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Summary In this paper, an optimal energy dissipation control algorithm is applied into a semi-active suspension-type tuned mass damper (SA-STMD) to suppress excessive vibration by means of variable pendulum length. The SA-STMD mechanism consists of a mass block, a suspension rope, and a movable fulcrum that can be a short tube driven by a linear motor to vertically move along the suspension rope. As the fulcrum goes up, the pendulum length is extended, resulting in a smaller stiffness of the SA-STMD, and vice versa. Accordingly, the restoring force in the SA-STMD can be adjusted by varying the fulcrum positions. In the case where the energy dissipation ability by the original STMDs is insufficient, the movable fulcrum in the SA-STMD system can compensate the STMDs for stiffness according to the proposed optimal energy dissipation control algorithm to provide controllable restoring forces. The controllable restoring forces are designed to act as viscous dampers that can make up for the lack of energy dissipation capacity. The numerical results from the time domain and frequency domain analyses show that the proposed approach utilizing the optimal energy dissipation control algorithm to adjust the pendulum length can induce controllable restoring forces with a butterfly-shaped hysteresis loop, supplying a sufficient energy dissipation capacity to reduce responses to the unexpectedly large external vibration. Another potential benefit is cost reduction because of use of a less number of conventional viscous dampers in the STMD system. Copyright © 2016 John Wiley & Sons, Ltd.

An isolation system is not very effective when an inappropriate level of damping is used. This paper proposes a theoretical method which can be used to determine the optimal frictional coefficient of an isolation system. Only a one-dimensional isolation system and ground motion are considered. The frictional coefficient is optimized by minimizing the sum of squares of structural absolute accelerations, with the optimization results being validated graphically. Sensitivity studies were used to verify the feasibility of the optimal frictional coefficient, coupled with a practical example in Taipei under the conditions of the Hualien and El Centro earthquakes. Consequently, the feasibility and reliability of the proposed optimal design were verified.

The present study aims at proposing an innovative phase control methodology for semi-active tuned mass dampers (SA-TMDs) that intend to minimize the off-tuned problems associated with passive tuned mass dampers (P-TMDs). The phase control algorithm is first developed, the essential of which is to apply the variable friction force to slow down the mass block at specific moments when the phase lag of the SA-TMD with respect to the structure is different from 90°, resulting in the SA-TMD back to the desired phase lag, i.e., −90° phase deviation, so that the SA-TMD has the maximum power flow to reduce the structural vibration. The feasibility of the application of the phase control in SA-TMDs is verified by performing numerical analyses of a simplified Taipei 101 structure model with a SA-TMD subjected to sinusoidal loads and design level wind loads. The numerical simulation results show that the SA-TMD implemented with phase control can enable the mass block to vibrate in a manner with a phase lag close to the −90° when the structure model is under sinusoidal excitations with frequencies different from the structural fundamental mode. The SA-TMD with phase control not only exhibits better performance than the optimal P-TMD in terms of suppressing the structural vibration, but also enhances its robustness, particularly when the SA-TMD is off-tuned to the structure.

Recently, the benefit of nonlinear isolation systems under resonance or near-fault earthquake has been investigated. In this paper, an eccentric rolling isolation system (ERIS) with additional friction damping is proposed. The isolation object is eccentrically pinned on a set of circular isolators so that the restoring force is nonlinear. To investigate the advantage of the ERIS, a corresponding isolation system with linear restoring force is also considered for comparison. The friction parameters of the two systems with linear and nonlinear restoring force are designed under the far-field El Centro earthquake. The performances of the two isolation systems are inspected under excitations other than the design one. In free vibration, the response of the ERIS decays faster than the corresponding linear system. In resonance sinusoidal excitation, the responses are divergent for the linear system but convergent for the ERIS. The linear system is ineffective but the ERIS is effective due to the nonlinearity under the near-fault Chi-Chi earthquake with various peak ground accelerations.

SUMMARY Optimal design for tuned mass dampers (TMDs) with linear or nonlinear viscous damping is formulated in order for design practitioners to directly compute the optimal parameters of a TMD in a damped structure subjected to wind excitations. The optimal TMD tuning frequency ratio and damping coefficient for a viscous TMD system installed in a damped structure under 10 white noise excitations are determined by using the time-domain optimization procedure, which minimizes the structural response. By applying a sequence of curve-fitting schemes to the obtained optimal values, design formulas for optimal TMDs are then derived. These are expressed as a function of the mass ratio and damping power-law exponent of the TMD as well as the damping ratio of the structure. The feasibility of the proposed optimal design formulas is verified in terms of formulary accuracy and of comparisons with existing formulas from previous research works. In addition, one numerical example of the Taipei 101 building with a nonlinear TMD, which is redesigned according to the proposed optimal formulas, is illustrated in effort to describe the use of the formulas in the TMD design procedure and to investigate the effectiveness of the optimal TMD. The results indicate that the proposed optimal design formulas provide a convenient and effective approach for designing a viscous TMD installed in a wind-excited damped structure. Copyright © 2011 John Wiley & Sons, Ltd.

The algorithm of modified predictive control (MPC) is derived with the partial-state concept of direct output feedback (DOF) to reduce the number of sensors for real implementation. The feasibility of using modified predictive control with direct output feedback (MPCwDOF) is verified through numerical and experimental study. According to the MPCwDOF algorithm, the online control forces are simply generated from the actual output measurements that are multiplied by a prescribed constant output feedback gain matrix. An off-line numerical method is introduced to find the feedback gain systematically and efficiently. Numerical examples of two control systems with respect to single-controller and multiple-controller systems are illustrated for validating the feasibility of using the MPCwDOF algorithm and the application of the decentralized control strategy to the MPCwDOF algorithm. An experiment of a large-scale 5-story structural model with an MPCwDOF-controlled active mass damper on the roof is also performed. Results indicate that the controlled structures achieve good performance under environmental excitations. Simple online calculations and a small number of sensors make the proposed control algorithm more favorable to real implementation. Copyright © 2010 John Wiley & Sons, Ltd.

Optimal design theory for linear tuned mass dampers (TMD) has been thoroughly investigated, but is still under development for nonlinear TMDs. In this paper, optimization procedures in the time domain are proposed for design of a TMD with nonlinear viscous damping. A dynamic analysis of a structure implemented with a nonlinear TMD is conducted first. Optimum design parameters for the nonlinear TMD are searched using an optimization method to minimize the performance index. The feasibility of the proposed optimization method is illustrated numerically by using the Taipei 101 structure implemented with TMD. The sensitivity analysis shows that the performance index is less sensitive to the damping coefficient than to the frequency ratio. Time history analysis is conducted using the Taipei 101 structure implemented with different TMDs under wind excitation. For both linear and nonlinear TMDs, the comfort requirements for building occupants are satisfied as long as the TMD is properly designed. It was found that as the damping exponent increases, the relative displacement of the TMD decreases but the damping force increases.

The seismic response of a structural system equipped with friction-type energy dissipation devices is generally nonlinear. The main reason for this nonlinearity is the friction mechanism that possesses two possible motion states, referred to as stick and slip states. The essential force and kinematic conditions of a friction damper, in these two states, are different. In this paper, by employing a state-space formulation and a linear integration scheme, the discrete-time solution of dynamic response of a structural system equipped with multiple friction devices, which can be in either a stick or slip state, was derived in a single and unified form. The nonlinear friction forces, in each time step of analysis, were solved by satisfying both the force and kinematic conditions of certain motion states. Based on a derived discrete-time solution, a numerical analysis procedure was proposed, which allows the time interval of analysis to remain constant, even at the transition of stick and slip states; thus, it is a systematic and efficient method for numerical implementation. The solution of the method was compared with the analytical free-vibration response of a single DOF system, and also with the harmonic and seismic responses simulated by other conventional numerical methods. These examples demonstrate the accuracy and stability of the proposed method.

The essential feedback signals for direct output feedback control are limited to velocities and direct acceleration feedback control is found to be unfeasible even though accelerometers are favorable sensors from the viewpoint of measurement. In this paper, acceleration feedback control becomes feasible when the feedback data is extended to cover accelerations of the previous time-steps. A multi-step acceleration feedback control algorithm is derived through an optimization process such that a certain prescribed quadratic performance index is minimized. Control forces are simply generated from acceleration information of the current and previous time-steps. The feasibility of the proposed control algorithm is verified numerically by the tendon control of structures subjected to real earthquake excitation. The control effectiveness of the proposed control algorithm is close to that of state feedback control algorithm. Simple on-line calculation and availability of accelerometers make the proposed control algorithm favorable to realtime control implementation.

Publisher Summary Direct absolute acceleration feedback control is considered to be unfeasible even though accelerometers are favorable sensors for measuring the dynamic structural responses from the viewpoint of measurement. Absolute acceleration feedback control becomes feasible when the feedback data is extended to cover the absolute accelerations of the previous time steps. Multi-step acceleration feedback control algorithm is derived through an optimization process such that a certain prescribed quadratic performance index is minimized. Control forces are simply generated from absolute acceleration information of the current and previous time steps multiplied by the pre-calculated optimal feedback gain matrix. The control effectiveness of the proposed control algorithm is verified through numerical simulation to be close to that of state feedback control algorithm. Simple on-line calculation and availability of accelerometers make the proposed control algorithm favorable to real-time control implementation.