• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.69-78
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• 1997

Main sources of the vibration in gear driving system are transmission error and backlash. Transmission error is the difference of the rotation between driving and driven gear due to tooth deformation and profile error. Vibro-impacts induced by backlash between meshing gears lead to excessive vibration and noise in many geared rotation systems. Nonlinear dynamic characteristics of the gear driving system due to transmi- ssion error and backlash are investigated. Transmission error is calculated for spur gear. Nonlinear equation of motion for the gear driving system is developed with the calculated transmission error and backlash. Numerical analysis of the equation and the experimental results show the existence of meshing frequency, superharmonic compon- ents. Instability of the gear driving motion is found on the basis of Mathieu equation. Rattle vibration due to backlash is also discussed on the basis if nonlinear jump phenomenon.

• Structural Engineering and Mechanics
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• v.8 no.3
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• pp.243-256
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• 1999

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

• Proceedings of the KIEE Conference
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• 2005.07c
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• pp.2315-2317
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• 2005

In this paper, an iterative method to model the electromagnetic heating of electrically large lossy dielectrics is presented. Frequency domain finite element (FEM) solutions of the wave equation are determined for the lossy inhomogeneous dielectric as the material properties are change with temperature and time. The power absorbed from microwave losses is applied to a finite element time domain (FETD) calculation of the heat diffusion equation. Time steps appropriate for updating the piecewise material properties in the wave equation and the time stepping of the heat equation are presented. The effects of preheating and source frequency are investigated.

• Journal of Korean Association for Spatial Structures
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• v.15 no.4
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• pp.99-105
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• 2015

The serviceability design of the high-rise building is affected by the wind response vibration such as the acceleration, at this time it is important to calculate the natural frequency correctly. Since the suggestion equation of the natural frequency being used in the design phase is not the regression equation obtained from the vibration measurement of the high-rise building, the verification to use for the serviceability design of the high-rise building is necessary. This thesis conducted an ambient vibration measuring on the high-rise building through the mobile-phone application to calculate the natural frequency and suggested a natural frequency approximate expression following the building's height, and compared with the domestic/foreign standard and the result of the eigen-value analysis.

• Journal of Korean Association for Spatial Structures
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• v.16 no.2
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• pp.47-54
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• 2016

It is very important to calculate natural frequency of the observatory tower correctly because it is keenly affected by wind response vibration due to its large slenderness ratio, weight and small damping ratio. Additionally, suggestion equation of natural frequency being used in the design phase has considerable difference between actual measured value thereby making it inappropriate to be used in the serviceability design of the observatory tower. Therefore, this paper conducted an ambient vibration measuring on 10 observatory towers through mobile-phone application thereby calculating the natural frequency and comparing the result with the domestic and foreign standards and that of the eigen-value analysis. This paper suggested approximate equation of the natural frequency of the observatory tower; T=0.0266H. The square of the corelation coefficient is 0.940, which is high.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.2
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• pp.118-124
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• 2004

The objective of the paper is to demonstrate the noise reduction characteristics of an air-gap resonator, which is composed of an air gap and a partition sheet. By means of installing the air-gap resonator in an enclosed cavity, acoustic resonance can be effectively suppressed using a small space. In particular, it is revealed from a simple, one-dimensional model that the air-gap resonator serves as the Helmholtz resonator that generally absorbs acoustic resonance energy at its resonance frequency. As a result, the air-8ap resonator also has a resonance frequency, which can be predicted with a simple frequency equation derived in the paper. Finally, verification experiments show that the air-gap resonator can be effectively designed by predicting a reasonable gap thickness using the simple frequency-equation.

• Structural Engineering and Mechanics
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• v.41 no.6
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• pp.751-758
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• 2012

We study thickness-shear (TSh) free vibrations of an unbounded, laminated elastic plate with three layers of different materials. One of the two interfaces is slightly weakened as described by the shear-lag model that allows the displacement to be discontinuous across the interface. A frequency equation is obtained from the linear theory of elasticity. A perturbation solution of the frequency equation is obtained from which the frequency shifts of TSh modes due to the weakened interface can be calculated. It is shown that the frequency shifts of TSh modes of different orders are different, and they satisfy different conditions when different interfaces are weakened. These conditions are obtained which can potentially be used as criteria for determining specifically which interface is weakened.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.812-819
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• 2007

Acoustic Target Strength (TS) is a major parameter of the active sonar equation, which indicates the ratio of the radiated intensity from the source to the re-radiated intensity by a target. This research provides the time pattern of TS in time domain, which is applicable to pulse modulated acoustic pressure field. If the time pattern of TS is predicted by using TS equation in frequency domain, it takes long time and difficult since time function pulsed acoustic wave may be decomposed into their frequency domain components. But TS equation in time domain has a convenience. If the expression for pulsed acoustic field has been obtained, the problem can be solved. Furthermore this paper introduces about mathematical equivalence quantities between EM wave and Acoustic Wave.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.1139-1153
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• 2016

Elastic constraints are usually simplified as "spring forces" exerted on beam ends without considering the "spring deformation". The partial differential equation governing the free vibrations of a cantilever Bernoulli-Euler beam considering the deformation of elastic constraints is firstly established, and is nondimensionalized to obtain two dimensionless factors, $k_v$ and $k_r$, describing the effects of elastically vertical and rotational end constraints, respectively. Then the frequency equation for the above Bernoulli-Euler beam model is derived using the method of separation of variables. A numerical analysis method is proposed to solve the transcendental frequency equation for the continuous change of the frequency with $k_v$ and $k_r$. Then the mode shape functions are given. Finally, effects of $k_v$ and $k_r$ on free vibration characteristics of the beam with different slenderness ratios are calculated and analyzed. The results indicate that the effects of $k_v$ are larger on higher-order free vibration characteristics than on lower-order ones, and the impact strength decreases with slenderness ratio. Under a relatively larger slenderness ratio, the effects of $k_v$ can be neglected for the fundamental frequency characteristics, while cannot for higher-order ones. However, the effects of $k_r$ are large on both higher- and lower-order free vibration characteristics, and cannot be neglected no matter the slenderness ratio is large or small.

• The Journal of the Acoustical Society of Korea
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• v.10 no.1
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• pp.12-19
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• 1991

A numerical analysis is carried out for the nonlinear phenomena of the bubble oscillator. The model is based on the Keller's formulation for the bubble dynamics. Interpretation of the bubble interior is based on the formulation by Prosperetti. His formulation adopts the energy equation for the analysis of the bubble interior. The numerical simulation Shows typical nonlinear phenomena in its frequency response. Among such nonlinear aspects are the jump phenomenon, the shift of natural frequency of the system, and the appearance of superharmonic resonances. It is deduced that the nonlinear frequency response is dependent upon the initial condition of the bubble oscillator and some multi-valued frequency region can appear in the response curve. Nonlinear phenomena appeared in the bubble oscillator is compared with those of the Duffing equation and it may be said that the bubble dynamic equation has similar nonlinear aspects to the Duffing equation.