Optimal design of nonlinear multiple tuned mass dampers with frictional mechanism

Abstract

Modern development of design techniques and material science in architectural engineering contributes to increase in demand for buildings with longer span and light weight structure. In spite of its advantageous aspects, such advances in technologies often leads to problems with undesired discomfort caused by excessive vibration. In order to help dampen the unwanted excessive vibration, a variety of relevant techniques have been investigated, among which tuned mass damper (TMD) is one of the most widely used techniques so as to control the problematic vibration.

This study first investigates the optimal solution of linear multiple tuned mass dampers (linear MTMDs, LMTMDs) of various configurations. The configurations considered in this study include the cases where the frequency ratios are linearly distributed, the damping coefficients are uniformly distributed, the mass distributions are linearly distributed, or these constraints are combined in some ways. Two different optimization techniques are employed: Nominal Performance Optimization (NPO) and Robust Performance Optimization (RPO). The NPO searches a solution that minimizes the objective function deterministically, while the RPO minimizes the mean value of the objective function, assuming that the associated structural parameters are probabilistic rather than deterministic. Further, this study provides contour maps for the root-mean-square (RMS) displacement of main structure and the largest RMS displacement of LMTMDs, which can be useful in the design process.

Next, this study seeks the optimal solution of frictional multiple tuned mass dampers (FMTMDs) in which the Coulomb-type frictional force is incorporated in either purposefully or unintentionally. In this study, four of the feasible FMTMD configurations are formulated and comparably analyzed. The investigated configurations involve: 1) no constraint on either the frequency ratios or the coefficient of friction (COF) is imposed

2) the frequency ratios are linearly distributed and equally spaced

3) the COFs are identically distributed

4) the frequency ratios are equally spaced and the COFs are identical. In order to cope with the difficulties inherent in nonlinearity of the problem, this study adopts a statistical linearization technique, which enables the complicated nonlinear force terms to be linearized in a statistical sense. Some miscellaneous considerations such as stroke limitations and design procedure are also aptly included.

This study mainly addresses RMS responses and extreme value distributions for the frictional multiple tuned mass dampers (FMTMDs). In designing of optimal FMTMD, the original nonlinear system arising from the frictional elements is replaced with an equivalent linear system by means of statistical linearization. In order to improve the accuracy for the estimation of peak distribution of MTMDs, this study exploits a statistical nonlinearization technique which replaces the nonlinear system at hand with a class of other nonlinear systems whose exact solution has been already explicitly derived. A correction factor that defines the ratio of RMS displacement between nonlinear and linear system is derived based on the results of statistical nonlinearization technique. This study also provides an explicit formula for evaluating a peak factor for frictional TMDs. The correction factor and the peak factor proposed are validated with Monte Carlo Simulation.

Several application examples of MTMDs are included in this thesis. of multiple tuned mass dampers (MTMDs). In the first section, a mechanism-based frictional pendulum tuned mass damper (FPTMD) is proposed, which contributes to overcome some shortcomings of conventional translational TMDs with viscous damping. In the second section, a numerical study is carried out to provide a design procedure of MTMDs, which covered modal analysis based on finite element method, optimal design of tuned mass dampers, and evaluating their control performance and robustness under the frequency-perturbed states. The final section presents a project in an attempt to mitigate an excessive vibration of a problematic structure. The overall process of the project includes the vibration performance evaluation, modal analysis based on finite element method and optimal design and manufacturing of tuned mass dampers.