• Steel and Composite Structures
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• v.28 no.5
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• pp.589-606
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• 2018

The previous studies reflected the significant effect of neutral-axis position and coupling of in-plane and out-of-plane displacements on behavior of functionally graded (FG) nanobeams. In thin FG beam, this coupling can be eliminated by a proper choice of the reference axis. In shear deformable FG nanobeam, not only this coupling can't be eliminated but also the position of neutral-axis is dependent on through-thickness distribution of shear strain. For the first time, in this paper it is avoided to guess a shear strain shape function and the exact shape function and consequently the exact position of neutral axis for arbitrary gradation of higher order nanobeam are obtained. This paper presents new methodology based on differential transform and collocation methods to solve coupled partial differential equations of motion without any simplifications. Using exact position of neutral axis and higher order beam kinematics as well as satisfying equilibrium equations and traction-free conditions without shear correction factor requirement yields to better results in comparison to the previously published results in literature. The classical rule of mixture and Mori-Tanaka homogenization scheme are considered. The Eringen's nonlocal continuum theory is applied to capture the small scale effects. For the first time, the dependency of exact position of neutral axis on length to thickness ratio is investigated. The effects of small scale, length to thickness ratio, Poisson's ratio, inhomogeneity of materials and various end conditions on vibration and buckling of local and nonlocal FG beams are investigated. Moreover, the effect of axial load on natural frequencies of the first modes is examined. After degeneration of the governing equations, the exact new formulas for homogeneous nanobeams are computed.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.3 s.96
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• pp.251-258
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• 2005

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings (HDB) in an HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Reynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigen value problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• The Journal of the Acoustical Society of Korea
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• v.37 no.4
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• pp.181-187
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• 2018

In this paper, sound absorption of micro-perforated elastic plates installed in an impedance tube of a circular cross-section is discussed using an analytic method. Vibration of the plates and sound pressure fields inside the duct are expressed in terms of an infinite series of modal functions, where modal functions in the radial direction is given in terms of the Bessel functions. Under the plane wave assumption, a low frequency approximation is derived by including the first few plate modes, and the sound absorption coefficient is given in terms of an equivalent impedance of a single surface. The sound absorption coefficient using the proposed formula is in excellent agreement with the result by the FEM (Finite Element Method), and shows dips and peaks at the natural frequencies of the plate. When the perforation ratio is very small, the sound absorption coefficient is dominated by the vibration effect. However, when the perforation ratio reaches a certain value, the sound absorption is mainly governed by the rigid MPP (Micro-Perforated Plate), while the vibration effect becomes very small.

• Earthquakes and Structures
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• v.11 no.6
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• pp.1123-1141
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• 2016

To explore the application of traditional tuned mass dampers (TMDs) to the earthquake induced vibration control problem, a pounding tuned mass damper (PTMD) is proposed by adding a viscoelastic limitation to the traditional TMD. In the proposed PTMD, the vibration energy can be further dissipated through the impact between the attached mass and the viscoelastic layer. More energy dissipation modes can guarantee better control effectiveness under a suite of excitations. To further reduce mass ratio and enhance the implementation of the PTMD control, multiple PTMDs (MPTMD) control is then presented. After the experimental validation of the proposed improved Hertz based pounding model, the basic equations of the MPTMD controlled system are obtained. Numerical simulation is conducted on the benchmark model of the Canton Tower. The control effectiveness of the PTMD and the MPTMD is analyzed and compared under different earthquake inputs. The sensitivity and the optimization of the design parameters are also investigated. It is demonstrated that PTMDs have better control efficiency over the traditional TMDs, especially under more severe excitation. The control performance can be further improved with MPTMD control. The robustness can be enhanced while the attached mass for each PTMD can be greatly reduced. It is also demonstrated through the simulation that a non-uniformly distributed MPTMD has better control performance than the uniformly distributed one. Parameter study is carried out for both the PTMD and the MPTMD systems. Finally, the optimization of the design parameters, including mass ratio, initial gap value, and number of PTMD in the MPTMD system, is performed for control improvement.

• Tribology and Lubricants
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• v.33 no.1
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• pp.9-14
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• 2017

This paper presents a rotordynamic analysis and the operation of a power turbine applied to a 250 kW super-critical $CO_2$ cycle. The power turbine consists of a turbine wheel and a shaft supported by two fluid film bearings. We use a tilting pad bearing for the power turbine owing to the high speed operation, and employ copper backing pads to improve the thermal management of the bearing. We conduct a rotordynamic analysis based on the design parameters of the power turbine. The dynamic coefficients of the tilting pad bearings were calculated based on the iso-thermal lubrication theory and turbine wheel was modeled as equivalent inertia. The predicted Cambell diagram showed that there are two critical speeds, namely the conical and bending critical speeds under the rated speed. However, the unbalance response prediction showed that vibration levels are controlled within 10 mm for all speed ranges owing to the high damping ratio of the modes. Additionally, the predicted logarithmic decrement indicates that there is no unstable mode. The power turbine uses compressed air at a temperature of $250^{\circ}C$ in its operation, and we monitor the shaft vibration and temperature of the lubricant during the test. In the steady state, we record a temperature rise of $40^{\circ}C$ between the inlet and outlet lubricant and the measured shaft vibration shows good agreement with the prediction.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.572-578
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• 2003

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings in a HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Raynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• Journal of KSNVE
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• v.10 no.6
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• pp.1083-1093
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• 2000

This paper is concerned with the real-time automatic tuning of the positive position feedback controller for smart structures by the genetic algorithms. The genetic algorithms haute proven its effectiveness in searching optimal design parameters without falling into local minimums thus rendering globally optimal solutions. The advantage of the positive position feedback controller is that if it is tuned properly it can enhance the damping value of a target mode without affecting other modes. In this paper, we develop for the first time a real-time algorithm for determining a tuning frequency of the PPF controller based on the genetic algorithms. To this end, the digital PPF control law is downloaded to the DSP chip and a main program, which runs the genetic algorithms in real time, updates the parameter of the controller in real time. Hence, any kind of control including the positive position feedback controller can be used in adaptive fashion in real time. Experimental results show that the real-time tuning of the positive position feedback controller can be achieved successfully. so that vibrations are suppressed satisfactorily.

• Smart Structures and Systems
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• v.17 no.2
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• pp.209-230
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• 2016

The Canton Tower is a high-rise slender structure with a height of 610 m. A structural health monitoring system has been instrumented on the structure, by which data is continuously monitored. This paper presents an investigation on the identified modal properties of the Canton Tower using ambient vibration data collected during a whole day (24 hours). A recently developed Fast Bayesian FFT method is utilized for operational modal analysis on the basis of the measured acceleration data. The approach views modal identification as an inference problem where probability is used as a measure for the relative plausibility of outcomes given a model of the structure and measured data. Focusing on the first several modes, the modal properties of this supertall slender structure are identified on non-overlapping time windows during the whole day under normal wind speed. With the identified modal parameters and the associated posterior uncertainty, the distribution of the modal parameters in the future is predicted and assessed. By defining the modal root-mean-square value in terms of the power spectral density of modal force identified, the identified natural frequencies and damping ratios versus the vibration amplitude are investigated with the associated posterior uncertainty considered. Meanwhile, the correlations between modal parameters and temperature, modal parameters and wind speed are studied. For comparison purpose, the frequency domain decomposition (FDD) method is also utilized to identify the modal parameters. The identified results obtained by the Bayesian method, the FDD method and a finite element model are compared and discussed.