need to calculate the inverse of the zero matrix. Numerical applications investigate the effect of rotational inertia and local shear on the accuracy of the proposed results compared to results from the finite element method. To this end, a parametric analysis of 1560 different cases covering a wide range of typical behaviors in individual structural systems and tall buildings is conducted. The results exhibit promising accuracy, showing that the qualities of the proposed continuous model significantly improve precision compared to classical continuous models and therefore justify its practical application by academics and practicing engineers. Furthermore, the proposed mathematical approach is easily applicable in various domains of composite materials engineering.