• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.15 no.10 s.103
• /
• pp.1137-1147
• /
• 2005

The dynamic response due to the unbalance and crack and the quasi-static response due to gravity are analytically derived based on the complex transfer matrix. The additional slope is expressed as function of the bending moment at crack position based on the fracture mechanics concept, and inversely the bending moment is expressed as function of the additional slope at the crack Position. At each angle step during the shaft revolution, the additional slope and bending moment are calculated by an iterativemethod. The transient behavior is considered by introducing Fourier series expansion concept for the additional slope. Simulation is carried out for a simple rotor similar to those available in the literature and comparison of the basic crack behavior is shown. Using the additional slope, the cracked rotor behavior is explained with the crack depth increased: the magnitude of the additional slope increases and the closed crack duration during a revolution decreases as the crack depth increases. The direction of unbalance is also shown as a factor to affect the crack breathing. Whirl orbits are shown near the sub-critical speed ranges of the rotor.

• Journal of the Korean Institute of Telematics and Electronics S
• /
• v.36S no.11
• /
• pp.128-139
• /
• 1999

This paper proposes a linearization technique for the space vector modulation method, which increases the linear control range of inverter up to the 6-step inverter. This method is based on fourier series expansion of the desired output voltage of the inverter to calculate the compensation angle in continuous switching mode and holding angle in discontinuous switching including the 6-step mode respectively. The approximation equation of these angles are used for compensation of fundamental voltage in overmodulation range. Therefore, it is possible to obtain the linear control and the maximized utilization of PWM inverter output voltage.

• Journal for History of Mathematics
• /
• v.21 no.3
• /
• pp.67-96
• /
• 2008

In the 19th century Fourier and Dirichlet studied the expansion of "arbitrary" functions into the trigonometric series and this led to the development of the Riemann's definition of the integral. Riemann's integral was considered to be of the highest generality and was discussed intensively. As a result, some weak points were found but, at least at the beginning, these were not considered as the criticism of the Riemann's integral. But after Jordan introduced the theory of content and measure-theoretic approach to the concept of the integral, and after Borel developed the Jordan's theory of content to a theory of measure, Lebesgue joined these two concepts together and obtained a new theory of integral, now known as the "Lebesgue integral".

• Journal of Ocean Engineering and Technology
• /
• v.18 no.5
• /
• pp.7-14
• /
• 2004

The interaction of incident manochromatic waves with an array of N surface-piercing porous dual cylindrical structures is investigated in the frame of three-dimensional linear potential theory. The dual cylindrical structure is camposed of concentric two cylinders. The exterior cylinder is porous and the interior cylinder is impermeable. The fluid domain is divided into N+1 regions i.e. a single exterior region and N interior regions. The diffraction potentials in each region representing the scattering of incident waves by an array of porous cylindrical structures are expressed by the Fourier Bessel series. The unknown coefficients in each region are determined by applying the porous boundary condition and continuity of mass flux at the matching boundary. It is found that an array of porous cylindrical structures reduces both the wave forces and the wave run-up, and shows the excellent performance of wave blocking. The results show that various types of breakwater exchanging seawater are prospective by controlling the porosity and the configuration of cylindrical structures.

• Structural Engineering and Mechanics
• /
• v.17 no.5
• /
• pp.641-654
• /
• 2004

This paper presents a theoretic model of a smart structure, a transversely isotropic piezoelectric thick square plate constructed with three laminas, piezoelectric-elastic-piezoelectric layer, by adopting the first order shear deformation plate theory and piezoelectric theory. This model assumes that the transverse displacements through thickness are linear, and the in-plane displacements in the mid-plane of the plate are not taken to be account. By using Fourier's series expansion, an exact Navier typed analytical solution for deflection and electric potential of the simply supported smart plate is obtained. The electric boundary conditions are being grounded along four vertical edges. The external voltage and non-external voltage applied on the surfaces of piezoelectric layers are all considered. The convergence of the present approach is carefully studied. Comparison studies are also made for verifying the accuracy and the applicability of the present method. Then some new results of the electric potentials and displacements are provided. Numerical results show that the electrostatic voltage is approximately linear in the thickness direction, while parabolic in the plate in-plane directions, for both the deflection and the electric voltage. These results are very useful for distributed sensing and finite element verification.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.11 no.3
• /
• pp.362-367
• /
• 1987

Cylinder pressure level is defined the value of sound pressure level derived from relations of pressure and frequency which are obtained Fourier series expansion of cylinder pressure. CPL is alone in general use in combustion analysis without regarding attenuation coefficient determined by engine structure because it is almost constant in various kinds of engines. Combustion pressure fluctuation and influence of CPL was investigated in this paper using Wiebe combustion function superposition th obtain the effect of premixed and diffusive combustion. The results are as follow. (1) Influence of combustion maximum pressure(P$\sub$max/) on CPL is correspond with total energy per cycle well. (2) P$\sub$max/, .DELTA.P$\sub$max/, (dp/d.theta.)$\sub$max/ and (d$\^$2/p/d.theta.$\^$2/)$\sub$max/ are very effective on CPL in the range of low frequency, mid-low frequency, mid-high frequency and high frequency respectively.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.18 no.1
• /
• pp.123-130
• /
• 2008

An analytical method for the free vibration of a flexible rectangular plate in contact with water is developed by the Rayleigh-Ritz method. The plate clamped along the edges is partially contacted with water at both sides. It is assumed that the contained water is incompressible and inviscid. The wet mode shape of the plate is assumed as a combination of the dry mode shapes of a clamped beam. The liquid motion is described by using the liquid displacement potential and determined by using the compatibility conditions along the liquid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict excellently the fluid-coupled natural frequencies comparing with the finite element analysis result.

• Structural Engineering and Mechanics
• /
• v.70 no.5
• /
• pp.525-534
• /
• 2019

An analytical research on buckling of simply supported thin plate with variable thickness under bi-axial compression is presented in this paper. Combining the perturbation technique, Fourier series expansion and Galerkin methods, the linear governing differential equation of the plate with arbitrary thickness variation under bi-axial compression is solved and the analytical expression of the critical buckling load is obtained. Based on that, numerical analysis is carried out for the plates with different thickness variation forms and aspect ratios under different bi-axial compressions. Four different thickness variation forms including linear, parabolic, stepped and trigonometric have been considered in this paper. The calculated critical buckling loads and buckling modes are presented and compared with the published results in the tables and figures. It shows that the analytical expressions derived by the theoretical method in this paper can be effectively used for buckling analysis of simply supported thin plates with arbitrary thickness variation, especially for the stepped thickness that used in engineering widely.

• Structural Engineering and Mechanics
• /
• v.76 no.6
• /
• pp.765-779
• /
• 2020

This article presents a nonclassical size dependent model based on the modified couple stress theory to study and analyze the bending behavior of perforated microbeams under different loading patterns. Modified equivalent material and geometrical parameters for perforated beam are presented. The modified couple stress theory with one material length scale parameter is adopted to incorporate the microstructure effect into the governing equations of perforated beam structure. The governing equilibrium equations of the perforated Timoshenko as well as the perforated Euler Bernoulli are developed based on the potential energy minimization principle. The Poisson's effect is included in the governing equilibrium equations. Regular square perforation configuration is considered. Based on Fourier series expansion, closed forms for the bending deflection and the rotational displacements are obtained for simply supported perforated microbeams. The proposed methodology is validated and compared with the available results in the literature and an excellent agreement is detected. Numerical results demonstrated the applicability of the proposed methodology to investigate the bending behavior of regularly squared perforated beams incorporating microstructure effect under different excitation patterns. The obtained results are significantly important for the design and production of perforated microbeam structures.

• Korean Journal of Soil Science and Fertilizer
• /
• v.23 no.2
• /
• pp.87-93
• /
• 1990

A statistical model to predict soil temperature from the ambient meteorological factors including mean, maximum and minimum air temperatures, precipitation, wind speed and snow depth combined with Fourier time series expansion was developed with the data measured at the Suwon Meteorolical Service from 1979 to 1988. The stepwise elimination technique was used for statistical analysis. For the yearly oscillation model for soil temperature with 8 terms of Fourier expansion, the mean square error was decreased with soil depth showing 2.30 for the surface temperature, and 1.34-0.42 for 5 to 500-cm soil temperatures. The $r^2$ ranged from 0.913 to 0.988. The number of lag days of air temperature by remainder analysis was 0 day for the soil surface temperature, -1 day for 5 to 30-cm soil temperature, and -2 days for 50-cm soil temperature. The number of lag days for precipitaion, snow depth and wind speed was -1 day for the 0 to 10-cm soil temperatures, and -2 to -3 days for the 30 to 50-cm soil teperatures. For the statistical soil temperature prediction model combined with the yearly oscillation terms and meteorological factors as remainder terms considering the lag days obtained above, the mean square error was 1.64 for the soil surfac temperature, and ranged 1.34-0.42 for 5 to 500cm soil temperatures. The model test with 1978 data independent to model development resulted in good agreement with $r^2$ ranged 0.976 to 0.996. The magnitudes of coeffcicients implied that the soil depth where daily meteorological variables night affect soil temperature was 30 to 50 cm. In the models, solar radiation was not included as a independent variable ; however, in a seperated analysis on relationship between the difference(${\Delta}Tmxs$) of the maximum soil temperature and the maximum air temperature and solar radiation(Rs ; $J\;m^{-2}$) under a corn canopy showed linear relationship as $${\Delta}Tmxs=0.902+1.924{\times}10^{-3}$$ Rs for leaf area index lower than 2 $${\Delta}Tmxs=0.274+8.881{\times}10^{-4}$$ Rs for leaf area index higher than 2.