scholarly journals Refined Study on Free Vibration of a Cable with an Inertial Mass Damper

2019 ◽  
Vol 9 (11) ◽  
pp. 2271 ◽  
Author(s):  
Zhihao Wang ◽  
Fangfang Yue ◽  
Hao Wang ◽  
Hui Gao ◽  
Buqiao Fan
Keyword(s):  
Flexural Rigidity ◽  
Damping Ratio ◽  
Inertial Mass ◽  
Experimental Results ◽  
Complex Eigenvalue ◽  
Cable Model ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Mass Damper ◽  
Actual Design

To accurately predict the optimum supplemental modal damping ratio of the cable and the corresponding size of the inertial mass damper (IMD), combined effects of the cable sag, the cable flexural rigidity, and the boundary conditions on the control performance of the cable with the IMD are well investigated in this refined study. An analytical model of the cable-IMD system considering these effects is developed. The equation of motion of the cable-IMD system is transformed into a complex eigenvalue problem through the finite difference method. Experimental results from a scaled cable model with an IMD are then used to verify theoretical solutions. Three typical cables in actual cable-stayed bridges are selected for case studies. The results show that the theoretically predicted modal damping ratios of the cable with an IMD, taking into account the sag and the flexural rigidity, agree well with those identified from experimental results, while would be often overestimated with a taut-cable model. Moreover, experimental damping ratios of the cable always fall between those theoretically calculated with fixed ends or pinned ends for each case. Finally, to be conservative in actual design, it is recommended to use the cable-IMD system model with fixed ends to calculate the required damper size and predict the resulting modal damping ratio of the cable, since the corresponding theoretical solution often gives the lower bound of supplemental damping ratio of the cable.

Theoretical Study on Cable’s Vibration Control by Single TMD

2014 ◽  
Vol 935 ◽  
pp. 211-214 ◽  
Author(s):  
Dong Liang ◽  
Ji Xiang Song
Keyword(s):  
Damping Ratio ◽  
Tuned Mass Damper ◽  
Design Parameters ◽  
Stay Cable ◽  
Coupling Vibration ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Vibration Model ◽  
Mass Damper ◽  
Complex Models

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.

Research on the Modal Damping Ratio for Stay Cable with Viscoselasticity Damper in Cable-Stayed Bridges

2013 ◽  
Vol 779-780 ◽  
pp. 671-674
Author(s):  
Shui Sheng Chen ◽  
De Shan Wang
Keyword(s):  
Damping Ratio ◽  
Bending Stiffness ◽  
Complex Eigenvalue ◽  
Stay Cable ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Out Of Plane ◽  
Damper Design ◽  
Inclined Angle ◽  
Separation Strategy

Taking the bending stiffness, cable static sag and cable inclined angle into consideration, equations of space free vibration of the cable-damper system are derived in this paper. Joining the variable separation strategy and center difference method, the partial differential equations are discretized in space and a set of complex eigenvalue equations, which are solved by state space method, are derived, and both the maximum modal damping ration and the optimal damper parameter are obtained. Several typical stay cables are investigated for both the in-plane and out-of-plane modes under different cable parameters and damper parameters. The results demonstrate that modal damping ratio for the first in-plane mode is significantly affected by the cable static sag only, but those for the other modes affected by cable sag are slight, and cable static sag do not affect the optimal damper parameter for all modes, however the bending stiffness will changes both the maximum modal damping ratios and the optimal damper parameters. Some valuable suggestions are proposed for the optimal damper design.

scholarly journals Inertial mass damper for vibration control of cable with sag

2018 ◽  
Vol 39 (3) ◽  
pp. 749-760 ◽  
Author(s):  
Zhi-Hao Wang ◽  
Hui Gao ◽  
Bu-qiao Fan ◽  
Zheng-Qing Chen
Keyword(s):  
Inertial Mass ◽  
Damping Coefficient ◽  
Stay Cables ◽  
Modal Damping ◽  
Optimal Damping ◽  
Mass Damper ◽  
Negative Effect ◽  
Supplemental Damping ◽  
Antisymmetric Vibrations ◽  
General Dynamic

It has been theoretically predicted that superior supplemental damping can be generated for a taut cable with an inertial mass damper. This paper extends previous studies to investigate the effect of the cable sag on the efficiency of an inertial mass damper. The general dynamic characteristics of an inclined sag cable with an inertial mass damper installed close to the cable end are theoretically investigated. The parametric analysis of the inertial mass and the damping coefficient of the inertial mass damper are conducted to evaluate the control performance of the cable with different sags. The results show that the inertial mass damper can alleviate the negative effect induced by the cable sag, and the cable sag can even increase modal damping ratios provided by the inertial mass damper. Sags of stay cables used in actual bridges only affect nearly symmetric vibrations of cables, while having little impact on nearly antisymmetric vibrations. The effect of cable sags will reduce the optimal damping coefficient and inertial mass of the inertial mass damper for the first symmetric mode of the cable.

Modal damping ratio analysis of dynamical system with non-stationary responses

2016 ◽  
Vol 59 ◽  
pp. 138-146 ◽  
Author(s):  
Da Tang ◽  
Ran Ju ◽  
Qianjin Yue ◽  
Shisheng Wang
Keyword(s):  
Dynamical System ◽  
Damping Ratio ◽  
Ratio Analysis ◽  
Modal Damping Ratio ◽  
Modal Damping

scholarly journals Coupling of Flexural and Longitudinal Damped Vibration in a Two-Layered Beam

1998 ◽  
Vol 5 (5-6) ◽  
pp. 337-341
Author(s):  
F. Pourroy ◽  
S. Shakhesi ◽  
P. Trompette
Keyword(s):  
Damping Ratio ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Layered Beam ◽  
Flexural Vibrations

In dynamics, the effect of varying the constitutive materials’ thickness of a two-layered beam is investigated. Resonance frequencies and damping variations are determined. It is shown that for specific thicknesses the coupling of longitudinal and flexural vibrations influences the global modal damping ratio significantly.

ODS Analysis on the Rack of Batching System Mixer

2013 ◽  
Vol 437 ◽  
pp. 257-260
Author(s):  
Li Zhang ◽  
Guang Yuan Nie
Keyword(s):  
Working Condition ◽  
Damping Ratio ◽  
Side Surface ◽  
Modal Parameters ◽  
Modal Shape ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Before And After ◽  
Structure Vibration ◽  
Batching Machine

By using ODS (Operating Deflection Shapes) technology, the modal parameters of the rack of a batching system mixer under operating condition are identified and the modal shape and modal damping ratio of the rack in a few working frequencies are obtained. The results show that, the batching machine rack on working condition has a significant effect on some frequency and the work principal modes that appear as before and after exercise of two beams above the rack and swaying motion of the brackets of the two side surface. This paper provides a valuable reference for the structure vibration optimization of batching system mixer.

Free Vibration Analysis of Frame-Core Tube Structures Attached with Damped Outriggers

2012 ◽  
Vol 238 ◽  
pp. 648-651
Author(s):  
Zhi Hao Wang
Keyword(s):  
Damping Ratio ◽  
Free Vibration Analysis ◽  
Structural System ◽  
Viscous Dampers ◽  
Core Tube ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
New Energy ◽  
Energy Dissipation System ◽  
Simplified Calculation

The classical outrigger in frame-core tube structure cantilevering from the core tube or shear wall connected to the perimeter columns directly, which can effectively improve the lateral stiffness of the structure. A new energy-dissipation system for such structural system is studied, where the outrigger and perimeter columns are separate and vertical viscous dampers are equipped between the outrigger and perimeter columns to make full use of the relative big displacement of two components. The effectiveness of proposed system is evaluated by means of the modal damping ratio based on the proposed simplified model. The mathematic models of the structural system are obtained with both the assumed mode shape method and finite element method according to the simplified calculation diagram. Based on the modal damping ratio, the optimal damping coefficients of linear viscous dampers are determined, and effectiveness of proposed system is confirmed.

scholarly journals Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach

2011 ◽  
Vol 18 (1-2) ◽  
pp. 221-244 ◽  
Author(s):  
Zheng Ling ◽  
Xie Ronglu ◽  
Wang Yi ◽  
Adel El-Sabbagh
Keyword(s):  
Topology Optimization ◽  
Energy Dissipation ◽  
Design Variable ◽  
Optimization Design ◽  
Damping Ratio ◽  
Design Tool ◽  
Optimization Approach ◽  
Constrained Layer Damping ◽  
Modal Damping Ratio ◽  
Modal Damping

Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA) is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an invaluable design tool.

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