• Structural Engineering and Mechanics
• /
• v.23 no.6
• /
• pp.599-613
• /
• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.813-829
• /
• 2011

In this article, we present a numerical scheme for solving singularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and boundary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence of perturbation parameter and nonlinearity in the problem leads to severe difficulties in the solution approximation. To overcome such difficulties the present numerical scheme is constructed. In construction of the numerical scheme, the first step is the dicretization of the time variable using forward difference formula with constant step length. Then, the resulting non linear singularly perturbed semidiscrete problem is linearized using quasi-linearization process. Finally, differential quadrature method is used for space discretization. The error estimate and convergence of the numerical scheme is discussed. A set of numerical experiment is carried out in support of the developed scheme.

• 전기의세계
• /
• v.20 no.5
• /
• pp.15-18
• /
• 1971

Up to now, there have been numerous investigations about the effect of diffusion on the wave propagation in gaseous plasmas, but not so much in semiconductor magnetoplasmas. However, currently, it becomes the centor of interest to work with the latter problem, and this paper deals with the dispersion equation including diffusion effect in the latter case to see how diffusion affects the equation in which diffusion term is neglected in the first place, and the analysis is based on the assumption that the plasma can be treated as a hydrodynamical fluid, since, from a macroscopic view point, the plasma interacting with a magnetic field can be considered as a magneto-hydrodynamical fluid, an electrically conducting fluid subjected to electromagnetic force, and the system is linear. The results of the relation and computation show that in the non-streaming case the diffusion terms appear in the equation as perturbation terms and the amplitude of the wave vector changes parabolically with the variation of the angular frequency and the longitudinal modes are observed.

• 유체기계공업학회:학술대회논문집
• /
• 2005.12a
• /
• pp.803-809
• /
• 2005

This paper presents the theoretical model to investigate the effect of Coulomb damping in the sub-structure of a foil bearing. Foil deflection is restricted by friction of bumps. Equivalent viscous damping of the bump foils is derived from the Coulomb friction. Dynamic equation of the bumps is constituted by stiffness and damping terms. This point give the difference from Heshmat's frictionless and simple compliance bump model. The fluid is modeled with the compressible Reynolds equation. A perturbation approach is used to determine the static and dynamic performance of the bearing from the coupled fluid-structural model. The analysis result shows that the static and dynamic performance is enhanced by bump friction. This analysis technique would be extended to development of a high performance bearing.

• Journal of KSNVE
• /
• v.9 no.6
• /
• pp.1218-1226
• /
• 1999

In this paper, the extended Biot's semilinear model was developed. Combining the extended Biot model with the dynamic equation yields the nonlinear wave equation in poproelastic sound absorbing materials. Both perturbation and matching techniques are used to find solutions for nonlinear wave equations. By comparing results between linear and nonlinear wave solutions, characteristics of nonlinear waves in poroelastic sound abosrbing materials have been studied. Nonlinear waves were found to be attenuated faster than the linear ones. A maximum amplitude of the nonlinear wave occurred near its surface boundaries and decay quickly with distance from the surface. It has also been found that, if the amplitudes of linear waves are known at the surface boundaries, those of nonlinear ones can be determined. This will be the basis of finding effects of nonlinearity on the absorption coefficient and the transmission loss.

• Computational Structural Engineering
• /
• v.7 no.2
• /
• pp.131-138
• /
• 1994

Derivatives of eigenvalues and eigenvectors for statistical properties is presented. Dynamic response of random system including uncertainties for the design variable is calculated with the first order perturbation method to original governing equation. In optimal design methods, there is fundamental requirement for design gradients. A method for calculating the sensitivity coefficients is developed using the governing equation and first order perturbed equation.

• The KSFM Journal of Fluid Machinery
• /
• v.9 no.1 s.34
• /
• pp.47-55
• /
• 2006

This paper presents the theoretical model to investigate the effect of Coulomb damping in the sub-structure of a foil bearing. Foil deflection is restricted by friction of bumps. Equivalent viscous damping of the bump foils is derived from the Coulomb friction. Dynamic equation of the bumps is constituted by stiffness and damping terms. This point give the difference from Heshmat's frictionless and simple compliance bump model. The fluid is modeled with the compressible Reynolds equation. A perturbation approach is used to determine the static and dynamic performance of the bearing from the coupled fluid-structural model. The analysis result shows that the static and dynamic performance is enhanced by bump friction. This analysis technique would be extended to development of a high performance bearing.

• Computational Structural Engineering
• /
• v.7 no.3
• /
• pp.115-122
• /
• 1994

Design sensitivity analysis of the second order perturbed eigenproblems for random structural system is presented. Dynamic response of random system including uncertainties for the design variable is calculated with the first order and second order perturbation method to original governing equation. In optimal design methods, there is fundamental requirement for design gradients. A method for calculating the sensitivity coefficients is developed using the direct differentiation method for the governing equation and first order and second order perturbed equation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1997.10a
• /
• pp.145-153
• /
• 1997

Dynamic characteristics are investigated when a nonlinear system showing periodic and chaotic responses under harmonic excitation is exposed to random perturbation. About two well potential problem, probability of homoclinic bifurcation is estimated using stochastic generalized Meinikov process and quantitive characteristics are investigated by calculation of Lyapunov exponent. Critical excitaion is calculated by various assumptions about Gaussian Melnikov process. To verify the phenomenon graphically Fokker-Planck equation is solved numerically and the original nonlinear equation is numerically simulated. Numerical solution of Fokker-Planck equation is calculated on Poincare section and noise induced chaos is studied by solving the eigenvalue problem of discretized probability density function.

• Structural Engineering and Mechanics
• /
• v.86 no.3
• /
• pp.361-371
• /
• 2023

Boundary condition is an important factor affecting the vibration characteristics of structures, under different boundary conditions, structures will exhibit different vibration behaviors. On the basis of the previous work, this paper extends to the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. Based on nonlinear Kirchhoff plate theory, the motion equations are derived. Considering three boundary conditions, including four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS), the nonlinear ordinary differential equation system is obtained by Galerkin method, and then the equation system is solved to obtain the nonlinear ordinary differential control equation which only including transverse displacement. Subsequently, the resonance response of GPLRMF plates is obtained by perturbation method. Finally, the effects of different boundary conditions, material properties (including the GPLs patterns, foams distribution, porosity coefficient and GPLs weight fraction), geometric imperfection, and axial velocity on the resonance of GPLRMF plates are investigated.