• Korean Journal of Mathematics
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• v.19 no.1
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• pp.101-109
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• 2011

We get a theorem which shows that there exist at least two or three nontrivial weak solutions for the nonlinear parabolic boundary value problem with the variable coefficient jumping nonlinearity. We prove this theorem by restricting ourselves to the real Hilbert space. We obtain this result by approaching the topological method. We use the Leray-Schauder degree theory on the real Hilbert space.

• Geomechanics and Engineering
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• v.36 no.4
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• pp.367-380
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• 2024

Investigations has shown that the correct estimation of the effective amplification period is as important as the amplification value itself. It gets more important in 2D basins. This study presents a quantitative coefficient for consideration of the nonlinearity effect in terms of amplification value and the shift in its period which is missing or ineffectively considered in the previous studies. To attain this goal, by the application of a time domain fully nonlinear method, the deviation of the more common equivalent linear results from the basin nonlinear behavior under strong ground motions is investigated quantitatively. Also, despite the increase in the damping ratio, the possibility of the increase in the amplification due to the increase in motion strength is shown. To make the results useful in engineering practice, by introducing nonlinearity ratio, the effect of the nonlinearity is quantitatively estimated for two soft and stiff clayey basins with three different depths under a set of motions scaled to two target spectrum. Results show that at the 100 m depth soft clayey basin, while the nonlinearity ratio shows a 35% deviation at the basin edge part under DD1 motion level, its effect moves to the central part with 20% effect under DD3 motion level. By the increase in depth to 150 m, the results show a decrease in the overall effect of the nonlinear behavior for both clay types. At this depth, the nonlinearity ratio gives a 30% and 17% difference on a limited distance from outcrop at the soft clayey basin under DD1 and DD3 motion levels, respectively. At the 30 m depth basins, the nonlinearity ratio shows up to 25% difference for different cases. The presented ratio would be introduced as nonlinearity coefficients for consideration of the nonlinearity effects in the codes. The presented quantitative margins will help the designer to have a better understanding of the amplification period change because of nonlinearity over 2D basin surface.

• Journal of the Korean Ceramic Society
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• v.43 no.6 s.289
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• pp.383-388
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• 2006

The varistor properties and DC accelerated aging characteristics of $ZnO-Pr_{6}O_{11}-CoO-Cr_{2}O_{3}$-based varistors were investigated at different $La_{2}O_3$ contents in the range of $0{\sim}2.0mol%$. The varistors doped with 0.5 mol% $La_{2}O_3$ exhibited good nonlinearity, with 81.6 in nonlinear coefficient. Increasing the $La_{2}O_3$ content further to 2.0 mol% caused the sintered density to increase, and the breakdown voltage and nonlinearity to decrease abruptly. The varistors with 0.5 mol% $La_{2}O_3$ exhibited the high electrical stability, with -1.14% in variation rate of breakdown voltage, -3.7% in variation rate of nonlinear coefficient, and +100% in variation rate of leakage current for specified DC accelerated aging stress condition (95% of breakdown voltage/$150^{\circ}C$/24 h).

• Journal of Communications and Networks
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• v.1 no.2
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• pp.81-85
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• 1999

The regrowth of OQPSK power spectral sidelobes from AM/AM and AM/PM amplifier nonlinearity is analyzed. The time-domain expression for amplifier output shows how spectral re-growth will depend on the cubic coefficient of the Taylor's series of the amplifier nonlinearity as well as input amplitude ripple. Closed form spectrum calculations show that the spectral sidelobes produced by AM/PM take the same form as those produced by AM/AM. The rate of growth of AM/PM sidelobes is, however, not as great as for AM/AM.

• Structural Monitoring and Maintenance
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• v.5 no.2
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• pp.261-272
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• 2018

The commonly used TMD design method in the project assumes the TMD has pure linearity. However, in real engineering TMD will exhibit nonlinear behaviors. Without considering the nonlinearity of TMD, the control effect of the TMD that is designed by the linear design method, may be worse and even enlarge the structural response. In this paper, based on the previous study results of nonlinear TMD, the improved design method for engineering application is proposed. The linear design method and the improved design method are compared. Taking the best parameter obtained by the improved design method is less than or equal to 90% of that obtained by the original design method as the dividing line. The critical nonlinear coefficient, reaching which value the improved design method needs to be used, is given. Finally, numerical simulations on two engineering examples are conducted to proof the results.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.233-242
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• 2011

We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.26 no.8
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• pp.740-747
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• 2015

Recently, mobile communication systems using the millimeter-wave frequency band have been proposed, and the importance of efficient compensation of the nonlinearity caused by 60 GHz high-power amplifiers(HPAs) is increasing. In this paper, we propose a predistorter structure based on multiple coefficient sets which are separately used to different ranges of input power values. These ranges correspond to varying levels of nonlinearity characteristics. The structure is applied to the 60 GHz HPA FMM5715X and the performance of correcting the nonlinearity of LTE signals is evaluated. Evaluation results using a hardware testbed demonstrate that the proposed predistorter structure achieves the maximum of 6 dB gain over the conventional method in terms of the adjacent channel leakage ratio(ACLR).

• Korean Journal of Optics and Photonics
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• v.28 no.4
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• pp.158-165
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• 2017

The physical shape of an ultrasound transducer has not been considered in previous studies of the photoacoustic saturation effect, where a photoacoustic signal's magnitude linearly increases as an absorption coefficient increases and it is finally saturated. In this paper, the effect of a spherically focused ultrasound transducer on photoacoustic nonlinearity is investigated. The focused ultrasound transducer's spatial filtering effect on photoacoustic signals is analytically derived considering the combined concept of a virtual point detector and Green function approach. The ultrasound transducer's temporal response (i.e., transfer function) effect on photoacoustic signals is considered by integrating photoacoustic signal values within the absorption area covered by a spatial resolution of the ultrasound transducer. Results from the analytically derived expression show that the magnitude of photoacoustic signals measured by a spherical focused ultrasound transducer shows a maximum at a specific absorption coefficient, and decreases after that maximum point as an absorption coefficient is increased. The origin of this photoacoustic nonlinearity is physically understood by comparing the ultrasound transducer's transfer functions and photoacoustic resonance spectra. In addition, this physical interpretation implies that the photoacoustic nonlinearity is strongly dependent on the irradiance distribution inside an absorption medium.

• Coupled systems mechanics
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• v.4 no.4
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• pp.279-295
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• 2015

The article presents a theoretical-experimental approach developed for modeling the coefficient of sliding friction in the dynamic system tool-workpiece in slide diamond burnishing of low-alloy unhardened steels. The experimental setup, implemented on conventional lathe, includes a specially designed device, with a straight cantilever beam as body. The beam is simultaneously loaded by bending (from transverse slide friction force) and compression (from longitudinal burnishing force), which is a reason for geometrical nonlinearity. A method, based on the idea of separation of the variables (time and metric) before establishing the differential equation of motion, has been applied for dynamic modeling of the beam elastic curve. Between the longitudinal (burnishing force) and transverse (slide friction force) forces exists a correlation defined by Coulomb's law of sliding friction. On this basis, an analytical relationship between the beam deflection and the sought friction coefficient has been obtained. In order to measure the deflection of the beam, strain gauges connected in a "full bridge" type of circuit are used. A flexible adhesive is selected, which provides an opportunity for dynamic measurements through the constructed measuring system. The signal is proportional to the beam deflection and is fed to the analog input of USB DAQ board, from where the signal enters in a purposely created virtual instrument which is developed by means of Labview. The basic characteristic of the virtual instrument is the ability to record and visualize in a real time the measured deflection. The signal sampling frequency is chosen in accordance with Nyquist-Shannon sampling theorem. In order to obtain a regression model of the friction coefficient with the participation of the diamond burnishing process parameters, an experimental design with 55 experimental points is synthesized. A regression analysis and analysis of variance have been carried out. The influence of the factors on the friction coefficient is established using sections of the hyper-surface of the friction coefficient model with the hyper-planes.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.701-705
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• 2008

Design analysis and computer experiments (DACE) model is widely used to express efficiently the nonlinear responses in the field of engineering design. Kriging model, a DACE model, can approximately replace a simulation model that is very expensive or highly nonlinear. The kriging model is composed of the summation of a global model and a local model representing deviation from global model. The local model is determined by correlation coefficient of the pre-sampled points, where determination of the correct correlation coefficient has an effect on accuracy and robustness of the kriging model. Therefore, robustness of the correlation coefficient is explored with respect to degrees of the global model. Then we propose the range of correlation coefficient to make correct and robust kriging model and the influence of the correlation coefficients on the degrees of global model with respect to the nonlinearity of the pre-sampled responses.