Single variable shear deformation theory for free vibration and harmonic response of frames on flexible foundation

Abstract

A single variable shear deformation theory (SVSDT) is applied to free vibrations and harmonic response analysis of a multi-storey frame model considering flexibility of foundation. The column-foundation joints are modelled using three-spring approach instead of fixed support assumption to show the effects of soil-structure interaction (SSI) on the dynamic behaviour of frame model. The dynamic stiffness formulations are used for both free vibration and harmonic response analysis. The results that obtained using SVSDT and Timoshenko beam theory (TBT) are presented comparatively. The calculated natural frequencies are verified by finite element method (FEM). The convergence of FEM for the first three natural frequencies is presented for the fixed supported frame and frame considering SSI. The harmonic response curves are used to reveal the resonant and anti-resonant frequencies directly. It is seen that using a lateral displacement response for harmonic response curves may cause to miss natural frequencies of axial dominant modes of the frame model. However, all required natural frequency values of multi-storey frames considering foundation flexibility can be obtained via harmonic response curves that plotted by using a vertical displacement response of a node of model. Moreover, the proposed approach is validated by experimental data for scaled frame models, which are fixed supported and flexibly supported, respectively. The computation times for harmonic responses are tabulated for frame model on flexible foundation as well as fixed support assumption.