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The hysteretic damping tuned mass damper (HD-TMD), which exhibits linear damping force, has been achieved by variable friction devices. Such devices own the advantages of stable mitigation capacity and easy maintenance compared to viscous damping devices. Previous studies have mainly concentrated on the vibration mitigation effect of the HD-TMD system without explicit consideration of structural acceleration control. In this context, seismic optimizations of HD-TMD for structural acceleration control were presented, and the effective damping of HD-TMD was investigated. H∞ optimizations of the HD-TMD were considered for undamped and lightly damped structures with fixed-point theory, where the closed-form solutions of optimal and improved parameters were derived. Parametric analysis for the dynamic amplification factors (DAFs) of structural acceleration revealed that the closed-form solutions effectively tuned the DAF into double peaks and reduced the maximum response overall frequency. H2 optimizations were conducted with residue theory for the optimization of the undamped structure, and the optimal parameters of HD-TMD subjected to stochastic ground excitation were obtained by numerical searching and curve-fitting techniques. Effective damping of the HD-TMD was consequently examined using the stochastic stationary process in which the damping effect additionally provided to the structure was measured. The effectiveness of the proposed optimal solutions for the HD-TMD in the form of an available engineering variable friction device was thereby corroborated by twenty sets of seismic ground motions. Spectrum's results indicated that the proposed optimal parameters greatly improved the absolute structural acceleration response and provided excellent seismic mitigation capacity for structural displacement response. The response of the equivalent SDOF demonstrated almost the same trend of absolute structural acceleration reduction, which revealed the successful application of effective damping of HD-TMD for designers. Detailed analysis of the earthquake record indicated the functionality and effectiveness of the proposed methods of HD-TMD with the average absolute structural acceleration reduction ratio of 65.86% and 42.66% for maximum reduction and standard deviation reduction, respectively. [ABSTRACT FROM AUTHOR]

The hysteretic damping tuned mass damper (HD-TMD) is composed of a spring element, a hysteretic damping (HD) element, and a mass. The HD force is proportional to the displacement of the tuned mass damper (TMD). Recently, the application of HD-TMD has emerged, but its optimal design is still lacking. To fill this academic gap, numerical solutions for optimal parameters of HD-TMD subjected to white-noise excitation were obtained based on the H2 optimization criterion. Performance balance optimization with a weighting factor was carried out to improve the response of a structure with the HD-TMD system. A set of earthquake records and harmonic excitations were conducted to prove the effectiveness of the optimal numerical solutions and the performance balance design. It was found that the performance of the HD-TMD is slightly better than that of the traditional optimized TMD. As a real TMD application of HD-TMD, the variable friction pendulum TMD (VFP-TMD) was selected to experience earthquakes with the proposed optimal methods. Results showed that the optimal solutions provided the best performance but raised the problem of difficulty in maintaining linearity with a large displacement. Nevertheless, the performance balance design helped reduce this defect and provided impressive seismic mitigation capacity. Compared with the optimal numerical solution results, the performance balance design demonstrated 2.847% of loss in the maximum structural displacement reduction rate and 3.709% of loss in the root mean square reduction rate during the earthquake-excited period, respectively. [ABSTRACT FROM AUTHOR]

• The nonlinear behavior of the PTMD with different damping is fully described. • Damping nonlinearity and stiffness nonlinearity of structure-PTMDs system are illustrated. • The attenuation characteristics of the PTMDs are obtained with closed-form expressions. • Nonlinear performance oriented optimization is based on amplitude robustness. • The optimization achieves an enlarged damping dissipation capacity of PTMD with HD. The inherent nonlinearity of the pendulum motion becomes increasingly pronounced as excitation amplitudes rise, leading to the uncertainty of vibration and the loss of predictive accuracy owing to the linear assumption. To address this concern, this study introduces the pendulum tuned mass damper (PTMD) with hysteretic damping (HD) to realize the nonlinear performance oriented optimal seismic design. The primary contribution of this study is introducing the nonlinear performance of the PTMD with HD, thereby proposing amplitude robustness optimization based on nonlinear dynamic performance. Theoretical configurations of PTMD that facilitate different types of damping, including viscous damping (VD), constant damping, and hysteretic damping (HD), are compared. The Krylov–Bogoliubov (K–B) method is originally adopted to analyze the nonlinear effect of the PTMDs in the case of forced oscillation and free vibration. The nonlinear frequency response functions (FRFs) of the structure-PTMD system are derived, and the coupled systems are evaluated. The presence of stiffness softening, the persistence of stable solutions, and the occurrence of unstable frequency response loops demonstrate the inherent nonlinearity and sensitivity of control effectiveness. Attenuation characteristics of the PTMDs are obtained to determine the damping dissipation properties with accuracy compared with the dynamic solutions. Prue HD shows a similar dynamic interaction with an exponential decay in damping dissipation as the VD, which exhibits the linear damping performance for the coupled control system. A nonlinear performance oriented optimal seismic design based on the amplitude robustness index is proposed to consider the amplitude uncertainty impact on the structure-PTMD system. A case study is assessed based on the 20-story benchmark structure to investigate the functionality of the proposed optimization for the PTMD with HD. The results confirm the effectiveness of optimization from the perspective of FRFs, where the optimal PTMD with HD exhibited an FRF with a lower peak in structural amplitude compared to the optimal PTMD with VD. Seismic validations of the spectral analysis and specific earthquake evaluations verify the applicability of the proposed optimization for PTMD with HD, enabling an enlarged damping dissipation capacity as earthquake excitation increases to provide better structural protection. [Display omitted] [ABSTRACT FROM AUTHOR]

Flexible high-rise buildings are extremely vulnerable to wind, especially when synchronously subjected to alongwind and crosswind forces. In this scenario, acceleration-sensitive targets (such as delicate instruments) are at risk of damage. Moreover, occupant comfort and structural safety may be degraded due to excessive bi-directional vibrations. To resolve this problem, a bi-directional rail variable friction pendulum-tuned mass damper (BRVFP-TMD) is used to achieve optimal bi-directional wind-induced vibration control. The modeling of the BRVFP-TMD for bi-directional high-rise buildings under bi-directional winds was performed. Further, the physical interaction forces of the BRVFP-TMD with a multi-degree-of-freedom structure and the governing equations for the modal structure with the BRVFP-TMD were derived, with experimental results confirming the effectiveness of the linear variable friction force. For the BRVFP-TMD with a lightly damped structure, acceleration optimizations were conducted to obtain closed-form solutions for optimal parameters. However, the deployment position of the tuned mass damper (TMD) was found to degrade the optimal control performance significantly. Therefore, for the convenience of engineers, improved optimal solutions were obtained by considering the actual deployment position of the TMD and the influence of inherent structural damping. The stochastic linearization method was used to evaluate the effect of linear hysteretic damping (HD) with equivalent viscous damping (VD) in the field of random theory. Accordingly, a closed-form expression for the VD ratio was proposed to represent HD. Numerical verifications of a Chinese landmark (Canton Tower) subjected to bi-directional winds were assessed through time history and frequency decomposition analyses. The results verified the effectiveness, correctness, and necessity of the BRVFP-TMD; the improved optimal solutions were also confirmed. Compared with the closed-form solution, which neglects the deployment position of the TMD, and the classic TMD, the improved optimal solutions of the BRVFP-TMD demonstrated superior performance in mitigating both structural displacement and acceleration. The vibration reduction ratios achieved were 44.55% for the displacement at the top of the mast and 46.69% for the acceleration at the top of the main tower. • The constitutive relation of BRVFP-TMD equipped with MDOF structure is provided. • Closed-form solutions for optimal acceleration control of BRVFP-TMD are obtained. • Improved optimal solutions of BRVFP-TMD considering deploy position are acquired. • SLM is verified by MCS to illustrate the connection between VD and HD. • Closed-form expression of equivalent VD ratio to represent HD ratio is obtained. [ABSTRACT FROM AUTHOR]

• Pendulum tuned mass damper (PTMD) with geometric nonlinear dampers (GND) is proposed. • Nonlinear behavior of the PTMD with GND characterized by the "unavailable" points. • The stochastic linearization method is adopted to simplify the nonlinear model. • Closed-form solution and optimal design procedure are built for the PTMD with GND. • The optimal design provides significant reduction by the dynamic damping mechanism. In engineering applications, the geometric nonlinear (GN) arrangement of pendulum-tuned mass dampers (PTMDs) may induce the damping force to deviate from its intended state. Therefore, this study extends the scope of the structural control strategy by introducing a pendulum-tuned mass damper considering geometric nonlinear dampers (GND). Specifically, the damper developed in this study, termed PTMD with GND, is an inconspicuous pendulum-type tuned mass damper with different GN settings in the initial state. A nonlinear mathematical model of the PTMD with GND is developed, identifying its significant nonlinear characteristics, particularly the "unavailable" locations. The stochastic linearization method (SLM) is adopted to simplify the nonlinear model using the Kanai-Tajimi modified spectrum. The SLM agrees well with the numerical results obtained using the Monte Carlo simulation method. Furthermore, the control strategy of PTMD with GND is proposed with the consideration of filtered random excitation. Several numerical cases have been conducted to investigate the availability of PTMD with GND and the proposed optimal design strategy under 178 real seismic excitations. The results show that the PTMD with GND is nearly as effective as the ideal transitional TMD in mitigating the seismic response of the primary structure and more effective than the inverted rough linear adjustment. It can be concluded that the proposed optimal design strategy for the PTMDs with GND efficiently suppressed the structural vibration through multiple performance indices and used the nonlinearity of the damping mechanism of the GND to provide a sufficient damping energy dissipation effect adaptively. [Display omitted] [ABSTRACT FROM AUTHOR]

• Bi-directional rail variable friction pendulum-tuned mass damper (BRVFP-TMD) was proposed. • Bi-directional traditional friction pendulum systems were improved by geometric nonlinearity. • The impact of bi-direction motion to the bi-directional friction pendulum systems was revealed. • Closed-form solutions for the optimal parameters of BRVFP-TMD were obtained. • Bi-directional loadings were conducted to illustrate the superiority of BRVFP-TMD. The shape of hysteretic loops for a friction pendulum system transforms when excited by bi-directional motion, which exhibits unexpected dynamic behavior compared with unidirectional motion. Therefore, a novel bidirectional rail variable friction pendulum-tuned mass damper (BRVFP-TMD) with two independent rails that satisfied the purpose of bidirectional structural response control and provided a full bidirectional friction force was proposed. The variable friction arrangement was applied to the rails so that the BRVFP-TMD could be accomplished with a linear hysteretic damping property that is contributed by the displacement-dependent variable friction force. Using unidirectional harmonic excitations with attack angle as bi-directional loading, illustrations were created to investigate the control effect of traditional pendulum friction TMDs with a spherical sliding surface. This demonstrated the collapse of hysteretic loops of traditional pendulum friction TMDs and superiority of BRVFP-TMD in terms of mechanism. For the BRVFP-TMD with a lightly damped structure, the optimizations of the fixed-point theory were accessed to obtain the closed-form solutions of the optimal parameters of the BRVFP-TMD. Numerical verifications based on bidirectional motions were conducted to evaluate the performance of the BRVFP-TMD. The bidirectional earthquake results indicated stable and excellent performance of the BRVFP-TMD in terms of either frequency response reduction or friction energy dissipation efficiency. Meanwhile, bidirectional wind-induced vibrations confirmed the correctness of the optimization and the stable robustness of the optimized BRVFP-TMD. [ABSTRACT FROM AUTHOR]

A variable friction pendulum-tuned mass damper (VFP-TMD) with hysteretic damping characteristics was proposed. The mechanism of the proposed VFP-TMD demonstrated linear behavior and nonlinear properties. Further, the fully nonlinear (FN) and partial linear (PL) equations of motion of the structure with the VFP-TMD system were derived. The VFP-TMD demonstrated stable and excellent seismic mitigation capacities and stroke limitation functionality. Based on the fixed-point theory, the closed-form exact solutions to design parameters of an undamped structure with a VFP-TMD system subjected to the ground motion were presented for different performance indices. The parametric studies showed that optimal designed VFP-TMD can be perfectly tuned in the frequency domain, which proved the applicability of closed-form solutions. To better understand VFP-TMD with hysteretic damping, constant friction pattern and multi-stage variable friction pattern were proposed for comparison. In contrast with constant friction and multi-stage variable friction, VFP-TMD with hysteretic damping characteristic was significantly optimized by the closed-form solutions. To verify the effectiveness of the closed-form solutions on VFP-TMD, twenty sets of real earthquake records were conducted which exhibited the superiority of linear variable friction patterns on seismic mitigation simultaneously. Results showed that the optimized VFP-TMD had an "infinitely large bandwidth", which enabled it to reach its full potential according to the excitation amplitude. • A variable friction pendulum tuned mass damper (VFP-TMD) was proposed. • VFP-TMD exhibits stable, excellent and stroke limitation performance. • Closed-form solutions of VFP-TMD were presented for different performance indices. • VFP-TMD revealed an "infinitely large bandwidth" along with excitation amplitude. • Performance of VFP-TMD was optimized by the closed-form solutions. [ABSTRACT FROM AUTHOR]

• The analytical expression of the TID effective damping ratio is derived under the hypothesis of white-noise seismic excitations. • The effective damping ratio enhancement (EDRE) effect of TID is investigated for seismic response control of civil structures. • The theoretical formula of TID optimal design parameters is proposed based on the EDRE effect for both damped and undamped primary structures. Tuned inerter dampers (TIDs) are widely recognized as promising inerter-based devices for controlling the seismic response of civil structures. However, the effective damping ratio enhancement (EDRE) effect of a TID has not been investigated thoroughly. In this study, the TID control effectiveness is considered as the effective damping ratio (EDR) applied to the main structure, and the analytical expression of the EDR is derived based on the white-noise seismic excitation hypothesis. The theory of the EDRE effect is introduced to explain the superior control effectiveness of a TID to that of a bare dashpot. Theoretical formulas of TID optimum parameters are proposed based on the EDRE effect for both damped and undamped main structures. These formulas ensure that the optimum control effectiveness and EDRE effect of a TID are achieved simultaneously. For this purpose, the TID is supposed to provide the highest EDR with the lowest damping ratio cost for the optimum EDRE effect. Compared to another well-known inerter-based device, i.e., a tuned viscous mass damper, a TID is particularly recommended when the damping ratio is restricted to less than 0.03. Moreover, the TID control effectiveness and EDRE effect are verified numerically under real seismic ground motions recommended by ATC-40. The numerical analysis results show that the TID is effective in controlling the structural seismic response, primarily because of its good performance in suppressing the system input energy. [ABSTRACT FROM AUTHOR]

• A novel concept of the effective damping ratio enhancement (EDRE) effect is proposed for depicting the better control performance of TVMD compared to a bare EDE with the same damping coefficient. • The analytical expression of the TVMD effective damping ratio is derived. • A closed-form solution of TVMD optimal design parameters is proposed to obtain the maximum EDRE factor and effective damping ratio. • The proposed closed-form solution can ensure the control performance of TVMD better than a bare EDE. This paper proposes a novel concept of the effective damping ratio enhancement (EDRE) effect to describe the better seismic control performance of a tuned viscous mass damper (TVMD) compared to a bare energy dissipation element (EDE) with the same damping coefficient, in which the TVMD control performance is regarded as an effective damping ratio added to the primary structure. The analytical expression of the TVMD effective damping ratio is derived for the primary structure subjected to the white noise excitations. The essential relationship between the response mitigation ratio, effective damping ratio, and the EDRE factor is revealed via theoretical derivation and parametric study. Moreover, a closed-form solution of TVMD optimal design parameters is proposed to obtain the maximum value of the EDRE factor and effective damping ratio. In contrast with the classical fixed-point solution, the TVMD designed by the proposed closed-form solution has an improved control performance level. Additionally, the optimal EDRE effect is obtained with a lower damping coefficient when the mass ratio is below 0.20. The proposed closed-form solution can ensure the control performance of TVMD better than a bare EDE, making its application more meaningful. The TVMD design procedure based on the EDRE effect is eventually established. Several numerical examples are conducted to verify the proposed TVMD design methodology under the selected real earthquake records. Time-domain analysis results show that the TVMD control performance is improved by the composite effect of its energy dissipation performance and the reduction in the system input energy, which should be represented by the effective damping ratio and EDRE effect. [ABSTRACT FROM AUTHOR]

• Three closed-form solutions of the optimal design parameters of TVMD are proposed. • An analytical expression for the TVMD effective damping ratio added to the primary structure is derived. • A novel concept of effective damping ratio enhancement (EDRE) effect is proposed. The tuned viscous mass damper (TVMD) is one of the effective inerter-based systems for vibration control of civil structures. TVMD is composed of an inerter, a spring, and an energy dissipation element (EDE). Although the optimal design of TVMD has already been well investigated, the research findings focusing on the TVMD design for acceleration response control of the primary structure under seismic excitations are sparse. In this study, three closed-form solutions of TVMD optimal design parameters are proposed under the hypothesis of harmonic and white noise seismic excitation to mitigate the acceleration response of the undamped primary structure. Numerical analysis results indicate that the proposed closed-form solutions can still provide a good estimating of the TVMD optimal design parameters for the lightly damped primary structure whose damping ratio is less than 0.05. The control performance of TVMD is regarded as the effective damping ratio added to the primary structure, and the analytical expression of the effective damping ratio of TVMD is therefore derived. Further, a novel concept of effective damping ratio enhancement (EDRE) effect is proposed to explain the better control performance of a TVMD than a bare EDE with the same damping coefficient. It is found that TVMD designed by the proposed closed-form solutions (with the hypothesis of white noise seismic excitation) can ensure its better control performance than a bare EDE with the same damping coefficient. The control performance of three TVMDs (named as TVMD1, TVMD2, and TVMD3, respectively) designed by the proposed closed-form solutions is eventually corroborated by twenty sets of real seismic ground motions. The results show that TVMD2 is the most economical and efficient control scheme for structural seismic response control. Combining with the restricted condition for the proposed closed-form solutions, TVMD1 is still recommended in the case of mass ratio in the range of 0.25 to 0.50. If the higher control performance of TVMD is expected with its damping ratio larger than 0.125, TVMD3 is a better choice. [ABSTRACT FROM AUTHOR]