Structural Vibration Control of Nonlinear Systems Using the Smart Tuned Mass Damper (STMD) and the Nonlinear Tuned Mass Damper (NTMD) in Parallel
Doctor of Philosophy
Structural vibration control systems can be divided into four categories: 1) active control; 2) passive control; 3) semi-active control; and 4) hybrid control. It is well established that the semi-active control can provide control effect comparable to that of the active control but requires orders of magnitude smaller external energy. In this regard, researchers in this field have proposed and developed many promising semi-active control methodologies and devices, of which the semi-active or smart tuned mass damper (STMD) is very effective in reducing structural vibrations. In addition, adaptive-passive tuned mass damper (APTMD) which is tuned mechanically provides better reduction than the conventional passive TMD. In the present study, two kinds of TMDs: the smart tuned mass damper (STMD) which has variable frequency and variable damping ratio, and the adaptive passive tuned mass damper (APTMD) are investigated for the control of both linear and nonlinear structures. Vibration of nonlinear systems is characterized by multiple solution branches and instability, such as bifurcations (the jump phenomenon), and chaos. For a hardening D\"uffing oscillator subjected to harmonic excitations, a nonlinear tuned mass damper (NTMD) provides better and more robust control effect than the linear TMD; however, the NTMD will result in high amplitude ''detached resonance" in the lower frequency region in the frequency response curve. To address this issue, a smart tuned mass damper (STMD) is connected to the primary D\"uffing system in parallel with an NTMD. It is found that through the introduction of the STMD, the structural response is attenuated significantly and the detached resonance branch becomes minimal. In addition, the combination of the STMD and the NTMD can attenuate the transient responses more effectively than a single STMD. For the two degrees of freedom (DOF) system of the primary linear structure and an STMD, closed-form solutions are derived for the system under harmonic excitation and ground motions. The solutions for the dynamic system provide insight into the two DOF system: the variation of the damping ratio and the mass ratio can affect the attenuation through influencing the phase angle of the structure, the phase angle of the STMD, and the phase difference between the structure and the STMDs. As the mass ratio increases or the damping ratio decreases or both thereof, the phase difference $\theta_r$ approaches $\pi/2$ which corresponds to a maximum energy flow and dissipation, thereby attenuating the structural response more effectively. To examine the effectiveness of the STMD for seismic protection, an STMD with variable damping coefficient and stiffness is evaluated under seismic excitations. Variation of the damping ratio of the STMD is implemented through tracking the displacement of the STMD. If the tracked amplitude of the STMD is increasing, damping ratio of the STMD is set to zero; else it is set to an appropriate non-zero value. Stiffness of the STMD is tuned through tracking the displacement of the primary structure which is analyzed using a short time Fourier transform (STFT) based control algorithm. Both far-field and near-fault ground motions are used to examine the effectiveness of the STMD and the control algorithm. Displacement time history and response (displacement and acceleration) spectra are obtained for the cases of an optimal passive TMD and an STMD. It is found that the STMD with variable damping ratio and frequency can effectively attenuate the seismic responses and outperforms the optimal passive TMD. In addition, results are obtained for the case that damage occurs to the primary structure during an earthquake. The study indicates that the STMD controlled by the proposed algorithm can rapidly capture the variation of the structure and remains tuned with the primary structure while the optimal TMD becomes off-tuned when damage occurs. Experimental validation is performed to identify the high amplitude detached resonance and to examine the effectiveness of an adaptive pendulum TMD (APTMD) in attenuating the resonance curve. The experimental system consists of a primary D\"uffing oscillator, an NTMD and an APTMD with adjustable length in parallel. An adaptive passive stiffness (APS) device is proposed and installed to provide cubic nonlinearity for the primary structure. High amplitude detached resonance is identified in the experiment when an NTMD is used alone. By using the APTMD in parallel with the NTMD, it is observed that the high amplitude detached resonance is attenuated to a minimal level. In addition, numerical simulation is conducted to compare with the experimental data. The numerical results are found to be in good agreement with the experiment data.