Lateral shear‐St. Venant torsion coupled vibration of asymmetric‐plan frame structures

Free vibration analysis is presented for asymmetric‐plan frame structures. Emphasis of the analysis is given to the lateral–torsional vibration of the structures, where lateral shear vibrations in two orthogonal directions are coupled with St. Venant torsion vibration. Based on the continuum approach in tall building analysis, the governing equation of coupled vibration of the problem is developed, and the corresponding eigenvalue equation is then derived. A theoretical method of solution is proposed to solve the eigenvalue problem and a general solution is given to determine the natural frequencies and associated mode shapes of the structure. By following the proposed calculation procedure, frequencies of the coupled vibration are quickly determined and the corresponding mode shapes can clearly be displayed. The numerical investigation pertaining to coupled vibration analysis of a general asymmetric‐plan frame building shows that the results from the proposed method and FEM analysis agree very well.