• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.27 no.1
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• pp.87-97
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• 1997

The purpose of this study was to evaluate the method for quantitative assessment of bone mass from aluminum-equivalent value of hydroxyapatite by using digital imaging system consisted of Power Macintosh 7200/120, 15-inch color monitor, and GT-9000 scanner with transparency unit. After aluminum-equivalent image made from correlation between aluminum thickness and grey scale, the accuracy of conversion to mass from aluminum-equivalent value was evaluated. Measured bone mass was compared with converted bone mass from aluminum-equivalent value of hydroxyapatite block by correlation formula between aluminum-equivalent value of hydroxyapatite block and hydroxyapatite mass. The results of this study were as follow; 1. Correlation between aluminum thickness and grey level for obtaining aluminum-equivalent image was high positively associated(r²=0.99). Converted masses from aluminum-equivalent value were very similar to measured masses. There was, statistically, no significant difference(P<0.05) between them 2. Correlation between hydroxyapatite aluminum-equivalent and hydroxyapatite mass was shown to linear relation (r²=0.95). 3. Converted masses from aluminum-equivalent value of 3 dry mandible segments were similar to measured masses. The difference between the exposure directions was not significantly different(P<0.05).

• Structural Engineering and Mechanics
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• v.21 no.6
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• pp.713-735
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• 2005

Due to the complexity of mathematical expressions, the literature concerning the free vibration analysis of plates carrying multiple three-degree-of-freedom (dof) spring-mass systems is rare. In this paper, the three degrees of freedom (dof's) for a spring-mass system refer to the translational motion of its lumped mass in the vertical ($\bar{z}$) direction and the two pitching motions of its lumped mass about the two horizontal ($\bar{x}$ and $\bar{y}$) axes. The basic concept of this paper is to replace each three-dof spring-mass system by a set of equivalent springs, so that the free vibration characteristics of a rectangular plate carrying any number of three-dof spring-mass systems can be obtained from those of the same plate supported by the same number of sets of equivalent springs. Since the three dof's of the lumped mass for each three-dof spring-mass system are eliminated to yield a set of equivalent springs, the total dof of the entire vibrating system is not affected by the total number of the spring-mass systems attached to the rectangular plate. However, this is not true in the conventional finite element method (FEM), where the total dof of the entire vibrating system increases three if one more three-dof spring-mass system is attached to the rectangular plate. Hence, the computer storage memory required by using the presented equivalent spring method (ESM) is less than that required by the conventional FEM, and the more the total number of the three-dof spring-mass systems attached to the plate, the more the advantage of the ESM. In addition, since manufacturing a spring with the specified stiffness is much easier than making a three-dof spring-mass system with the specified spring constants and mass magnitude, the presented theory of replacing a three-dof spring-mass system by a set of equivalent springs will be also significant from this viewpoint.

• Nuclear Engineering and Technology
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• v.35 no.1
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• pp.1-13
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• 2003

In this study, an effective method to estimate the fundamental frequencies of co-axial cylinders immersed in fluid is proposed. The proposed method makes use of the equivalent mass or density that is derived from the added mass matrix caused by the fluid-structure interaction (FSI) phenomenon. The equivalent mass is defined from the added mass matrix based on a 2-D potential flow theory. The theory on two co-axial cylinders extended to the case of three cylinders. To prove the validity of the proposed method, the eigenvalue analyses upon coaxial cylinders coupled with fluid gaps are peformed using the equivalent mass. The analyses results upon various fluid gap is conditions reveal that the present method could provide accurate frequencies and be suitable for expecting the fundamental frequencies of fluid coupled cylinders in beam mode vibration.

• Structural Engineering and Mechanics
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• v.28 no.6
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• pp.659-676
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• 2008

The reports regarding the free vibration analysis of uniform beams carrying single or multiple spring-mass systems are plenty, however, among which, those with inertia effect of the helical spring(s) considered are limited. In this paper, by taking the mass of the helical spring into consideration, the stiffness and mass matrices of a spring-mass system and an equivalent mass that may be used to replace the effect of a spring-mass system are derived. By means of the last element stiffness and mass matrices, the natural frequencies and mode shapes for a uniform cantilever beam carrying any number of springmass systems (or loaded beam) are determined using the conventional finite element method (FEM). Similarly, by means of the last equivalent mass, the natural frequencies and mode shapes of the same loaded beam are also determined using the presented equivalent mass method (EMM), where the cantilever beam elastically mounted by a number of lumped masses is replaced by the same beam rigidly attached by the same number of equivalent masses. Good agreement between the numerical results of FEM and those of EMM and/or those of the existing literature confirms the reliability of the presented approaches.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.339-348
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• 1990

Techniques which are able to predict and control dynamic characteristics, not affecting the vibrational characteristics on the modification of structural design, are being studied. As one of these techniques, experimental modal analysis is widely applied by many researchers. In this study, modal analysis is performed using transfer matrix method by a macro computer. The developed program would estimate the structural modal parameters precisely, and the validity of this program is certified by comparing with the experimental results of .GAMMA A. structure. Estimated modal parameters(natural frequency, vibrational mode, equivalent mass, etc.) are in accord with the experimental results. Also, the optimal location of the additive mass is determined by the evaluation of the vibrational mode and the equivalent mass. The relation between the additive mass and the equivalent mass is specified, and we come to know that the ratio of equivalent mass to additive mass alter linearly within the range of 20%.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1218-1223
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• 2007

In this study, we experimentally investigate the equivalent ring theory for a slightly asymmetric ring. The slightly asymmetric ring has mode pair and frequency pair due to the small asymmetry and this mode pair generates beat in vibration and sound. In this paper, a slightly asymmetric ring is modeled as the equivalent ring, i.e., the assemblage of a symmetric ring and imperfect point masses. The equivalent ring has the same mode pair condition as that of the original asymmetric ring. Effect of the additional mass attachment is investigated by the equivalent ring theory and the result is compared with those of the measurement and the finite element analysis. It is confirmed that the original ring and the equivalent ring show the same change in frequency and mode under the various additional imperfection mass conditions. The equivalent ring theory explains how the asymmetric elements influence the mode characteristics and provides useful information to tune the beat property.

• The Journal of the Acoustical Society of Korea
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• v.30 no.6
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• pp.344-352
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• 2011

In this paper, the resonant characteristic of a Tonpilz transducer with a fixed tail mass has been studied by means of an equivalent circuit approach. An equivalent circuit has been designed to describe the characteristic of a Tonpilz transducer that has an additional resonance because of its fixed tail mass. The transmitting voltage response of the transducer calculated by the designed circuit has been compared with that by the FEA (finite element analysis) to confirm the validity of the circuit. This equivalent circuit approach produces identical results with the FEA, in which the variation of resonant frequencies and TVR has been clearly figured out in relation to the stiffness of the mounting fixture and the mass of the tail mass. The suggested equivalent circuit can be utilized to figure out the characteristics of the Tonpilz transducer more efficiently than FEA that requires much calculation time and revision of the models in accordance with the variation of design variables.

• Nuclear Engineering and Technology
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• v.54 no.3
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• pp.1109-1114
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• 2022

The SMART (System-integrated Modular Advanced ReacTor) is an integral-type small modular reactor developed by KAERI (Korea Atomic Energy Research Institute). This paper discusses the feasibility and applicability of a 3D-based equivalent model using dynamic condensation method for seismic analysis of a SMART control rod drive mechanism. The equivalent model is utilized for complicated seismic analysis during the design of the SMART. While the 1D-based beam-mass equivalent model is widely used in the nuclear industry for its calculation efficiency, the 3D-based equivalent model is suggested for the seismic analysis of SMART to enhance the analysis accuracy of the 1D-based equivalent model while maintaining its analysis efficiency. To verify the suggested model, acceleration response spectra from seismic analysis based on the 3D-based equivalent model are compared to those from the 1D-based beam-mass equivalent model and experiments. The accuracy and efficiency of the dynamic condensation method are investigated by comparison to analysis results based on the conventional modeling methodology used for seismic analysis.

• Journal of the Korean Society of Radiology
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• v.10 no.8
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• pp.591-596
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• 2016

The purpose of this study is to determine the equivalent energy of a 6MV X-ray beam in the experiment. The half-value layer (HVL) of lead for the 6 MV X-ray beam was measured using an ionization chamber. The linear attenuation coefficients were calculated with HVL. And, the mass attenuation coefficient was obtained by dividing the linear attenuation coefficient by the density of lead. The equivalent energy of mass attenuation coefficient was determined using the photon energy versus mass attenuation coefficient data of lead given by National Institute of Standards and Technology (NIST). In conclusion, the equivalent energy of the 6 MV X-ray beam was determined to be 1.61 MeV. This equivalent energy was determined to be about 30% lower than reported by Reft. The reason is presumed to be due to the presence of an air cavity between the lead attenuators.

• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1241-1260
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• 2015

Any rational approach to define the configuration and size of viscous fluid dampers in a structure should be based on the dynamic properties of the system with the dampers. In this paper we propose an alternative representation of the complex eigenvalues of multi degree of freedom systems with dampers to calculate new equivalent natural frequencies. Analytical expressions for the dynamic properties of a two-story building model with a linear viscous damper in the first floor (i.e. with a non-proportional damping matrix) are derived. The formulas permit to obtain the equivalent damping ratios and equivalent natural frequencies for all the modes as a function of the mass, stiffness and damping coefficient for underdamped and overdamped systems. It is shown that the commonly used formula to define the equivalent natural frequency is not applicable for this type of system and for others where the damping matrix is not proportional to the mass matrix, stiffness matrix or both. Moreover, the new expressions for the equivalent natural frequencies expose a novel phenomenon; the use of viscous fluid dampers can modify the vibration frequencies of the structure. The significance of the new equivalent natural frequencies is expounded by means of a simulated free vibration test. The proposed approach may offer a new perspective to study the effect of viscous dampers on the dynamic properties of a structure.