• Coupled systems mechanics
• /
• 제7권6호
• /
• pp.707-729
• /
• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제2권3호
• /
• pp.119-126
• /
• 2010

The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamical models and then applied for ship roll dynamics under random impulsive white noise excitation.

• 한국공작기계학회논문집
• /
• 제15권5호
• /
• pp.21-28
• /
• 2006

Vibration of a non-linear system with multiple degrees of freedom under random parametric excitations was evaluated by probabilistic method. The non-linear characteristic terms of system structure were quasi-linearized and excitation terms were remained as they were. An analytical method where the expectation values of square mean of error was minimized was used. The numerical results were compared with those obtained by Monte Carlo simulation. A linear congruential generator and Box-Muller method were used in Monte Carlo simulation. The comparison showed the results by probabilistic method agreed well with those by Monte Carlo simulation.

• 한국소음진동공학회논문집
• /
• 제20권9호
• /
• pp.849-855
• /
• 2010

Damping may change the response characteristics of nonlinear oscillations due to the parametric excitation of a thin cantilever beam. When the natural frequencies of the first bending and torsional modes are of the same order of magnitude, we can observe the one-to-one combination resonance in the perturbation analysis depending on the characteristic parameters. The nonlinear behavior about the combination resonance reveals a chaotic motion depending on the natural frequencies and damping ratio. We can analyze the chaotic dynamics by using the eigenvalue analysis of the perturbed components. In this paper, we derived the equations for autonomous system and solved them to obtain the characteristic equation. The stability analysis was carried out by examining the eigenvalues. Numerical integration gave the physical behavior of each mode for given parameters.

• 한국소음진동공학회논문집
• /
• 제23권8호
• /
• pp.734-741
• /
• 2013

In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from the linear natural frequencies. The Mathieu equation is the simplest differential equation with periodic coefficients, which lead to the parametric excitation. The Mathieu equation may have the unbounded solutions. This work conducted the stability analysis for the Mathieu equation, using Floquet theory and numerical method. Using Lindstedt's perturbation method, harmonic solutions of the Mathieu equation and transition curves separating stable from unstable motions were obtained. Using Floquet theory with numerical method, stable and unstable regions were calculated. The numerical method had the same transition curves as the perturbation method. Increased stable regions due to the inclusion of damping were calculated.

• 소음진동
• /
• 제9권6호
• /
• pp.1157-1165
• /
• 1999

Dynamic stability of a flying structure undertaking constnat and pulsating thrust force is investigated in this paper. The equations of motion of the structure, which is idealized as a free-free beam, are derived by using the hybrid variable method and the assumed mode method. The structural system includes a directional control unit to obtain the directional stability. Unstable regions due to periodically pulsating thrust forces are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the constant force, the location of gimbal, and the frequency of pulsating force. The validity of the diagrams are confirmed by direct numerical simulations of the dynamic system.

• 대한조선학회논문집
• /
• 제28권1호
• /
• pp.69-82
• /
• 1991

축방향의 주기적인 하중으로 가진되는 긴 수직보의 동적안정성에 관하여 연구하였다. 해석방법으로서 Galerkin방법을 이용하여 무한원 연립 Mathieu형 미분 방정식을 얻었으며, 안정성영역을 나타내는 도표를 얻기 위하여, 섭동법과 수치적인 방법을 사용하였다. 또한 이두가지 방법으로 구한 결과를 서로 비교 검토하였다. 여러가지 경계조건에 대한 안정영역을 구했으며, 김쇠의 영향, 평균인장력 및 다중 주파수 파라메터 기진의 영향에 관해서 집중적으로 연구하였다.

• 한국해양공학회지
• /
• 제7권1호
• /
• pp.73-80
• /
• 1993

본 연구에서는 장주형 해양구조물의 횡방향 진동에 대한 파라메트릭 가진 효과를 고찰하였다. 먼저, 장주형 해양구조물의 횡방향 운동에 대한 4계 편미방지배방정식을 비선형 Mathieu 방정식으로 유도하였다. 비선형 mathieu 방정식의 해를 구하여 장주형 해양구조물의 동적 반응 특성을 해석하였다. 유체 비선형 감쇠력은 불안정 조건하에 있는 파라메트릭 진동의 반응크기를 제한 하는데 중요한 역활을 한다. 파라메트릭 진동의 경우 가장 큰 반응크기는 Mathieu 안정차트의 첫번째 불안정 구간에서 일어난다. 반면에, 파라메트릭 진동과 강제진동의 결합 진동인 경우, 가장 큰 반응 크기는 두번째 불안정 구간에서 발생된다. 파라메트릭 가진으로 인한 장주형 해양구조물의 횡방향 운동은 동적조건에 따라 subharmonic, superharmonic 또는 chaotic 운동이 되기도 한다.

• Journal of Astronomy and Space Sciences
• /
• 제20권3호
• /
• pp.205-216
• /
• 2003

회전안정화 로켓 모터를 이용하는 upper stage 위성체의 자세 불안정 현상을 연구하였다. 이 위성체는 대칭형의 본체와 내장된 유동질량으로 구성되며, 유동질량은 구진자로 모델링되었다. 종래의 선형모델이 갖는 단점을 보완하기 위해 정확한 시변 비선형 방정식을 사용하고, 본체 및 구진자 모두 회전 대칭축에 대해 정상상태에 있다고 가정하였다. 본 논문에서는 진자에 대한 준정상해(quasi-stationary solution) 및 공진조건을 파라미터의 함수로 결정하였다. 공진조건의 분석결과 유동질량은 계수자극 및 외부자극을 동시에 받으며, 자극을 받은 유동질량으로부터 에너지가 본체에 유입되면서 위성체는 불안정한 장동운동을 일으키는 것으로 확인되었다. 본 논문에서는 수치시뮬레이션 예시를 통하여 주어진 위성체 모델에 대해 발생가능한 공진조건에서 진자의 운동, 위성체 각 운동량 및 섭동모멘트의 관계 규명과 로켓모터 추진 후에 자세운동이 어떻게 변화하는가를 설명하였다.

• Structural Engineering and Mechanics
• /
• 제25권2호
• /
• pp.219-237
• /
• 2007

The effect of cable loosening on the nonlinear parametric vibrations of inclined cables is discussed in this paper. In order to overcome the small-sag limitation in calculating loosening for inclined cables, it is necessary to first derive equations of motion for an inclined cable. Using these equations and the finite difference method, the effect of cable loosening on the nonlinear parametric response of inclined cables under periodic support excitation is evaluated. A new technique that takes into account flexural rigidity and damping is proposed as a solution to solve the problem of divergence. The regions of inclined cables that undergo compression are also indicated.