Natural frequencies and harmonic responses of multi-story frames using single variable shear deformation theory

This study aims to perform free and forced vibration analyses of multi-story frames using the single variable shear deformation theory (SVSDT). The free vibration analysis begins with constructing dynamic stiffness matrices based on analytical solutions to motion equations for frame members according to SVSDT, as well as the Timoshenko beam theory. The natural frequencies are calculated via a global dynamic stiffness matrix of the frame for different column and beam dimensions, and elastic modulus values. The natural frequency results are tabulated with finite element method results to verify the dynamic stiffness method, thereby providing exact values. The mode shapes are plotted, and forced vibration analysis is accomplished using a global dynamic stiffness matrix of the frame for different dynamic lateral load amplitude values. The harmonic response curves are depicted in a logarithmic scale to observe the resonance and anti-resonance frequencies. The numerical examples demonstrate that the SVSDT can be used effectively for the dynamic analysis of frames.