• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.421-432
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• 2019

In high-speed railway (HSR) system, the structure-borne noise inside viaduct at low frequency has been extensively investigated for its mitigation as a research hotspot owing to its harm to the nearby residents. This study proposed a novel acoustic optimization method for declining the structure-borne noise in viaduct-like structures by separating the acoustic contribution of each structural component in the measured acoustic field. The structural vibration and related acoustic sourcing, propagation, and radiation characteristics for the viaduct box girder under passing vehicle loading are studied by incorporating Finite Element Method (FEM) with Modal Acoustic Vector (MAV) analysis. Based on the Modal Acoustic Transfer Vector (MATV), the structural vibration mode that contributes maximum to the structure-borne noise shall be hereinafter filtered for the acoustic radiation. With vibration mode shapes, the locations of maximum amplitudes for being ribbed to mitigate the structure-borne noise are then obtained, and the structure-borne noise mitigation performance shall be eventually analyzed regarding to the ribbing conduction. The results demonstrate that the structural vibration and structure-borne noise of the viaduct box girder mainly occupy both in the range within 100 Hz, and the dominant frequency bands both are [31.5, 80] Hz. The peak frequency for the structure-borne noise of the viaduct box girder is mainly caused by $16^{th}$ and $62^{th}$ vibration modes; these two mode shapes mainly reflect the local vibration of the wing plate and top plate. By introducing web plate at the maximum amplitude of main mode shapes that contribute most to the acoustic modal contribution factors, the acoustic pressure peaks at the field-testing points are hereinafter obviously declined, this implies that the structure-borne noise mitigation performance is relatively promising for the viaduct.

• Smart Structures and Systems
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• v.11 no.4
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• pp.411-433
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• 2013

Due to its easy operation and wide applicability, the ambient vibration method is commonly adopted to determine the cable force by first identifying the cable frequencies from the vibration signals. With given vibration length and flexural rigidity, an analytical or empirical formula is then used with these cable frequencies to calculate the cable force. It is, however, usually difficult to decide the two required parameters, especially the vibration length due to uncertain boundary constraints. To tackle this problem, a new concept of combining the modal frequencies and mode shape ratios is fully explored in this study for developing an accurate method merely based on ambient vibration measurements. A simply supported beam model with an axial tension is adopted and the effective vibration length of cable is then independently determined based on the mode shape ratios identified from the synchronized measurements. With the effective vibration length obtained and the identified modal frequencies, the cable force and flexural rigidity can then be solved using simple linear regression techniques. The feasibility and accuracy of the proposed method is extensively verified with demonstrative numerical examples and actual applications to different cable-stayed bridges. Furthermore, several important issues in engineering practice such as the number of sensors and selection of modes are also thoroughly investigated.

• Wind and Structures
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• v.29 no.3
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• pp.163-175
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• 2019

Multispan suspension bridges make a good alternative to single-span ones if the crossed strait or river width exceeds 2-3 km. However, multispan three-tower suspension bridges are found to be very sensitive to the wind load due to the lack of effective longitudinal constraint at their central tower. Moreover, at certain critical wind speed values, the aerostatic instability with sharply deteriorating dynamic characteristics may occur with catastrophic consequences. An attempt of an in-depth study on the aerostatic stability mode and damage mechanism of three-tower suspension bridges is made in this paper based on the assessment of strain energy and dynamic characteristics of three particular three-tower suspension bridges in China under different wind speeds and their further integration into the aerostatic stability analysis. The results obtained on the three bridges under study strongly suggest that their aerostatic instability mode is controlled by the coupled action of the anti-symmetric torsion and vertical bending of the two main-spans' deck, together with the longitudinal bending of the towers, which can be regarded as the first-order torsion vibration mode coupled with the first-order vertical bending vibration mode. The growth rates of the torsional and vertical bending strain energy of the deck after the aerostatic instability are higher than those of the lateral bending. The bending and torsion frequencies decrease rapidly when the wind speed approaches the critical value, while the frequencies of the anti-symmetric vibration modes drop more sharply than those of the symmetric ones. The obtained dependences between the critical wind speed, strain energy, and dynamic characteristics of the bridge components under the aerostatic instability modes are considered instrumental in strength and integrity calculation of three-tower suspension bridges.

• The Journal of the Acoustical Society of Korea
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• v.34 no.3
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• pp.219-226
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• 2015

In this paper, derivation of the STL (Sound Transmission Loss) of a square plate installed in an impedance tube is discussed using an analytic method. Coupled motion of the plate vibration and acoustic field is considered. Vibration of the plate and pressure field inside the tube are expressed in terms of the infinite series of modal functions. Under the plane wave assumption, it is shown that consideration of the first few modes yields sufficiently accurate results. When the boundary of the plate is clamped, vibration mode is assumed as a multiplication of the beam modes corresponding to the crosswise directions. The natural frequencies of the clamped plate are calculated using the Rayleigh-Ritz method. It is found that the STL shows a dip at the lowest natural frequency of the plate, and increases as the frequency decreases below the natural frequency. Comparison of the result in this paper with the STL obtained by measurements and FE computations in the reference shows an excellent agreement.

• Journal of KSNVE
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• v.9 no.1
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• pp.196-205
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• 1999

The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

• Journal of Advanced Navigation Technology
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• v.4 no.2
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• pp.103-113
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• 2000

There are several methods in the mathematical modeling of a satellite with flexible appendages. In this paper, the hybrid Lagrange's equations of motion using assumed modes method are derived. The assumed modes method is one of approximate methods which have shorter calculation time due to low-dimension compare with FEM. These consist of three-equations about angular velocities and two-equations about flexible deformations, and physically represent interaction between hub and solar panel. In an attitude control, a control law is designed to minimize a given performance index considering not only control input but also vibration suppression. For these purpose, this paper applies LQG and LQG/LTR schemes to this model and finally show the capability for attitude control including vibration suppression. Especially, this paper shows the method of assumption as nonsingular system through singular value division for LQG/LTR design.

• Structural Engineering and Mechanics
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• v.52 no.1
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• pp.51-73
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• 2014

A three-dimensional finite element model for the Jiashao Bridge, the longest multi-span cable-stayed bridge in the world, is established using the commercial software package ANSYS. Dynamic characteristics of the bridge are analyzed and the effects of structural system measures including the rigid hinge, auxiliary piers and longitudinal constraints between the girders and side towers on the dynamic properties including modal frequency, mode shape and effective mass are studied by referring to the Jiashao Bridge. The analysis results reveal that: (i) the installation of the rigid hinge significantly reduces the modal frequency of the first symmetric lateral bending mode of bridge deck. Moreover, the rigid hinge significantly changes the mode shape and effective mass of the first symmetric torsional mode of bridge deck; (ii) the layout of the auxiliary piers in the side-spans has a limited effect on changing the modal frequencies, mode shapes and effective masses of global vibration modes; (iii) the employment of the longitudinal constraints significantly increases the modal frequencies of the vertical bending modes and lateral bending modes of bridge deck and have significant effects on changing the mode shapes of vertical bending modes and lateral bending modes of bridge deck. Moreover, the effective mass of the first anti-symmetric vertical bending of bridge deck in the longitudinal direction of the fully floating system is significantly larger than that of the partially constrained system and fully constrained system. The results obtained indicate that the structural system measures of the multi-span cable-stayed bridge have a great effect on the dynamic properties, which deserves special attention for seismic design and wind-resistant design of the multi-span cable-stayed bridge.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2007.04a
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• pp.7-12
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• 2007

Swirl injector with multi-stage tangential entry was analyzed to suppress high-frequency combustion instability in Liquid Rocket Engines. In order to analyze the effect of swirl injector as an acoustic absorber, swirl injector was regarded as a quarter-wave resonator and it's damping capacity is verified in atmospheric temperature. It has a finite mode of vibration and natural frequencies which can be tuned to the natural frequencies of a model combustion chamber. When the targeted injector for each modes is located at anti-node point, the amplitude of modes was decreased. And when the injector of large diameter is mounted, the split of mode which accompanies the decrease of amplitude appeared. From the experimental data, it is proved that if the location of injector mounted is located at an anti-node position of the targeted modes with proper volume, the amplitude of modes is decreased and the split of modes occurs at anti-node point.

• Journal of the Korea institute for structural maintenance and inspection
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• v.13 no.3 s.55
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• pp.101-109
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• 2009

An algorithm is proposed for estimating dynamic displacements of a bridge by using FBG sensors and by superposing some measurable low modes. Modal displacements are obtained from the beam theory and the generalized coordinates are deduced from the strains measured by FBG sensors. By considering flexural and torsional modes occurred in bridges only as flexural modes of a simply supported beam by separating a bridge into multiple girders or parts, the proposed algorithm can be applied to various types of bridges. Guidelines are provided theoretically for determining the number of modes and the number of strain gages to be used. The proposed algorithm has been examined through simulation studies on various types of bridges, laboratory experiments on a model bridge, and field tests on a simple span PC Box girder bridge. Through the simulation study, the effects of the error in the vibration modes and measurement noise on estimating the dynamic displacements are analyzed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.3
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• pp.127-132
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• 2018

In this paper, a scheme for the evaluation of variability in the eigen-modes of functionally graded material(FGM) beams is proposed within the framework of perturbation-based stochastic analysis. As a random parameter, the spatially varying elastic modulus of FGM along the axial direction at the mid-surface of the beam is chosen, and the thru-thickness variation of the elastic modulus is assumed to follow the original form of exponential variation. In deriving the formulation, the first order Taylor expansion on the eigen-modes is employed. As an example, a simply supported FGM beam having symmetric elastic modulus with respect to the mid-surface is chosen. Monte Carlo analysis is also performed to check if the proposed scheme gives reasonable outcomes. From the analyses it is found that the two schemes give almost identical results of the mean and standard deviation of eigen-modes. With the propose scheme, the standard deviation shape of respective eigen-modes can be evaluated easily. The deviated mode shape is found to have one more zero-slope points than the mother modes shapes, irrespective of order of modes. The amount of deviation from the mean is found to have larger values for the higher modes than the lower modes.