Seismic control mechanism of tuned viscous mass damper (TVMD) outriggers


 
 
 This study gives an explanation to design analysis and performance evaluation of a novel multi-cantilever foil bearing (MCFB). The aim of this study is to develop a theoretical model that will explain the working principles of the cantilever foil bearing. A theoretical derivation of structural and vibration models were developed to find structural stiffness, equivalent viscous damping and maximum deflection. Findings show that the theoretical results of structural models have an equivalent structural stiffness of 58.59kN/mm, equivalent viscous damping of 0.599kNs/m and maximum deflection of 0.5675mm. The equivalent viscous damping is computed at a near zero circumferential coordinate (0.0350). The results obtained from vibration models show an equivalent structural stiffness of 58.74kN/mm, equivalent viscous damping of 0.228kNs/m and maximum deflection of 0.5675mm. Theoretical viscous damping coefficient varies from 0.23kNs/m at 24Hz to 0.026kNs/m at 200Hz when determined at maximum deflection of 0.5675mm and phase angle of 0.0350. This means the higher the frequency, the lower the viscous damping coefficient. The validation was done over frequency range 24-200Hz and at amplitude of 50mm at a 450 phase angle. The models were found to have compared well with experimental results in the prediction of equivalent viscous damping coefficient. The models can be relied upon to analyze the behaviour of MCFB and it can also form a theoretical background for the design and manufacture of Multi-Cantilever Foil Bearing.
 
 

Match of negative stiffness and viscous damping in a passive negative stiffness damper (NSD) is studied for the vibration control of stay cables in this paper. At first, a discrete model of the stay cable with an NSD attached perpendicularly near the support is established. Under sinusoidal excitations, forced responses of the system are derived theoretically, which results in an asymptotic form for the additional modal damping ratios. Then, experimental results are presented to verify the discrete model and the corresponding theoretical derivations. Subsequently, numerical analysis is performed further to show the optimal match of negative stiffness and viscous damping, which is a function of the attachment location. The energy dissipated by the NSD and the cable energy are analyzed, thereby demonstrating the change trend of the additional modal damping ratios. Moreover, the energy distribution along the cable is investigated to reveal the effect of the negative stiffness and viscous damping. This study demonstrates the control mechanism of negative stiffness and viscous damping in the passive damper and is of practical significance for designing the optimal match of the damper parameters for cable vibration control.

Cables in cable-stayed bridges are subjected to the problem of multi-mode vibrations. Particularly, the first ten modes of long cables can have a frequency less than 3[Formula: see text]Hz and hence are vulnerable to wind-rain induced vibrations. In practice, mechanical dampers are widely used to mitigate such cable vibrations and thus they have to be designed to provide sufficient damping for all the concerned vibration modes. Meanwhile, the behaviors of practical dampers are complicated and better to be described by mechanical models with many parameters. Furthermore, additional mechanical components such as inerters and negative stiffness devices have been proposed to enhance the damper performance on cables. Therefore, it is increasingly difficult to optimize the damper parameters for suppressing multi-mode cable vibrations. To address this issue, this study proposes a novel damper design method based on the genetic algorithm (GA). The procedure of the method is first introduced where the damper performance optimization is formulated as a single-objective multi-parameter optimization problem. The effectiveness of the method is then verified by considering a viscous damper on a stay cable. Subsequently, the method is applied to optimize three typical dampers for cable vibration control, i.e. the positive stiffness damper, the negative stiffness damper, and the viscous inertial mass damper. The results show that the GA-based method is effective and efficient for cable damper design to achieve best multi-mode control effect and it is particularly useful for dampers with more parameters.

An exact solution for steady forced vibrations of a two-degree-of-freedom system with two viscous dampers and one Coulomb damper subjected to a simple, harmonic ground excitation is presented. The solution is valid for motions without standstill. The results are expressed in terms of nondimensional parameters that allow evaluations of response amplitudes and phase angles for various frequency ratios, mass ratios, and amounts of viscous and Coulomb damping. In the limits, the resulting expressions agree properly with those for a system without the Coulomb damper and with Den Hartog's [J. P. Den Hartog, “Forced Vibrations with Combined Viscous and Coulomb Damping,” Phil. Mag. 9, 801–817 (1930); “Forced Vibrations with Combined Coulomb and Viscous Friction,” Trans. ASME 53, APM 107–115 (1931).] expressions for a single-degree-of-freedom system with a Coulomb damper. Formulations for the special case of a two-degree-of-freedom system with a Coulomb damper (without viscous dampers) are also obtained. One numerical example of the general formulation is presented and the results are compared with those based on the approximate method of equivalent viscous damping. In Appendix A, numerical results are presented to compare the exact and approximate solutions for a single-degree-of-freedom system with combined Coulomb and viscous damping. The exact solution obtained in this paper can be used to estimate the accuracy of approximate methods for analyzing more-complex systems containing Coulomb damping.

For a multibody system with friction-affected constraints, responses with the same period as the harmonic excitation are considered. Equivalent viscous damping factors are defined, with the requirement that the systems with friction and viscous damping have the same oscillation amplitudes. Accelerations and reaction forces of the system with friction and equivalent damping are compared. Significant differences become evident which suggest that viscous damping concepts provide only a vague equivalence for motion resistances due to friction.

This research presents methods to control vibration of suspended bridges decks by incorporating a self-centering friction damping mechanism to (1) mitigate damaging ambient vibrations and (2) maintain a necessary potential of energy dissipation during major seismic excitation. To achieve this, a thorough investigation of the relationship between viscous and friction damping is conducted both analytically and in a numerical computer model. The objective of this paper is to introduce friction damping concepts as well as methods of approaching equivalent viscous damping. Necessary design parameters for friction dampers will be identified and compared to that of their viscous damping counterpart in an effort achieve equal energy dissipation. Furthermore, this paper introduces the modified self-centering friction damping brace (SFDB) and discusses the concept of design and analysis for replacement of viscous dampers in suspended bridges. The modified SFDB is analyzed in a single degree of freedom system and compared to a typical viscously damped system. The free vibration behavior of the modified SFDB is compared to viscous damping behavior and evaluated for future research involving the retrofit of the Vincent Thomas Bridge in San Pedro, CA.

Seismic design framework for steel structures with hysteretic and viscous dampers

Seismic response control of core wall structures using tuned viscous mass damper (TVMD) outriggers

To evaluate the energy dissipation differences between metal dampers and viscous dampers and to gauge the degree of equivalence between bilinear hysteresis and viscous damping, we studied the equivalence of bilinear hysteresis and viscous damping. Using a MATLAB program and the principle of equal energy dissipation, the energy dissipation effect of bilinear hysteresis was equated based on the effect of viscous damping. Under a state of sinusoidal excitation, the displacement response of the numerical method, which strictly considers the bilinear hysteresis, was compared with the displacement response of the equivalent viscous damping calculation method. The results show that the oscillation periods for the two models demonstrate high consistency, with the displacement curves in the steady-state response stage nearly identical. Because of the lag in hysteresis energy dissipation, the bilinear hysteresis system always reaches the steady-state stage slower than the equivalent viscous damping system, implying that the metal damper responds more slowly to transient energy. In the free vibration stage, the bilinear hysteresis system cannot return to the initial position, while the displacement of the equivalent viscous damping system approaches zero, suggesting that the self-resetting effect of the viscous damper is better.

Stay cables used in cable-stayed bridges are prone to vibration due to their low-inherent damping characteristics. Many methods have been implemented in practice to mitigate such vibration. Recently, negative stiffness dampers have gained attention because of their promising energy dissipation ability. The viscous inertial mass damper (VIMD) has been shown to have properties similar to negative stiffness dampers. This paper examines the potential of the VIMD to enhance the damping, and mitigate the vibration, of stay cables. First, a control-oriented model of the cable is employed to formulate a system level model of the cable–VIMD system for small in-plane motion. After carefully classifying and labeling the mode order, the modal characteristics of the system are analyzed, and the optimal damper parameters for the several lower frequency modes are determined numerically. The results show that the achievable modal damping ratio can be up to nearly an order of magnitude larger than that of the traditional linear viscous damper; note that the optimal parameters of the VIMD are distinct for each mode of interest. These results are further validated through analysis of the cable responses due to the distributed sinusoidal excitation. Finally, a case study is conducted for a cable with a length of 307 m, including the design of practical damper parameters, modal-damping enhancement, and vibration mitigation under wind loads. The results show that the VIMD is a promising practical passive damper that possesses greater energy dissipation capacity than the traditional viscous damper for such cable–damper systems.

Due to their high lateral flexibility and low inherent damping, stay cables are prone to dynamic excitations. Application of dampers to improve the energy dissipation capacity of stay cables and mitigate their excessive vibrations has been extensively studied, and design tools have been proposed to select the optimum damper size and predict the maximum achievable damping ratio of a cable-damper system. In this study, the effectiveness of external viscous dampers in controlling stay cable vibrations is investigated by considering the negative stiffness behavior of passive dampers. An analytical model is developed to include the damper stiffness effect for further refinement of existing damper design tools, of which the influence of cable sag, cable flexural stiffness, and damper support stiffness has already been considered. The performance of passive negative stiffness dampers (NSDs) and conventional zero or positive stiffness dampers (PSDs) is investigated in detail via parametric studies using the refined design formula. In particular, a criterion is defined for selecting the negative stiffness in NSD based on the stability limits. Two design examples are presented to illustrate the application of the proposed refined damper design tool to the selection of optimum damper size and evaluation of damper performance for a passive viscous PSD and NSD. Results show that compared with the conventional viscous dampers, a passive NSD demonstrates superior performance in stay cable vibration control. Results are also compared and verified with the numerical solution of the proposed analytical model.

Vibration isolation via a scissor-like structured platform

Simultaneously primary and super-harmonic resonance of a van der Pol oscillator with fractional-order derivative

With the aim of unifying the damping concept and evaluating the amount of damping in a structure, this paper investigates whether friction action can be equivalent to traditional viscous damping. The research focused on purely concave friction distribution cases, uniform friction distribution cases, and their combination cases in a spring-friction isolation system. The dynamic responses of a numerical method using friction action were compared with those of another numerical methods using equivalent viscous damping under sine wave ground motions. The comparison of results shows that the friction action can be converted to the equivalent viscous damping action with some errors by using an equation. The conversion accuracy of uniform friction distribution cases using the first term of the equation is much worse than that of the purely concave friction distribution cases using the second term of the equation. The reason for this being that the uniform friction distribution can prevent the structure from sliding back to its center after the ground motion; however, the viscous damping action does not have such a negative function. The comparison errors, between using the friction action and using the equivalent viscous damping, are directly proportional to the ratio of the component of uniform friction distribution to the component of purely concave friction distribution.

Passive energy dissipation devices or supplemental damping devices have been successfully implemented into structures for controlling the excessive vibrations under wind and seismic excitation. Recent developments in the form of negative stiffness dampers (NSDs) and inerter-based vibration absorbers (IVAs) as potential energy dissipation devices are of considerable interest to researchers. The present study evaluates the performance of the combined NSD and IVA as a possible alternative to the traditional energy dissipation devices such as viscous dampers (VDs) and viscoelastic dampers (VEDs). The mathematical formulation and optimal design of the combined NSD and IVA mechanism are presented. A 20-storey benchmark building is modeled as a multi-degree-of-freedom (MDOF) shear building. The dynamic equations for the MDOF building are written in the state-space form, and a simple optimization approach based on effective modal damping is prescribed. Comparative performance between traditionally applied and novel IVA and NSD is investigated. The design considerations to analyze structures employing combined NSDs and IVAs are developed. It is demonstrated that NSDs and IVA-based passive energy dissipation devices are the most efficient devices in reducing inter-storey drifts and floor accelerations compared with VDs and VEDs using the same damping coefficient.