• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.9 s.114
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• pp.919-925
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• 2006

An accurate mathematical model for complex stiffness of the pneumatic spring would be necessary for an efficient design of a pneumatic spring used in vibration isolation tables for precision instruments such as optical devices or nano-scale equipments. A diaphragm, often employed for prevention of air leakage, plays a significant role of complex stiffness element as well as the pressurized air itself Therefore, effects of the diaphragm need to be included in the dynamic model for a more faithful description of dynamic behavior of pneumatic spring. But the complex stiffness of diaphragm is difficult to predict In an analytical way, since it is a rubber membrane of complicated shape in itself. Moreover, the diaphragm should be expandable in response to pressurization inside a chamber, which makes direct measurement of complex stiffness of diaphragm extremely difficult. In our earlier research, the complex stiffness of diaphragm was indirectly measured, which was just to eliminate the theoretical stiffness of pressurized air from the measured complex stiffness of the pneumatic spring. In order to reflect complex stiffness of inflated diaphragm on the total stiffness at the initial design or design improvement stage, however. it is required to be able to predict beforehand. In this paper, how to predict the complex stiffness of inflated rubber diaphragm by commercial FE codes (e.g. ABAQUS) will be discussed and the results will be compared with the indirectly measured values.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.844-849
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• 2006

Accurate modeling of complex dynamic stiffness of the pneumatic springs is crucial for an efficient design of vibration isolation tables for precision instruments such as optical devices or nano-technology equipments. Besides pressurized air itself, diaphragm made of rubber materials, essentially employed for prevention of air leakage, plays a significant contribution to the total complex stiffness. Therefore, effects of the diaphragm should be taken care of precisely. The complex stiffness of an inflated diaphragm is difficult to predict or measure, since it is always working together with the pressurized air. In our earlier research, the complex stiffness of a diaphragm was indirectly estimated simply by subtracting stiffness of the pressurized air from measurement of the total complex stiffness for a single chamber pneumatic spring. In order to reflect dynamic stiffness of inflated diaphragm on the total stiffness at the initial design or design improvement stage, however, it is required to be able to predict beforehand. In this presentation, how to predict the complex stiffness of inflated rubber diaphragm by commercial FE codes(e.g. ABAQUS) will be discussed and the results will be compared with the indirectly measured values.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.1
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• pp.110-122
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• 2008

Pneumatic vibration isolator typically consisting of dual-chamber pneumatic springs and a rigid table are widely employed for proper operation of precision instruments such as optical devices or nano-scale equipments owing to their low stiffness- and high damping-characteristics. As environmental vibration regulations for precision instruments become more stringent, it is required to improve further the isolation performance. In order to facilitate their design optimization or active control, a more accurate mathematical model or complex stiffness is needed. Experimental results we obtained rigorously for a dual-chamber pneumatic spring exhibit significantly amplitude dependent behavior, which cannot be described by linear models in earlier researches. In this paper, an improvement for the complex stiffness model is presented by taking two major considerations. One is to consider the amplitude dependent complex stiffness of diaphragm necessarily employed for prevention of air leakage. The other is to employ a nonlinear model for the air flow in capillary tube connecting the two pneumatic chambers. The proposed amplitude-dependent complex stiffness model which reflects dependency on both frequency and excitation amplitude is shown to be very valid by comparison with the experimental measurements. Such an accurate nonlinear model for the dual-chamber pneumatic springs would contribute to more effective design or control of vibration isolation systems.

• Smart Structures and Systems
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• v.17 no.5
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

• Journal of the Korean Society for Nondestructive Testing
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• v.30 no.6
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• pp.578-586
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• 2010

This paper describes a theoretical model and acoustic analysis of hysteresis of contacting surfaces subject to compression pressure. Contacting surfaces known to be nonlinear and hysteretic is considered as a simple spring that has a complex stiffness connecting discontinuous displacements between two solid contact boundaries. Mathematical formulation for 1-D interfacial wave propagation between two contacting solids is developed using the complex spring model to derive the dispersion relation between the interface wave speed and the complex interfacial stiffness. Existence of the interface wave propagating along the hysteretic interface is studied in theory and discussed by investigating the solution to the dispersion equation. Unlike the linear interface without hysteresis, there can exist only one distinct mode of interface waves for the hysteretic interface, which is anti-symmetric motion. The anti-symmetric mode of interface wave propagates with the velocity faster than the Rayleigh surface wave but less than the shear wave depending on the interfacial stiffness. If the contacting surfaces are compressed so much that the linear interfacial stiffness is very high, the hysteretic stiffness does not affect the interface wave velocity. However, it has an effect on the speed of interface wave for a loosely contact surfaces with a relatively low linear stiffness. It is also found that the phase velocity of anti-symmetric wave mode converges to the shear wave velocity in despite of the linear stiffness value if the hysteretic stiffness approaches 0.5.

• The Journal of Korean Physical Therapy
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• v.34 no.1
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• pp.38-44
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• 2022

Purpose: The purpose of this study was to investigate the effects of complex training on injury, flexibility, and muscle stiffness in high school male football players. Methods: A total of 60 football players were included in the study and were divided into three groups viz. the complex training group (CTG), 11+ training group (11+TG), and traditional training group (TTG). Injuries were recorded based on the prospective investigation method after starting the study, and the flexibility and muscle stiffness of the subjects were evaluated. Results: The research results showed that the injury rate per match was significantly lower in the CTG and 11+TG than the TTG. In the CTG, the flexibility of the hamstrings significantly increased and the stiffness of the rectus femoris (RF), biceps femoris (BF), and tensor fascia latae (TFL) muscles significantly decreased (p<0.05). In the 11+TG, the stiffness of the RF significantly decreased (p<0.05). In the TTG, the flexibility of the hamstrings significantly increased (p<0.05). Hamstring flexibility showed a significantly higher increase in the CTG and TTG compared to the 11+TG (p<0.05). Also, the stiffness of the RF and TFL muscles showed a significantly higher decrease in the CTG compared to the 11+TG and TTG (p<0.05). The stiffness of the BF muscles too showed a more significant decrease in the CTG compared to the TTG (p<0.05). Conclusion: The complex training method of the Fédération International de Football Association (FIFA) 11+ and self-myofascial release (SMFR) as a warm-up program, prevent injuries, enhance flexibility, and lower muscle stiffness of football players in high school. Thus, it is necessary to ensure the widespread use of the complex training program by instructors and players under the supervision of the Korea Football Association (KFA), given its reliability in preventing injuries and improving the performance of football players.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11b
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• pp.194-199
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• 2005

Body-on-frame type vehicle has a set of frame bushes which are installed between body and frame fur vibration Isolation. Such frame bushes are important vibration transmission paths to passenger space. In order to reduce the vibration level of passenger space, therefore, the change of complex stiffness of the frame bushes is more efficient than modification of other parts of the vehicle such as body, frame and suspension. The purpose of this study is to reduce the vibration level for ride comfort by optimization of complex stiffness of frame bushes. In order to do this end, simple finite element vehicle model was constructed and the complex stiffness of frame bushes was set to be design variable. Objective function was defined to reflect passenger ride comfort and genetic algorithm and sub-structure synthesis were applied for minimization of the objective function.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.6 s.111
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• pp.619-626
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• 2006

Body-on-frame type vehicle has a set of frame bushes between body and frame for vibration isolation. Such frame bushes are important vibration transmission paths to passenger space for excitations during driving. In order to reduce the vibration level of passenger space, therefore, change of complex stiffness of the frame bushes is more efficient than modification of other parts of the vehicle such as body, frame and suspension. The purpose of this study is to reduce the vibration level for ride comfort by optimization of complex stiffness of frame bushes. In order to do this, a simple finite element vehicle model was constructed and complex stiffness of the frame bushes was set to be design variables. The objective function was defined to reflect frequency dependence of passenger ride comfort. Genetic algorithm and sub-structure synthesis were applied for minimization of the objective function. After optimization level at a position of interest on the car body was reduced by about 43.7 % in RMS value. Causes for optimization results are discussed.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.6 no.2
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• pp.22-27
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• 2007

In this study, the two methods of stiffness measurement(Spring constant) of cantilever were proposed for quantitative measurement in Atomic Force Microscopy(AFM). As the 1st method for the measurement of stiffness, the probe method, which is used in the measurement of the semiconductor mechanical and electrical properties, was applied to the measurement of the cantilever. Experiments by the probe method were performed finding the resistance value of cantilever. As the results, the resistance was measured differently along with the dimension and the thickness of cantilever that determined the stiffness(spring constant) of the lever. As the 2nd method, the vibration characteristics(Dunkerley expression) is used to obtain the stiffness of the complex structure which is combined by AFM cantilever and the standard cantilever. We measured the resonant frequency from the complex structure using the micro stages and stereo microscope. As the results, we confirmed that the vibration characteristics(Dunkerley expression) is effected the micro complex structure of AFM cantilever.

• Journal of KSNVE
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• v.8 no.5
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• pp.949-956
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• 1998

Complex and large lattice type structures are frequently used in design of bridge, tower, crane and aerospace structures. In general, in order to analyze these structures we have used the finite element method(FEM). This method is the most widely used and powerful method for structural analysis lately. However, it is necessary to use a large amount of computer memory and computational time because the FEM requires many degrees of freedom for solving dynamic problems exactly for these complex and large structures. For analyzing these structures on a personal computer, the authors developed the transfer stiffness coefficient method(TSCM). This method is based on the concept of the transfer of the nodal dynamic stiffness coefficient matrix which is related to force and displacement vector at each node. And we suggested TSCM for free vibration analysis of complex and large lattice type structures in the previous report. In this paper, we formulate forced vibration analysis algorithm for complex and large lattice type structures using extened TSCM. And we confirmed the validity of TSCM through computational results by the FEM and TSCM, and experimental results for lattice type structures with harmonic excitation.