On the Application of Weak Form Integral Equations to Free Vibration Analysis of Tall Structures

In this paper, an analytical approach is presented for free vibration analysis of tall structures with various lateral resisting systems and variable properties along the height. Primarily, according to replacement beam theory, the tall structure is modeled by a non-prismatic Timoshenko beam with shear and global bending stiffness which is supported laterally by a beam with local bending stiffness. The vibration frequencies of shear beam, bending beam and as well as Timoshenko beam are calculated and the vibration frequencies of tall structure are obtained by combination of the obtained vibration frequencies. Presented analytical approach is also used to calculate the mode shape functions and internal forces of the tall structure. The efficiency and accuracy of the current approach are confirmed through comparison of the numerical results to those obtained using available finite-element software and other references.