System Modal Damping Research Articles

Frequency and damping of hybrid cable networks with cross-ties and external dampers: Full-scale experiments

This paper presents a full-scale experimental study on dynamics of hybrid cable networks composed of three real cables, a rigid cross-tie and three viscous-shear dampers. For comparison, an improved numerical model of cable networks considering cross-ties, dampers, and cross-tie pretension is also provided. The measured frequencies and mode shapes of the cable networks with different configurations and cross-tie locations are found in good agreement with corresponding theoretical predictions. The characteristics of damping variation with respect to cross-tie location and the layout observed from the experiments are generally consistent with the theoretical analysis, although there is a discrepancy between identified and computed values of damping. The experiments show that the cross-tie when located close to the dampers can lead to a reduction in modal damping of low-frequency modes. The dampers in the cable networks provide relatively large damping to global modes and modes dominated by vibrations of cable segments to which the damper is connected. Furthermore, when the cross-tie is installed far away from the external dampers, the cross-tie extended to the ground can effectively improve the system modal damping, as the length of the cable is reduced equivalently and the relative distance of the damper away from the closest anchor as compared to the cable length is increased.

Study on coupled modes panel flutter stability using an energy method

In this paper, an energy method is presented to study the coupled modes type panel flutter stability. The aeroelastic system continuous motion equation is built by adopting the first order piston theory aerodynamic loading. This continuous motion equation can be transformed by applying Galerkin method and constructed into a two-degree-of-freedom reduced order model (2-DOF ROM). Based on this ROM consisting of the first two structural modes, energy method is presented to investigate the system coupled modes type panel flutter stability. The obtained stability condition can be validated by comparing with its counterpart derived by Routh-Hurwitz criteria. Additionally, the critical system parameters can be evaluated and validated. Comparing with previous Ritz averaging method, the relationship between the modal coordinate amplitudes ratio and the modal damping coefficients ratio is believed to be firstly derived. The system damping paradoxical effect on coupled modes type panel flutter stability can be investigated after introducing the parameter, modal damping coefficients ratio. For given system modal damping coefficients, the phase difference and the modal coordinate amplitudes ratio of the first two modal coordinates can be specified. Based on the system power flow equations and the calculated parameters, the energy transfer characteristic between the supersonic airflow and the first two structural modes can be clarified. Such energy transfer procedure can be done within a half of oscillation period to sustain a neutrally stable single period oscillation.

Wide area oscillation damping controller for DFIG using WAMS with delay compensation

Several studies have reported the improvement of system stability with a doubly-fed induction generator (DFIG) based wind turbines. Due to the remote location of DFIG, the local signals measured may not contain the complete oscillation information of the power system. This study describes an optimisation enabled wide area damping control (WADC) for DFIG to mitigate both local and inter area oscillations. Wide area measurement systems (WAMSs) which include phasor measurement units and synchrophasors are used for a centralised controller for damping inter-area and local oscillatory modes. The proposed damping controller parameters are optimised along with the local power system stabiliser settings for maximising the impact on system modal damping. The challenging shortcoming of WAMS based controller is the variable communication latency which can adversely affect the controller if not accounted in the controller design process. The proposed WADC algorithm addresses this issue and compensates for the delayed and time stamped error signals. The variable latencies are normalised in the optimisation algorithm in the design of controller parameters. The proposed algorithm is verified with transient simulation in PSCAD/EMTDC for the most severe three-phase faults. A set of comprehensive case studies are performed to analyse the effectiveness of the proposed algorithm for the noisy, delayed communication signals.

A novel energy dissipation outrigger system with rotational inertia damper

Rotational inertia damper, a novel damper, possessing the advantage of displacement amplification, has been employed in outrigger system for seismic mitigation. The equivalent analysis model composed by a uniform cantilever beam and an equivalent spring was proposed to simulate the rotational inertia damper outrigger system, by which the corresponding dynamic characteristic equation was derived based on numerical assembly technique. To gain the response of the damped system, finite element method and state space method have been utilized. Finally, the results show that the pseudo-undamped natural frequency ratios and system modal damping ratios are significantly influenced by stiffness parameter of the exterior column, while the mass parameter of the rotational inertia damper has little effect on them. The optimal damping ratio can be acquired for one mode, but it may be worse for the other mode in the same position equipping rotational inertia damper. Furthermore, numerical simulation results for the typical earthquake records have verified that the rotational inertia damper outrigger has excellent control performance in displacement as well as acceleration. A good agreement between damping force and equivalent force also suggests that the damping force of rotational inertia damper is predominant and the inertial force has no significant effect on the structure.

Influence of cable dampers on cable-stayed bridges

Cable-stayed bridges have seen a wider application in recent years, with many having longer and longer spans. Modern cable-stayed bridges use numerous cables to support the stiffening girders. Many cable dampers are installed to mitigate cable vibration. This paper focuses on the effect of a cable damper on the dynamic characteristics of the whole cable-stayed bridge, especially modal damping. A practical model comprising the cable, girder and damper is developed to analyse the relationship between system modal damping and the performance of a cable damper with the complex mode method. A test model with cable, girder and damper was made to verify the theoretical results. A finite-element model of a simplified cable-stayed bridge based on a test model is adopted to assess the effects of cable dampers on the anti-seismic performance and wind-resistant behaviour of the cable-stayed bridge. The results show that the cable dampers of a cable-stayed bridge can increase the modal damping of the whole bridge.

Theoretical Study on Cable’s Vibration Control by Single TMD

The commonly used viscous dampers for cable’s vibration mitigation have some unfavorable factors, such as the damping effect is not obvious for super long stay cable, the limitation of installation position, coupling vibration, etc. The cable-tuned mass damper system vibration model is put forward to solve this problem. The optimal cable-tuned mass damper system modal damping ratio and optimum design parameters, including cable vibration order, TMD’s stiffness, TMD’s mass, and TMD’s damping, were obtained by the method of complex models. The results can provide important reference for the design of TMD for stay cable.

Influence of Cable Dampers on Cable-Stayed Bridges

Cable-stayed bridges have seen a wider application in recent years, with many having longer and longer spans. Modern cable-stayed bridges are using numerous cables to support the stiffing girders. Many cable dampers are installed to mitigate cable vibration. This paper focuses the attention on the effect of cable damper on the dynamic characteristics of the whole cable-stayed bridge, especially the modal damping. A practical model comprised of the cable, girder, and damper is developed to analyze the relationship between system modal damping and the performance of cable damper with complex mode method. A test model with cable, girder and damper was made to verify the theoretical results. A finite element model of a simplified cable-stayed bridge based on test model is adopted to assess the effects of cable dampers on the anti-seismic performance and wind-resistant behavior of the cable-stayed bridge. The results show that the cable dampers of cable-stayed bridge can increase the modal damping of the whole bridge.

Comparison of deck-anchored damper and clipped tuned mass damper on cable vibration reduction

Excessive cable vibrations are detrimental to cable-stayed bridges. Increasing the system damping of cables is a key solution to resolve this severe problem. Equations representing the dynamic characteristics of an inclined cable with a Deck-Anchored Damper (DAD) or with a Clipped Tuned Mass Dampers (CTMD) are reviewed. A theoretical comparison on the performance of cable vibration reduction between the cable-DAD system and the cable-CTMD systems is thoroughly discussed. Optimal system modal damping for the free vibration and transfer functions for the forced vibration for the two cabledamper systems are addressed and compared in detail. Design examples for these two different dampers are also provided.

Theoretical exploration of a taut cable and a TMD system

A Tuned Mass Damper-Magnetorheological (TMD-MR) damper that can be placed anywhere along a cable was proposed and tested in the previous study by the writers to overcome the deficiency of the traditional mechanical dampers. In the present study, free vibrations of a taut horizontal cable with an attached TMD model that represents the proposed TMD-MR damper are investigated in detail using analytical formulations of a complex equation of motion, which comes to be an eigenvalue problem in terms of the location of the damper, the mass, and the frequency ratios between the TMD damper and the cable, and the damping ratio of the TMD damper. The solution of this complex eigenvalue problem represents the dynamic characteristics of the cable–damper system. Two special cases (over-damped and zero-damped oscillation) are discussed. Effects of parameters such as the positions and properties of the TMD damper on the system dynamic characteristics are investigated in terms of system modal damping. Parametric results show that a considerable modal damping can be obtained using the TMD damper if an appropriate balance between the TMD component and the MR component is achieved. This numerical procedure provides a basis for a rational design of the TMD-MR damper for any specific cable. A design example is provided for demonstration purposes.

Cable Vibration Reduction with a Hung-on TMD System, Part II: Parametric Study

Based on the theoretical derivations of the free vibration problem for a cable-TMD system in the companion paper, a parametric study is carried out in the present paper to investigate the influence on the solutions, and thus the system modal damping and frequency, of the cable geometry-elasticity parameter, cable inclination, damper position, mass ratio, frequency ratio, damper damping ratio, and tuning mode. Emphasis is put on the system modal damping, as this is an important index of the performance of the TMD. The features and mechanisms of energy transfer and damping redistribution from the TMD to each mode of the cable-TMD system are also investigated and discussed.

Damping Effects on the State-Switched Absorber Used for Vibration Suppression

A state-switched device is conceptually capable of instantaneously changing its mass, stiffness, or damping. Such a device will exhibit different dynamical response properties (modes and resonance frequencies) depending on its current state. A state-switched vibration absorber exploits the state-switching concept for the purposes of enhanced vibration suppression. Between each state switch, it is fundamentally a passive vibration absorber, but one which exhibits a different tuning frequency for each possible state. A state-switched vibration absorber therefore has a greater effective bandwidth than a classical passive absorber. This paper considers the role of damping in the state-switching concept for a simple one-degree of freedom system and for a two-degree of freedom system. Certain values of damping in the system improve performance, while other values hinder the performance of the state-switched absorber, as compared to classical absorbers. The predicted performance of the system also depends upon the particular damping model used, such as viscous absorber or system modal damping. Damping values also affect the frequency of switch events that occur during the response of the system. In general, the highest relative performance of the state-switched absorber as compared to a classical vibration absorber occurs at low values of damping.

Dynamic characteristics and vibration control of a cable system with substructural interactions

Free and forced vibration analyses of a cable system, which consists of two identical sagged cables in parallel connected by another sagged cross cable, are conducted using a modal synthesis method with substructural formulation. The analyses are carried out in order to investigate the system behavior, while paying attention to the substructural interaction. It is shown that the secondary cable contribution in the system modal damping can be dominant and can cause greater damping in the case of coupled motion of main and secondary cables. The importance of the secondary cable in transferring the energy from one substructure to another through the substructural interaction is also discussed for the passive control of harmonically forced vibration in the main cable.

Experimental Analysis of Impact-Damped Flexible Beams

Statistical analysis of the phenomenon of impact damping is performed on 60 steady-state vibration tests of a flexible beam to relate the system's modal damping to system parameters. Compared with other measures of effectiveness of the impact damper, modal damping ratios are useful in predicting the response of continuous systems under arbitrary forcing functions. Contour plots show that the modal damping ratio is nonlinearly dependent on the damper's mass and gap. However, these are not the only parameters that control the effectiveness of the impact damper. Multiple nonlinear regression analysis of the data is used to test the dependence of the system's modal damping on a number of parameters. It is hypothesized that the system's parameters are the mass and gap of the impact damper, the excitation frequency, the peak of the frequency response function, and the modal amplitude at the location of the impact damper. Multiple nonlinear regression analysis shows the validity of the hypothesis and the ability of the derived formula to predict the modal damping ratio of the beam.

Component modes damping assignment methodology for articulated, multiflexible body structures

To simulate the dynamical motion of articulated, multiflexible body structures, one can use multibody simulation packages such as DISCOS. To this end, one must supply appropriate reduced-order models for all of the flexible components involved. The component modes projection and assembly model reduction (COMPARE) methodology is one way to construct these reduced-order component models, which when reassembled capture important system input-to-output mapping of the full-order model at multiple system configurations of interest. In conjunction, we must also supply component damping matrices which when reassembled generate a system damping matrix that has certain desirable properties. The problem of determining the damping factors of components' modes to achieve a given system damping matrix is addressed here. To this end, we must establish from first principles a matrix-algebraic relation between the system's modal damping matrix and the components' modal damping matrices. An unconstrained/constrained optimization problem can then be formulated to determine the component modes' damping factors that best satisfy that matrix-algebraic relation. The effectiveness of the developed methodology, called ModeDamp, has been successfully demonstrated on a high-order, finite element model of the Galileo spacecraft.

Inherent limitations in digital incremental oscillator-analyser systems for mechanical vibration testing

Consideration of the limiting conditions under which the existence of a resonant state can be identified and a circular arc fitted to discrete points of a complex plane plot have shown that useful measurements of mechanical system parameters can be made only within closely related limits of system modal damping ratio and frequency. The limitations are particularly important when one wants to use high frequency extension units to digital instrumentation in order to test just beyond the highest frequency of the basic unit. It is shown that a suitable digital system for the determination of parameters in mechanical vibration comprises a basic system with five-digit frequency to 1 kHz and an extension unit extending the frequency by one decade only.