Consistent assembly method for elemental damping

This study proposes a new assembly method to address the problems of using the conventional direct assembly method for assembling elemental damping matrices for a global damping matrix. These problems include the challenges in calibrating an elemental damping ratio for a desired global damping ratio, significantly low and high global damping ratios associated with lower and higher modes, respectively, and unintended huge coupling effects between modes. The new assembly method is based on the recently proposed bell-shaped damping model. It gives a global damping ratio consistent with the elemental damping ratio used in a structure. It maintains modal orthogonality such that all global modes are uncoupled if the same damping ratio is used for all the elements. It also allows the damping ratio to be different from element to element or even from material to material, facilitating a broader damping theory that relates global damping to elemental damping, material damping, and internal state variables other than stiffness. Examples of response history analysis have been carried out to showcase the performance of the proposed assembly method compared to the direct assembly method.