Improving the performance of tuned mass dampers by considering geometric nonlinear effects in an integrated identification-control approach

Tuned mass damper (TMD) is considered a common and effective device in structural control during catastrophic events such as earthquakes. This paper presents a promising method to improve the performance of TMD on vibratory structures with unknown parameters, by addressing the geometric nonlinear effects in an integrated identification-control approach. To evaluate the efficiency of this method, the reductions of the maximum displacement, shear force, acceleration of the top floor, and the mechanical energy of the structure are considered as performance indicators. Firstly, a proper relationship based on stiffness reduction is provided to consider geometric nonlinearity and perform second-order analysis. Secondly, the virtual synchronization method (VSM) is employed to identify the unknown parameters of the structures including stiffness and damping coefficients. Subsequently, an appropriate algorithm is developed to represent the integrated identification-control approach which utilizes the current properties of structures identified by VSM, for tuning the TMD. Afterward, these methods are employed to determine the circumstances where second-order analysis is preferable to first-order analysis, considering performance indicator differences. These circumstances deal with three variables including the characteristics of earthquakes and structures as well as the level of damage. To incorporate the first two variables, studies are conducted on several structures with different periods subjected to ten earthquakes with various frequency contents. Furthermore, for inclusion of the last variable, structures experience different levels of damage. As a result, this study determines the ranges based on the three mentioned variables wherein incorporating geometric nonlinear effects improves the performance of TMD and should be considered in structural analysis. Furthermore, similar relationships are provided for the assessment of the performance of the VSM. Finally, a study is provided to validate the performance of the integrated identification-control approach.