• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2002년도 춘계학술대회논문집
• /
• pp.836-841
• /
• 2002

The nonlinear vibration of moving viscoelastic belts excited by the eccentricity of pulleys is investigated through experimental and analytical methods. Laboratory measurements demonstrate the nonlinearities in the responses of the belt, particularly in the resonance region and with the variation of tension. The measurements of the belt motion were made using a noncontact laser sensor Jump and hysteresis phenomenon are observed experimentally and are studied with a model which considers the nonlinear relation of belt stretch. An ordinary differential equation is derived as a working form of the belt equation of motion. Numerical results show good agreements with the experimental observations, which demonstrates the nonlinearity of viscoelastic moving belts

• 대한조선학회논문집
• /
• 제31권2호
• /
• pp.57-64
• /
• 1994

본 논문은 비선형 확률 미분 방정식의 시뮬레이션 기법을 다루었다. Monte-Carlo 해를 이 시뮬레이션 기법에 적용하였다. 이 방법은 불규칙 해상의 선박에 대한 비선형 횡요 운동을 해석하는데 적용하였다. 본 연구에서 제시한 방법의 유용성을 검증하기 위해서 시뮬레이션의 결과를 등가 선형화법과 등가 비선형화법의 결과와 비교하였다.

• 대한수학회보
• /
• 제49권6호
• /
• pp.1179-1192
• /
• 2012

In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u)=0$ in ${\Omega}{\times}[0,T]$, with Dirichlet boundary condition and initial data given. We prove the existence of a discrete approximate solution by means of the Rothe discretization in time method under some conditions on ${\beta}$, $f$ and $p$.

• 대한수학회지
• /
• 제57권2호
• /
• pp.313-329
• /
• 2020

In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.

• 충청수학회지
• /
• 제24권2호
• /
• pp.359-370
• /
• 2011

In this work, we obtain new solitary wave solutions for some nonlinear partial differential equations. The Jacobi elliptic function rational expansion method is used to establish new solitary wave solutions for the combined KdV-mKdV and Klein-Gordon equations. The results reveal that Jacobi elliptic function rational expansion method is very effective and powerful tool for solving nonlinear evolution equations arising in mathematical physics.

• Journal of Mechanical Science and Technology
• /
• 제15권8호
• /
• pp.1165-1173
• /
• 2001

This paper deals with dynamic analysis of Pipeline Inspection Gauge (PIG) flow control in natural gas pipelines. The dynamic behaviour of PIG depends on the pressure differential generated by injected gas flow behind the tail of the PIG and expelled gas flow in front of its nose. To analyze dynamic behaviour characteristics (e.g. gas flow, the PIG position and velocity) mathematical models are derived. Tow types of nonlinear hyperbolic partial differential equations are developed for unsteady flow analysis of the PIG driving and expelled gas. Also, a non-homogeneous differential equation for dynamic analysis of the PIG is given. The nonlinear equations are solved by method of characteristics (MOC) with a regular rectangular grid under appropriate initial and boundary conditions. Runge-Kutta method is used for solving the steady flow equations to get the initial flow values and for solving the dynamic equation of the PIG. The upstream and downstream regions are divided into a number of elements of equal length. The sampling time and distance are chosen under Courant-Friedrich-Lewy (CFL) restriction. Simulation is performed with a pipeline segment in the Korea gas corporation (KOGAS) low pressure system. Ueijungboo-Sangye line. The simulation results show that the derived mathematical models and the proposed computational scheme are effective for estimating the position and velocity of the PIG with a given operational condition of pipeline.

• 대한기계학회논문집
• /
• 제15권6호
• /
• pp.1897-1907
• /
• 1991

본 연구에서는 세 모드 사이의 내부공진을 고려하여 강제진동 중인 보의 비선 형 해석을 다루고자 한다. 이 문제에 관심을 갖게 된 동기는 "연속계의 비선형해석 에서 더 많은 모드를 포함시키면 어떤 결과를 낳게 될 것인가\ulcorner" 라는 질문에서 생겨난 것이다.

• Structural Engineering and Mechanics
• /
• 제37권4호
• /
• pp.401-413
• /
• 2011

The aerodynamic stability of orthotropic tensioned membrane structures with rectangular plane is theoretically studied under the uniform ideal potential flow. The aerodynamic force acting on the membrane surface is determined by the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics. Then, based on the large amplitude theory and the D'Alembert's principle, the interaction governing equation of wind-structure is established. Under the circumstances of single mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction equation into a system of second order nonlinear differential equation with constant coefficients. Through judging the stability of the system characteristic equation, the critical divergence instability wind velocity is determined. Finally, from different parametric analysis, we can conclude that it has positive significance to consider the characteristics of orthotropic and large amplitude for preventing the instability destruction of structures.

• 대한수학회보
• /
• 제49권4호
• /
• pp.705-714
• /
• 2012

In this paper, we study nonlinear equation arising in MEMS modeling electrostatic actuation. We will prove the local and global existence of solutions of the generalized parabolic MEMS equation. We present that there exists a constant ${\lambda}^*$ such that the associated stationary problem has a solution for any ${\lambda}$ < ${\lambda}^*$ and no solution for any ${\lambda}$ > ${\lambda}^*$. We show that when ${\lambda}$ < ${\lambda}^*$ the global solution converges to its unique maximal steady-state as $t{\rightarrow}{\infty}$. We also obtain the condition for the existence of a touchdown time $T{\leq}{\infty}$ for the dynamical solution. Furthermore, there exists $p_0$ > 1, as a function of $p$, the pull-in voltage ${\lambda}^*(p)$ is strictly decreasing with respect to 1 < $p$ < $p_0$, and increasing with respect to $p$ > $p_0$.

• Journal of applied mathematics & informatics
• /
• 제30권1_2호
• /
• pp.253-264
• /
• 2012

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in the mathematical physics via the (1+1)-dimensional Boussinesq equation by using the following two methods: (i) A further improved ($\frac{G}{G}$) - expansion method, where $G=G({\xi})$ satisfies the auxiliary ordinary differential equation $[G^{\prime}({\xi})]^2=aG^2({\xi})+bG^4({\xi})+cG^6({\xi})$, where ${\xi}=x-Vt$ while $a$, $b$, $c$ and $V$ are constants. (ii) The well known extended tanh-function method. We show that some of the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before which gives more exact solutions than the second method (ii).