• ETRI Journal
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• 제16권4호
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• pp.13-25
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• 1995

We have derived a nonlinear spatiotemporal differential equation for space-charge fields from Kukhtarev’s material equations in a moving coordinate system and obtained the spatial subharmonic instability boundaries by using linear stability analysis. It is also found that there is an analogy between the temporal subharmonic and the spatial subharmonc instabilities in the sense that the governing differential equations describing the instability boundaries are formally identical. The experiments for generating spatial subharmonic waves are performed in a photorefractive $Bi_{12}SiO_{20}$ crystal by using conventional moving grating technique. The threshold detunings are experimentally determined and the results are compared with the theory.

• 대한기계학회논문집B
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• 제29권1호
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• pp.95-102
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• 2005

Acoustic behavior in gas turbine combustor with acoustic resonator is investigated numerically by adopting linear acoustic analysis. Helmholtz-type resonator is employed as acoustic resonator to suppress acoustic instability passively. The tuning frequency of acoustic resonator is adjusted by varying its length. Through harmonic analysis, acoustic-pressure responses of chamber to acoustic excitation are obtained and the resonant acoustic modes are identified. Acoustic damping effect of acoustic resonator is quantified by damping factor. As the tuning frequency of acoustic resonator approaches the target frequency of the resonant mode to be suppressed. mode split from the original resonant mode to lower and upper modes appears and thereby complex patterns of acoustic responses show up. Considering mode split and damping effect as a function of tuning frequency, it is desirable to make acoustic resonator tuned to broad-band frequencies near the maximum frequency of those of the possible upper modes.

• 한국추진공학회지
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• 제22권3호
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• pp.46-52
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• 2018

액체산소 및 탄화수소를 사용하는 연소기의 고주파 연소불안정을 해석하기 위해 단순모델로서 Crocco의 $n-{\tau}$ 시간지연 연소모델을 적용하고, 음향과 커플된 연소기 내 유동에 대해 선형해석을 수행하였다. 변수분리를 통해 편미분 포텐셜함수 식을 원통좌표계 미분방정식으로 만들고, 연소기의 접선방향 공진모드에 대한 고유 값을 계산하였다. 분사면 및 노즐입구를 경계조건으로 적용하여 미분식의 해를 구했다. 시스템의 안정성 판정을 위해 전달함수를 주파수 해석 하였으며, 관심 영역 주파수인 1T 모드 주변 주파수에서 시스템 게인 및 위상각으로 안정성 여유를 평가하였다. 또한 1T 모드 안정성 향상을 위해 배플 길이 및 형상에 대한 영향을 평가하였다.

• 대한기계학회논문집B
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• 제27권4호
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• pp.415-423
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• 2003

The hydrodynamic instability of the three-dimensional boundary-layer over a rotating disk has been numerically investigated for these flows; Ro = -1, -0.5, and 0, using linear stability theory. Detailed numerical values of the disturbance wave number. wave frequency. azimuth angle. radius (Reynolds number, Re) and other characteristics have been calculated for the pre-swirl flows. On the basis of Ekman and Karman boundary layer theory, the instability of the pre-swirl flows have been investigated for the unstable criteria. The disturbance will be relatively fast amplified at small fe and within wide bands of wave number compared with previously known Karman boundary-layer results. The flow (Ro =-0.5) is found to be always stable for a disturbance whose dimensionless wave number is greater than 0.9. It has a larger range of unstable interval than Karman boundary layer and can be unstable at smaller Re.

• 한국자동차공학회논문집
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• 제11권6호
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• pp.93-100
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• 2003

This paper describes the thermoelastic instability arising from friction heat generation in braking and proposes the finite element methods to predict the variation of temperature and thermal deformation. In a conventional disc brake analysis, heat generation is only related with wheel speed and friction material and the interface pressure between disc and pad is assumed constant. But under dynamic braking conditions, the frictional heat causes the thermoelastic distortion that leads to more concentrated contact pressure distribution and hence more and more non-uniform temperature. In this paper, to complete the solution of the thermomechanically coupled problem, the linear relation model between pressure and temperature is proposed and demonstrated in examples of a simple two dimensional contact problem. And the two dimensional model has been extended to an annular three dimensional disc model in order to consider more realistic geometry and to provide a more accurate critical speed for automotive brake systems.

• Wind and Structures
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• 제5권6호
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• pp.479-492
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• 2002

A finite element aerodynamic model that can be used to analyse flutter instability of long span bridges in the time domain is presented. This approach adopts a simplified quasi-steady formulation of the wind forces neglecting the vortex shedding effects. The governing equations used are effective only for reduced velocities $V^*$ sufficiently great: this is generally acceptable for long-span suspension bridges and, then, the dependence of the wind forces expressions of the flutter derivatives can be neglected. The procedure describes the mechanical response in an accurate way, taking into account the non-linear geometry effects (large displacements and large strains) and considering also the compressed locked coil strands instability. The time-dependence of the inertia force due to fluid structure interaction is not considered. The numerical examples are performed on the three-dimensional finite element model of the Great Belt East Bridge (DK). A mode frequency analysis is carried out to validate the model and the results show good agreement with the experimental measurements of the full bridge aeroelastic model in the wind tunnel tests. Significant parameters affecting bridge response are introduced and accurately investigated.

• 대한기계학회논문집
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• 제14권3호
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• pp.526-533
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• 1990

본 연구에서는 단일 캠 구동기구의 안정성 해석을 위한 효율적인 방법이 제시 되고, 수치실험을 통하여 검증되었다. 우선 단일 캠 구동기구를 묘사하는 비선형 방 정식이 유도되고, 동안정성에 관여하는 변수들이 무차원화되어 도입된다. 유도된 방 정식은 캠 축의 입력각에 대하여 선형화되고, 선형화된 방정식에 조화균형법(harmonic balance method)을 적용하여 동안정성 해석을 수행하였다.

• Steel and Composite Structures
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• 제32권2호
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• pp.157-171
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• 2019

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

• Journal of Power Electronics
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• 제11권3호
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• pp.327-334
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• 2011

Single-phase power factor correction (PFC) converter circuits are non-linear systems due to the contribution of their multiplier. This non-linearity causes difficulties in analysis and design. Models that reduce the system to a linear system involve considerable approximation, and produce results that are susceptible to instability problems. In this paper a piecewise affine (PWA) system is introduced for describing the nonlinear averaged model. Then robust output feedback controllers are established in terms of the linear matrix inequality (LMI). Simulation and experiments results show the effectiveness of the proposed control method.

• Smart Structures and Systems
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• 제17권5호
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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.