• Structural Engineering and Mechanics
• /
• 제40권5호
• /
• pp.705-718
• /
• 2011

The aim of the investigation described in this paper is to study the nonlinear parametric vibrations and stability of a simply-supported viscoelastic beam with an intra-span spring. Taking into account a time-dependent tension inside the beam as the main source of parametric excitations, as well as employing a two-parameter rheological model, the equations of motion are derived using Newton's second law of motion. These equations are then solved via a perturbation technique which yields approximate analytical expressions for the frequency-response curves. Regarding the main parametric resonance case, the local stability of limit cycles is analyzed. Moreover, some numerical examples are provided in the last section.

• Structural Engineering and Mechanics
• /
• 제27권1호
• /
• pp.17-32
• /
• 2007

The main source of transverse vibration of a conveyor belt is frictional contact between pulley and belt. Also, environmental characteristics such as natural dampers and springs affect natural frequencies, stability and bifurcation points of system. These phenomena can be modeled by a small velocity fluctuation about mean velocity. Also, viscoelastic foundation can be modeled as the dampers and springs with continuous characteristics. In this study, non-linear vibration of a conveyor belt supported partially by a distributed viscoelastic foundation is investigated. Perturbation method is applied to obtain a closed form analytic solutions. Finally, numerical simulations are presented to show stiffness, damping coefficient, foundation length, non-linearity and mean velocity effects on location of bifurcation points, natural frequencies and stability of solutions.

• Tribology and Lubricants
• /
• 제22권2호
• /
• pp.93-98
• /
• 2006

The numerical analysis of the negative pressure porous gas bearings is presented. The pressure distribution is calculated using the finite difference method. The Reynolds equation and Darcy's equation are solved simultaneously. The air bearing stiffness and damping are evaluated using the perturbation method. Rectangular uniform grid is employed to model the bearing. The vacuum preloading is considered. The pressure in the vacuum pocket is assumed to be a constant negative pressure. The total load, stiffness, damping and flow rate are calculated fur several geometrical configurations and several values of negative pressure. It is found that too large vacuum pocket can result in negative total force.

• Journal of Ship and Ocean Technology
• /
• 제12권2호
• /
• pp.1-15
• /
• 2008

The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${\theta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.

• 한국항만학회지
• /
• 제8권1호
• /
• pp.41-47
• /
• 1994

The present paper discusses the nonlinear wave deformation due to a submerged coastal structure. Theory is based on the frequency-domain method using the third order perturbation and boundary integral method. Theoretical development to the second order perturbation and boundary integral method. Theoretical development to the second order Stokes wave for a bottom-seated submerged breakwater to the sea floor is newly expanded to the third order for a submerged coastal structure shown in Figure 1. Validity is demonstrated by comparing numerical results with the experimental ones of a rectangular air chamber structure, which has the same dimensions as that of this study. Nonlinear waves become larger and larger with wave propagation above the crown of the structure, and are transmitted to the onshore side of the structure. These characteristics are shown greatly as the increment of Ursell number on the structure. The total water profile depends largely on the phase lag among the first, second and third order component waves.

• Journal of applied mathematics & informatics
• /
• 제27권1_2호
• /
• pp.441-452
• /
• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Journal of applied mathematics & informatics
• /
• 제22권1_2호
• /
• pp.49-65
• /
• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• 한국소음진동공학회논문집
• /
• 제26권7호
• /
• pp.795-805
• /
• 2016

Nonlinear normal modes(NNMs) is a branch of periodic solution of nonlinear dynamic systems. Determination of stable periodic solution is very important in many engineering applications since the stable periodic solution can be an attractor of such nonlinear systems. Periodic solutions of nonlinear system are usually calculated by perturbation methods and numerical methods. In this study, numerical method is used in order to calculate the NNMs. Iteration of the solution is presented by multiple shooting method and continuation of solution is presented by pseudo-arclength continuation method. The stability of the NNMs is analyzed using Floquet multipliers, and bifurcation points are calculated using indirect method. Proposed analyses are applied to two nonlinear numerical models. In the first numerical model nonlinear spring-mass system is analyzed. In the second numerical model Jeffcott rotor system which has unstable equilibria is analyzed. Numerical simulation results show that the multiple shooting method can be applied to self excited system as well as the typical nonlinear system with stable equilibria.

• 수산해양기술연구
• /
• 제35권4호
• /
• pp.435-447
• /
• 1999

It is main objective of this approach to present a method to analyse stochastic design sensitivity for problems of structural dynamics with randomness in design parameters. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element approach. An alternative form of the constant functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations excited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition method: the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, whereas the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient : they can be readily adapted to fit into the existing finite element codes whose element derivative matrices can be explicitly generated. The numerical results of two cases -2 dimensional portal frame for the comparison with reference and 3-dimensional frame structure - for the deterministic sensitivity analysis are presented.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 1995년도 추계 학술대회논문집
• /
• pp.3-10
• /
• 1995

The compressible laminar and turbulent viscous flow on a slender body in supersonic speed as well as subsonic speed has been numerically simulated at high angle of attack. The steady and time-accurate compressible thin-layer Navier-Stokes code based on an implicit upwind-biased LU-SGS algorithm has been developed and specifically applied at angles of attack of 20, 30, 40 deg, respectively. The modified eddy-viscosity turbulence model suggested by Degani and Schiff was used to simulate the case of turbulent flow. Any geometric asymmetry and numerical perturbation have not been intentionally or artificially imposed in the process of computation. The purely numerical results for laminar and turbulent cases, however, show clear asymmetric formation of vortices which were observed experimentally. Contrary to the subsonic results, the supersonic case shows the symmetric formation of vortices as indicated by the earlier experiments.