Theoretical Investigation on the Impact of Two HDR Dampers on First Modal Damping Ratio of Stay Cable

Stay cables are one of the vital components of a cable-stayed bridge. Due to their flexible nature, stay cables are vulnerable to external excitation and often vibrate with large amplitude under wind action which leads to the fatigue failure of the cables. To suppress such kind of large amplitude vibration by improving the damping ratio of the cable various dampers such as magnetorheological damper, friction damper; oil damper; or high damping rubber (HDR) damper are utilized and gained popularity over time. This paper focuses on improving the damping ratio of stay cables using a combination of two HDR dampers. First, the theoretical model is formulated considering cable bending stiffness to evaluate the damping effect of cable-HDR dampers system. Then, the impact of various design parameters of HDR dampers on cable damping considering the cable stiffness is performed. The comparative analysis of results shows that the considered parameters such as loss factor, spring factor, and installation location of dampers have much effect on the stay cables damping ratio. Finally, the optimal parameters of the two HDR dampers are proposed for damper design.

Modal Parameter Tracking in a Carbon Fiber-Reinforced Structure over Different Carbon Fiber Angles

The dynamics of carbon fiber-reinforced plastic (CFRP) change according to the carbon fiber angle, and a mode order shift may occur in CFRP specimens. The variation trends in modal parameters differ in each mode; thus, an efficient mode-tracking method is needed to identify the reliable dynamic behavior of the CFRP structure. The mode-tracking method was assumed to be applicable for the same configuration of the tested specimen except for the differences in carbon fiber angle of the CFRP specimen. Simple rectangular specimens were prepared for one isotropic material, SS275, and five anisotropic CFRP specimens with five carbon fiber angles ranging from 0° to 90°. An experimental impact test was conducted to obtain all the modal parameters. The proposed mode-tracking method was applied using three indicators: the modal assurance criterion (MAC) and two modal parameters (resonance frequency and modal damping ratio). The MAC value was valid for the three bending modes at 0°, 30°, and 90°, but not for the two torsional modes. However, the variation in the resonance frequencies was a more efficient indicator with which to track all the modes of interest, except for the second torsional mode. The variation in the modal damping ratio was also a valid indicator for the two torsional modes. Therefore, the proposed three indicators were all required to derive reliable mode tracking for the CFRP specimens considering the mode order shift.

Optimization of VEDs for Vibration Control of Transmission Line Tower

This paper investigates the optimization of viscoelastic dampers (VEDs) for vibration control of a transmission line tower. Considering the stiffness of the steel brace connected to a VED, the mechanical model of the VED-brace system was established. Subsequently, the additional modal damping ratio of the transmission line tower attached with VEDs was obtained analytically. Furthermore, the finite element model of a two-circuit transmission line tower with VEDs was built in ANSYS software, and the influences of installation positions and parameters of VEDs on the additional modal damping ratio were clarified. In addition, the control performance of VEDs on the transmission line tower subjected to wind excitations was emphatically illustrated. The results show that the stiffness of the steel brace connected to a VED has a significant effect on the maximum additional modal damping ratio of the VED-brace system provided for the transmission line tower and the optimal parameters of the VED. Meanwhile, the installation positions of VEDs dramatically influence the additional modal damping ratio. Moreover, the increase of the brace stiffness and the loss factor is beneficial to improve the control performance of VEDs. Besides that, the VEDs present superior control performance on the top displacement of the transmission line tower as well as the transverse bending vibration energy.

Sensitivity of the Viscous Damping Coefficient of Carbon Fiber in Carbon-Fiber-Reinforced Plastic with Respect to the Fiber Angle

The variation in the viscous damping coefficient with the carbon fiber angle can be evaluated using the partial derivatives of the viscous damping coefficient with respect to the resonance frequency and modal damping ratio. However, the direct derivatives of the viscous damping coefficient were not effective solutions to the sensitivity analysis of carbon-fiber-reinforced plastic (CFRP) structures because the viscous damping from the binding matrix was not changed over the carbon fiber angle. If the identified viscous damping coefficients were assumed to be equivalent values from the parallel relationship between the binding matrix and carbon fiber, the relative error of the viscous damping coefficient of carbon fiber between the increased carbon fiber angle and reference angle could be used as the sensitivity index for the viscous damping coefficient of carbon fiber only. The modal parameters, resonance frequency, and modal damping ratio were identified from the experimental modal test of rectangular CFRP specimens for five different carbon fiber angles between 0° and 90°. The sensitivity of the viscous damping coefficient of carbon fiber was determined for two sensitivity indices: the direct derivative of the mass-normalized equivalent viscous damping coefficient and the relative error of the viscous damping coefficient of carbon fiber. The sensitivity results were discussed using the five mode shapes of the CFRP specimen, that is, three bending modes and two twisting modes.

Research on dynamic behavior and traffic management decision-making of suspension bridge after vortex-induced vibration event

Long-span suspension bridges are susceptible to wind loads due to their lightweight, low stiffness, and small structural damping. Recently, two large-span suspension bridges in China that closed for several months due to COVID-2019 experienced large-scale and continuous vortex-induced vibration shortly after reopening to traffic, and the traffic was closed again for safety consideration, which has aroused widespread concerns in society. To provide a reference for owners and related decision-making departments whether to restore the traffic, this article intends to explore the impact mechanism of traffic loads on the dynamic behavior of suspension bridges. First, two mechanical models for suspension bridges considering traffic loads and structural damping are proposed in this article. Then, based on the extended dynamic stiffness method, the explicit expressions of modal damping ratio in the two models are derived for the first time. Subsequently, Wittrick–Williams algorithm is employed to solve the frequency equation to obtain the modal frequency of the structure that considers the effect of traffic loads. A numerical case is studied to inspect the influence of traffic loads on the structural dynamic characteristics. Moreover, field monitoring data of accelerations of a suspension bridge are utilized to demonstrate the reasonability and accuracy of the approach proposed. Analysis shows that the theoretical results are consistent well with the measured ones, which indicates the traffic loads will affect the dynamic characteristics of the suspension bridge, thus reducing the modal frequency and increasing the modal damping ratio. Besides, the measured results further explain that the contribution of traffic loads to the structural damping is significant, which has a positive effect on preventing and eliminating vortex-induced vibration response. Some interesting and enlightening conclusions are also obtained in this article.

Mathematical modeling and experimental study of damping behavior of a cantilever carbon fiber–reinforced polymer composite hollow member with metal inserts

Metal inserts are widely used particularly in bolted connections for joining composite members. In this work, a theoretical basis is provided for analyzing the damping behavior of a cantilever composite square hollow member embedded with metal inserts along its length. Analytic stress solutions around the boundaries of the insert and the member are introduced while deriving the expression of modal damping ratio. Kelvin–Voigt and amplitude-dependent damping models are considered for the formulation. Experiments are performed on the perforated composite tube reinforced with brass, copper, and steel annular inserts subjected to transverse base motion of varying amplitudes. The acceleration responses recorded from the tests are analyzed to evaluate the damping ratio of the fundamental mode. It is observed that the damping ratio evaluated from the experiments matches well with the proposed value. Furthermore, it is found that the damping ratio increases when the holes are reinforced with the inserts. The reason for the increase in damping stems from (i) frictional effect at the boundaries of the insert and the tube and (ii) material damping of the inserts. For example, the damping amplification of the tube with five steel inserts is noted to be around 3.0 and 2.1 times with respect to the unperforated and perforated (with holes) cases, respectively.

Dynamics of a Pipeline Span on an Elastic Seabed

Natural frequencies, mode shapes and modal damping ratios must be estimated to assess subsea pipeline spans for vortex-induced vibrations (VIV) and response to direct wave loading. Several approximate solutions exist for a linearly elastic pipe under constant axial force supported by linearly elastic springs beyond the span’s shoulders. An exact analytical solution has only recently been published. That solution is used here in a Rayleigh-Ritz approximation to account for arch action arising from combined effects of sag under gravity loads and axial restraint at the shoulders. The method allows survey data to be used directly to quantify arch action. Its accuracy is confirmed by finite element analysis. Further, the modal damping ratio is estimated based on the fractions of the potential energy in bending, the axial force, and the soil springs, all of which are determined analytically. Thus, it is found that the effective modal damping ratio increases without a bound as the axial load approaches the buckling load in compression.

Modal damping ratio of symmetric laminate composite under the effect of attached mass using experimental design

Nowadays, the use of composite materials has taken a large place in civilian industries as well as in military and aerospace industries. Therefore, significant investigations about their mechanical and physical properties are needed. The present study addresses the effect of attached mass on damping ratio of symmetric angle ply laminate composite. Furthermore, factor influencing the effect of attached mass on damping ratio of laminate composite are studied using Taguchi method. The considered factors parameters are: attached mass locations from the clamped edge, stacking sequences and boundary conditions. The results of this study indicate that the damping ratio of the laminate composite plates is sensitive to the attached mass, where the damping ratio is found to be proportional to the locations of the attached mass. The findings of this study indicate that the attached mass decreases frequency parameter and increase the damping ratio of the composite plate, if it is inserted at a point other than a nodal line. In addition, the paper presents a good correlation between the numerical results of the fundamental frequency obtained by the ANSYS software and those obtained experimentally.