• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.8
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• pp.598-604
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• 2003

In this paper a general solution method is presented to obtain the unbalance response orbit from the finite element based equations of motion of a gear-coupled two-shaft rotor-bearing system, whose shafts rotate at their different speeds from each other. Particularly, are proposed analytical solutions of the maximum and minimum radii of the orbit. The method has been applied to analyze the unbalance response of a 800 refrigeration-ton turbo-chiller rotor-bearing system having a bull-pinion speed increasing gear. Bumps in the unbalance response of the driven high speed compressor rotor system have been observed at the first torsional natural frequency due to the coupling effect of lateral and torsional dynamics. Further, the proposed analytical solutions have agreed well with those obtained by a full numerical approach. The proposed analytical solutions can be generally applied to obtain the maximum and minimum radii of the unbalance response orbits of dual-shaft rotor-bearing systems coupled by bearings as well.

• Smart Structures and Systems
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• v.18 no.2
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• pp.355-374
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• 2016

This paper presents and compares a one-dimensional (1D) bending theory for piezoelectric thin beam-type structures with resistive-inductive electrodes to ANSYS$^{(R)}$ three-dimensional (3D) finite element (FE) analysis. In particular, the lateral deflections and vibrations of slender piezoelectric beams are considered. The peculiarity of the piezoelectric beam model is the modeling of electrodes in such a manner that is does not fulfill the equipotential area condition. The case of ideal, perfectly conductive electrodes is a special case of our 1D model. Two-coupled partial differential equations are obtained for the lateral deflection and for the voltage distribution along the electrodes: the first one is an extended Bernoulli-Euler beam equation (second-order in time, forth order in space) and the second one the so-called Telegrapher's equation (second-order in time and space). Analytical results of our theory are validated by 3D electromechanically coupled FE simulations with ANSYS$^{(R)}$. A clamped-hinged beam is considered with various types of electrodes for the piezoelectric layers, which can be either resistive and/or inductive. A natural frequency analysis as well as quasi-static and dynamic simulations are performed. A good agreement between the extended beam theory and the FE results is found. Finally, the practical relevance of this type of electrodes is shown. It is found that the damping capability of properly tuned resistive or resistive-inductive electrodes exceeds the damping performance of beams, where the electrodes are simply linked to an optimized impedance.

• Steel and Composite Structures
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• v.42 no.5
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• pp.699-710
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• 2022

This work presents a comprehensive study on the surface energy effect on the axial frequency analyses of AFGM nanorods in cylindrical coordinates. The AFGM nanorods are considered to be thin, relatively thick, and thick. In thin nanorods, effects of the inertia of lateral motions and the shear stiffness are ignored; in relatively thick nanorods, only the first one is considered; and in thick nanorods, both of them are considered in the kinetic energy and the strain energy of the nanorod, respectively. The surface elasticity theory which includes three surface parameters called surface density, surface stress, and surface Lame constants, is implemented to consider the size effect. The power-law form is considered for variation of the material properties through the axial direction. Hamilton's principle is used to derive the governing equations and boundary conditions. Due to considering the surface stress, the governing equation and boundary condition become inhomogeneous. After homogenization of them using an appropriate change of variable, axial natural frequencies are calculated implementing harmonic differential quadrature (HDQ) method. Comprehensive results including effects of geometric parameters and various material properties are presented for a wide range of boundary condition types. It is believed that this study is a comprehensive one that can help posterities for design and manufacturing of nano-electro-mechanical systems.

• Journal of Korean Society of Steel Construction
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• v.9 no.2 s.31
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• pp.269-275
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• 1997

Wind tunnel test results and their interpretations, which were performed to study the aerodynamic stability of tower of self-anchored suspension bridge, are presented in this paper. Tower and full models were tested under smooth and turbulent flow conditions. In the case of the tower with inclined two columns, the vibration due to wakes were occurred at wide velocity zone because the wakes with various frequencies were generated by inclined upstream column. It has to be emphasized that the vibration characteristics of the tower in the self-anchored suspension bridge may be very sensitive to the longitudinal boundary conditions of the girder at the supports. Because of the two natural frequency of the tower, out-of-plane bending and torsional, were not well separated, coupled motions were observed in a wide range of wind velocity. The effectiveness of corner cut, countermeasure to reduce the tower vibrations, was also studied. It has been found that 1:10, comer cut size to column width, may be the most effective ratio for reducing the vibrations.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.3 no.3
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• pp.27-37
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• 1983

A method of dynamic analysis is developed for torsional free vibrations of elliptical-box girder type or stiffening truss system suspension bridge. In this study, the method based on a finite element technique using a digital computer, is illustrated by two numerical examples, the Namhae Bridge which is located in Kyungsang nam-do opened on June, 1973, and the Mt. Chunma Bridge is simple span pedestrian's suspension bridge with lateral bracing system in Mt. Chunma, Kyungki-do, are used. In general, dynamic modes of complex suspension bridges are three-dimensional in form, i.e., coupling between vertical and torsional motions. However, introduced that amplitudes of oscillation are infinitesimal for coincidence with the purpose of it's use, thereupon, the torsional vibration analyses are treated without coupling terms. A sufficient number of natural frequencies and mode shapes for torsional free vibration are presented in this paper. In the case of Mt. Chunma Bridge, the natural frequencies and periods are computed with and without reinforcement, respectively, and compared their discrepancies. The influence of the auxiliary reinforcing cables is prevailing in the first few modes, namely, 1st and 2nd in symmetric and 1st, 2nd and 3rd in antisymmetric vibration, and conspicuous in the symmetric compared with the antisymmetric motion, but in the higher modes, this kind of simple accessory elucidates rether converse effects. In the Namhae Bridge, the results are compared with the Manual's obtained by wind tunnel test. It reveals commendable agreement.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.10
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• pp.967-975
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• 2007

A rotordynamic analysis was performed with a dry vacuum pump, which is a major equipment in modern semiconductor and LCD manufacturing processes. The system is composed of screw rotors, lobes picking air, helical gears, driving motor, and support rolling element bearings of rotors and motor. The driving motor-screw rotor system has a rated speed of 6,300 rpm, and was modeled utilizing a rotordynamic FE method for analysis, which was verified through 3-D FE analysis and experimental modal analysis. As loadings on the bearings due to the gear action were significant in the system considered, each resultant bearing load was calculated by considering the generalized forces of the gear action as well as the rotor itself. Each resultant bearing loading was used in calculating each stiffness of rolling element bearings. Design goals are to achieve wide separation margins of lateral and torsional critical speeds, and favorable unbalance responses of the rotor in the operating range. Then, a complex rotordynamic analysis of the system was carried out to evaluate its forward synchronous critical speeds, whirl natural frequencies and mode shapes, unbalance responses under various unbalance locations, and torsional interference diagram. Results show that the entire system is well designed in the operating range. In addition, the procedure of rotordynamic analysis for dry vacuum pump rotor-bearing system was proposed and established.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.8
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• pp.752-760
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• 2011

In tilting pad bearing design process, the selection of the proper configuration type of either a load-between-pad(LBP) or load-on-pad(LOP) as well as preload and pivot offset conditions is to be carefully considered. Also the bearing needs to be designed in order to be suited for the rotor-bearing system and operating condition. In this paper, it is observed that the dynamic characteristics in a five pad tilting pad bearing for the LBP and the LOP configurations are influenced by the variation of preload and pivot offset. In this context, rotor dynamic analysis of the 5 MW industrial gas turbine supported by the tilting pad bearing at the front and roller bearing at the rear is carried out based on the dynamic coefficients of the tilting pad bearing investigated. The result shows that two rigid body critical modes experience various changes according to the influence of the tilting pad bearing uniquely applied to one side of this machine. Mainly, the second critical speed, the rigid body mode of conical shape with high whirling in the tilting pad bearing, is significantly changed by preload and pivot offset regardless of the LBP and LOP configurations. And, the first critical mode, the rigid body mode of conical shape with high whirling in the roller bearing, is sensitively affected by preload applied to the LOP configuration and by its asymmetric dynamic properties.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.04a
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• pp.425-432
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• 2011

In tilting pad bearing design process, the selection of the proper configuration type of either a Load-Between-Pad (LBP) or Load-On-Pad (LOP) as well as preload and pivot offset conditions is to be carefully considered. Also the bearing needs to be designed in order to be suited for the rotor-bearing system and operating condition. In this paper, it is observed that the dynamic characteristics in a 5 pad tilting pad bearing for the LBP and the LOP configurations are influenced by the variation of preload and pivot offset. In this context, rotor dynamic analysis of the 5MW industrial gas turbine supported by the tilting pad bearing at the front and roller bearing at the rear is carried out based on the dynamic coefficients of the tilting pad bearing investigated. The result shows that two rigid body critical modes experience various changes according to the influence of the tilting pad bearing uniquely applied to one side of this machine. Mainly, the second critical speed, the rigid body mode of conical shape with high whirling in the tilting pad bearing, is significantly changed by preload and pivot offset regardless of the LBP and LOP configurations. And, the first critical mode, the rigid body mode of conical shape with high whirling in the roller bearing, is sensitively affected by preload applied to the LOP configuration and by the its asymmetric dynamic properties.

• Journal of the Korea institute for structural maintenance and inspection
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• v.18 no.1
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• pp.174-182
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• 2014

To monitor the wind-induced responses of buildings, conventional real-time kinematic (RTK) methods based on two global positioning system (GPS) receivers (e.g., a reference and a rover) are widely applied. However, these methods can encounter problems such as difficulty in securing and maintaining a space for a reference station. With the recently developed virtual reference station (VRS)-RTK approach, the position of a structure can be measured using only a rover receiver. In this study, to evaluate the applicability of VRS-RTK methods in monitoring the lateral structural responses of frame structures, we performed free vibration tests on a one-story frame model (the first natural frequency of 1 Hz) and a three-story frame model (the first natural frequency of 0.85 Hz). To assess the reliability of the displacement and acceleration responses measured by the GPS, we performed a concurrent measurement using laser displacement sensors and an accelerometer. The accelerometer results were consistent with the GPS measurements in terms of the time history and frequency content. Furthermore, to derive an appropriate sampling rate for the continuous monitoring of buildings, the errors in the displacement responses were evaluated at different GPS sampling rates (5, 10, 20 Hz). The results indicate that as the sampling rate increased, the errors in the displacement responses decreased. In addition, in the three-story model, all modal components (first, second, and third modes) could be recorded at a sampling rate of 20 Hz.

• Journal of the Earthquake Engineering Society of Korea
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• v.16 no.3
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• pp.23-33
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• 2012

Dynamic response measurements from natural excitation were carried out for three 18-story office buildings to determine their inherent properties. The beam-column frame system was adopted as a typical structural form, but a core wall was added to resist the lateral force more effectively, resulting in a mixed configuration. To extract modal parameters such as natural frequencies, mode shapes and damping ratios from a series of vibration records at each floor, the most advanced operational system identification methods based on frequency- and time-domain like FDD, pLSCF and SSI were applied. Extracted frequencies and mode shapes from the different identification methods showed a greater consistency for three buildings, however the three lower frequencies extracted were 1.2 to 1.7 times as stiff as those obtained using the initial FE models. Comparing the extracted fundamental periods with those estimated from the code equations and FE analysis, the FE analysis results showed the most flexible behavior, and the most simple equation that considers the building height as the only parameter correlated fairly well with test results. It is recognized that such a discrepancy arises from the fact that the present tests exclude the stiffness decreasing factors like concrete cracking, while the FE models ignore the stiffness increasing factors, such as the contribution of non-structural elements and the actual material properties used.