Development of the Discrete Singular Convolution Method for the Free Vibration Analysis of Coupled Shear Walls

Abstract

Discrete singular convolution is a new numerical method that its ability to vibrational analysis has been demonstrated in the last decade. A lot of research on how to apply the complex boundary conditions of the different issues using this method is carried out and a variety of solutions have been proposed in this regard. Applying the boundary conditions in the governing equations of coupled shear walls, is a challenging issue. This paper proposes a new algorithm for applying the boundary conditions in the vibration analysis of coupled shear walls using the DSC method. In order to validate the proposed method, several samples were analyzed using this algorithm and the results were compared with the values obtained from three conventional numerical methods of Finite element (FEM), Differential quadrature (DQM) and Finite difference (FDM) methods. The great conformity was found between the results which emphasized the validity and integrity of the proposed method. In addition, the ability of the DSC algorithm was explored in terms of the computational speed, computational effort and the amount of computer memory required aspect and compared with the other conventional numerical approaches. It is concluded that the DSC is more efficient than the compared numerical methods from the results of this study.

Keywords

• discrete singular convolution
• free vibration
• coupled shear wall
• boundary conditions
• numerical method