Abstract
To reduce the adverse vibrations of buildings, tuned mass dampers (TMDs), which are the most representative passive control devices, have been widely used and studied in aerospace, machinery, civil engineering, and other fields for many years. Most scholars used to treat the TMD as a linear damper, but they show some nonlinear characteristics owing to the use of limit devices and large displacements. It is necessary to consider the nonlinear coefficient of the TMD when designing its parameters. In this study, the mass ratio of the TMD was optimized by considering the nonlinear coefficient of the TMD. The complex variable average method and multiscale method were used for analysis. A mass ratio interval was found on the “\(\varepsilon - N_{2}\)” curve in which modulation response can occur, and then an analytical method for obtaining the optimal mass ratio of TMD was derived based on this phenomenon. The numerical results showed that taking the midpoint of this mass ratio interval as the optimal mass ratio can yield a better damping effect and robustness than using the traditional linear design method.
Highlights
Unpredictable natural disasters and human-induced attacks pose a great threat to the safety of buildings; research on vibration reduction of structures is important in the field of civil engineering
A mass ratio interval was found on the “ N2 ” curve in which modulation response can occur, and an analytical method for obtaining the optimal mass ratio of tuned mass dampers (TMDs) was derived based on this phenomenon
They simplified the system to one with a single degree of freedom in which the force of the primary structure acting on the TMD was regarded as an equivalent load, and they optimized the parameters of the TMD designed by the linear method [14]
Summary
Unpredictable natural disasters and human-induced attacks pose a great threat to the safety of buildings; research on vibration reduction of structures is important in the field of civil engineering. Based on the above defects, Den Harton introduced damping into the DVA, which greatly improved the damping effect [5], and the concept of TMD was established He optimized the frequency ratio and damping ratio of the TMD and provided their specific optimization formula [6]. Li and Cui analyzed the spontaneous nonlinearity in TMD and proposed that if this nonlinearity was ignored, it would cause adverse effects on vibration reduction They simplified the system to one with a single degree of freedom in which the force of the primary structure acting on the TMD was regarded as an equivalent load, and they optimized the parameters of the TMD designed by the linear method [14].
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