• 소음진동
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• 제10권5호
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• pp.800-805
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• 2000

To determine the modal matrix and modal frequency of engine mount system, we most solve so-called eigen-value problem. However eigen-value problem of engine mount system with hydraulic mount can not be solved by general eigne-analysis algorithm because the properties of hydraulic mount vary with frequency. so in this paper the method for modal analysis of rigid body motions of an engine supported by hydraulic mount is proposed. Natural frequencies and mode shapes of this nonlinear system are obtained by using complex exponential method and Laplace transformation method. In time domain, impulse response functions are calculated by (two-sided) discrete inverse Fourier Transformation of forced frequency response functions achieved by Laplace transformation of the differential equation of motion. Considering the fact that frequency response functions synthesized by modal parameters form proposed method are in good agreement with original FRFs, it is proved that the proposed method is very efficient and useful for the analysis of eigne-value problem of hydraulic engine mount system.

• Structural Engineering and Mechanics
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• 제34권4호
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• Advances in aircraft and spacecraft science
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• 제9권3호
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• pp.263-278
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• 2022

The time-varying structural reliability of an aeroelastic launch vehicle subjected to stochastic parameters is investigated. The launch vehicle structure is under the combined action of several stochastic loads that include aerodynamics, thrust as well as internal combustion pressure. The launch vehicle's main body structural flexibility is modeled via the normal mode shapes of a free-free Euler beam, where the aerodynamic loadings on the vehicle are due to force on each incremental section of the vehicle. The rigid and elastic coupled nonlinear equations of motion are derived following the Lagrangian approach that results in a complete aeroelastic simulation for the prediction of the instantaneous launch vehicle rigid-body motion as well as the body elastic deformations. Reliability analysis has been performed based on two distinct limit state functions, defined as the maximum launch vehicle tip elastic deformation and also the maximum allowable stress occurring along the launch vehicle total length. In this fashion, the time-dependent reliability problem can be converted into an equivalent time-invariant reliability problem. Subsequently, the first-order reliability method, as well as the Monte Carlo simulation schemes, are employed to determine and verify the aeroelastic launch vehicle dynamic failure probability for a given flight time.

• 한국해양공학회지
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• 제19권5호
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• pp.58-64
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• 2005

In this paper, a feedback linearizing anti-sway control law, using a 2-D model for container cranes, is investigated. The equations of motion are first derived from Lagrange's equation. Then, by substituting the sway dynamics into the trolley dynamics, a reduction of variables from three (trolley, hoist, sway) to two (trolley, hoist) is pursued. The anti-sway control law is designed based on the Lyapunov stability theorem. The proposed control law guarantees the uniform asymptotic stability of the closed-loop system. The simulation results of the derived control law, using MATLAB/Simulink, are compared with those of the sliding mode control law, noted in previous literature. Also, experimental results using a 3-D pilot crane are provided.

• 제어로봇시스템학회논문지
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• 제6권1호
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• pp.57-65
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• 2000

In this paper, a model reference adaptive control for the atomic force microscope (AFM) of tapping mode is investigated. The dynamics between the AFM system and al sample is mathematically modeled as a second order spring-mass-damper system with oscillatory inputs. The attractive and repulsive forces between the tip of the AFM system and the sample are derived using the Lennard-Jones potential energy. By non-dimensionalizing the displacement of the tip and the input frequency, the chaotic behavior near a resonance frequency is better depicted through the non-dimensionalized equations. Four nonlinear analysis techniques, a phase portrait, sensitive dependence on initial conditions, a power spectral density function, and a Pomcare map are investigated. Because the equations of motion derived in this paper involve unknown parameter values such as the damping effect of the air and the interaction constants between materials, the standard model reference adaptive control is adopted. Two control objectives, the prevention of chaos and the tracking of reference signal, are pursued. Simulation results are included.

• Steel and Composite Structures
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• 제44권2호
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• pp.155-169
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• 2022

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.

• 해양환경안전학회지
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• 제24권7호
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• pp.953-959
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• 2018

본 논문에서는 바람, 파도, 조류 등의 큰 외란조건에서 선박계류시스템의 계류안정성 확보를 위한 동적제어기 설계를 연구하였다. 선박계류시스템의 비선형 동요를 억제하기 위해 슈퍼트위스팅 알고리즘(STA)을 포함한 슬라이딩 모드 제어(SMC) 기법이 적용되었다. 외란이나 파라미터의 불확실성에 대한 강인성의 장점에도 불구하고, 채터링은 슬라이딩 모드 제어기를 적용하는데 주요 단점이 되고 있다. 1차계 SMC는 정확히 제어 목표치에 수렴 하도록 정밀한 제어는 가능하나, 채터링과 같은 파괴적인 현상과 연계되어 적용에 주요한 장애가 된다. 대신에, STA는 큰 외란에도 불구하고 비교적 높은 정확도를 보이며 채터링 현상을 완전히 제거한다. 1차계 슬라이딩 모드 제어기의 채터링 문제를 피할 수 있는 STA기반의 SMC는 비선형 계류시스템의 동적제어를 위한 아주 효과적인 수단으로 판단된다. 아울러, STA로 제어된 선박계류시스템의 위치오차 궤적은 경계 구역 내에서 형성된다. 끝으로, 슬라이딩 표면과 위치궤적의 오차결과를 통해 STA의 이득제어 효과도 관측할 수 있다.

• 대한기계학회논문집B
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• 제38권4호
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• pp.337-346
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• 2014

본 연구는 주기적 강제 진동이 가해지는 표면의 액적 모드 특성과 표면에 놓인 액적의 제거에 대한 조건을 실험적으로 이해하는 것을 목적으로 하고 있다. 액적의 거동을 명확하게 관찰하기 위해 아크릴 표면에 Teflon 코팅을 진행하여 접촉각을 높였고, 히스테리시스는 25도 이내로 진행하여 액적의 거동이 보다 쉽게 진행되도록 하였다. 본 실험은 먼지가 적은 청정실에서 실험이 진행되었다. 제작된 소수성 표면에 놓인 액적의 실제 공진 주파수를 예측하기 위해 이론 및 실험적 해석을 통해 두 접근방법의 타당성을 파악하였으며, 두 개의 초고속카메라를 액적의 상면과 측면에 설치하여 2가지 측면에서 액적의 다양한 형상 변형 특성- 모드 형상, 분리, 미소 액적의 발생, 그리고 좌우 비틀림의 특성을 관찰하였다. 이론 값 비교결과 실제 공진 주파수 값들의 차이가 약 18% 이하로 관찰되었으며, 이러한 차이는 접촉선 마찰, 비선형 벽 고착, 실험의 불확실성 등에 가장 큰 영향을 받는 것으로 판단된다. 사용된 스피커에 상대적으로 낮은 전압을 인가할 경우 액적의 접촉선은 고정된 상태에서 좌우 대칭적인 액적 형상진동이 나타났다. 반면, 높은 전압을 인가할 경우 액적의 접촉선은 비고정된 상태가 되면서 더 활발한 형상 진동이 나타났다. 가진 주파수가 모드 주파수와 일치할 경우에는 액적의 로브 크기가 주변부 주파수 일 때 보다 비교적으로 컸으며, 같은 전압을 인가 할 경우, 표면에 놓인 액적의 미소 액적 발생 및 완전한 제거는 2차 모드에서만 진행되는 것을 실험을 통해 규명하였다.

• 한국자동차공학회논문집
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• 제8권4호
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• pp.169-176
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• 2000

Longitudinal and lateral forces acting on tires are known to be closely related to the tract-ability braking characteristics handling stability and maneuverability of ground vehicles. In thie paper in order to develop tire force monitoring systems a monitoring model is proposed utilizing not only the vehicle dynamics but also the roll motion. Based on the monitoring model three monitoring systems are developed to estimate the tire force acting on each tire. Two monitoring systems are designed utilizing the conventional estimation techniques such as SMO(Sliding Mode Observer) and EKF(Extended Kalman Filter). An additional monitoring system is designed based on a new SKFMEC(Scaled Kalman Filter with Model Error Compensator) technique which is developed to improve the performance of EKF method. Tire force estimation performance of the three monitoring systems is compared in the Matlab simulations where true tire force data is generated from a 14 DOF vehicle model with the combined-slip Magic Formula tire model. The built in our Lab. simulation results show that the SKFMEC method gives the best performance when the driving and road conditions are perturbed.

• Structural Engineering and Mechanics
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• 제13권4호
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• pp.369-385
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• 2002

Ductility capacity is comprehensively studied for steel moment-resisting frames. Local, story and global ductility are being considered. An appropriate measure of global ductility is suggested. A time domain nonlinear seismic response algorithm is used to evaluate several definitions of ductility. It is observed that for one-story structures, resembling a single degree of freedom (SDOF) system, all definitions of global ductility seem to give reasonable values. However, for complex structures it may give unreasonable values. It indicates that using SDOF systems to estimate the ductility capacity may be a very crude approximation. For multi degree of freedom (MDOF) systems some definitions may not be appropriate, even though they are used in the profession. Results also indicate that the structural global ductility of 4, commonly used for moment-resisting steel frames, cannot be justified based on this study. The ductility of MDOF structural systems and the corresponding equivalent SDOF systems is studied. The global ductility values are very different for the two representations. The ductility reduction factor $F_{\mu}$ is also estimated. For a given frame, the values of the $F_{\mu}$ parameter significantly vary from one earthquake to another, even though the maximum deformation in terms of the interstory displacement is roughly the same for all earthquakes. This is because the $F_{\mu}$ values depend on the amount of dissipated energy, which in turn depends on the plastic mechanism, formed in the frames as well as on the loading, unloading and reloading process at plastic hinges. Based on the results of this study, the Newmark and Hall procedure to relate the ductility reduction factor and the ductility parameter cannot be justified. The reason for this is that SDOF systems were used to model real frames in these studies. Higher mode effects were neglected and energy dissipation was not explicitly considered. In addition, it is not possible to observe the formation of a collapse mechanism in the equivalent SDOF systems. Therefore, the ductility parameter and the force reduction factor should be estimated by using the MDOF representation.