Home  About us  Contact
 

Second-order Differential Equation (second-order + differential_equation)

Distribution by Scientific Domains
Engineering83%

Selected Abstracts

New approaches for non-classically damped system eigenanalysis

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2005
Karen Khanlari
Abstract This paper presents three new approaches for solving eigenvalue problems of non-classically damped linear dynamics systems with fewer calculations than the conventional state vector approach. In the latter, the second-order differential equation of motion is converted into a first-order system by doubling the size of the matrices. The new approaches simplify the approach and reduce the number of calculations. The mathematical formulations for the proposed approaches are presented and the numerical results compared with the existing method by solving a sample problem with different damping properties. Of the three proposed approaches, the expansion approach was found to be the simplest and fastest to compute. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Numerical analysis of Rayleigh,Plesset equation for cavitating water jets

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2007
H. Alehossein
Abstract High-pressure water jets are used to cut and drill into rocks by generating cavitating water bubbles in the jet which collapse on the surface of the rock target material. The dynamics of submerged bubbles depends strongly on the surrounding pressure, temperature and liquid surface tension. The Rayleigh,Plesset (RF) equation governs the dynamic growth and collapse of a bubble under various pressure and temperature conditions. A numerical finite difference model is established for simulating the process of growth, collapse and rebound of a cavitation bubble travelling along the flow through a nozzle producing a cavitating water jet. A variable time-step technique is applied to solve the highly non-linear second-order differential equation. This technique, which emerged after testing four finite difference schemes (Euler, central, modified Euler and Runge,Kutta,Fehlberg (RKF)), successfully solves the Rayleigh,Plesset (RP) equation for wide ranges of pressure variation and bubble initial sizes and saves considerable computing time. Inputs for this model are the pressure and velocity data obtained from a CFD (computational fluid dynamics) analysis of the jet. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Vibration of a porouse-cellular circular plate

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006
Ewa Magnucka-Blandzi
The subject of investigation is a circular porous-cellular plate under uniform pressure. Mechanical properties of the isotropic porous cellular metal vary accross the thickness of the plate. Middle plane of the plate is its symmetry plane. Fields of diseplacements and stresses with respect the nonlinear hypothesis are described. Basing on Hamilton principle three motion equations of the plate are formulated. These equations are approximately solved. The vibration problem is reduced to the second-order differential equation. Numerical investigations are realised for family of plates. Natural frequencies are determined. The obtained results are shown in Figures. To the end of the investigation comparition analyses with respect to homogeneous plates is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Critical damping of structures with elastically supported visco-elastic dampers

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2002
Yujin Lee
Abstract This paper presents a new formulation for critical damping of structures with elastically supported visco-elastic dampers.Owing to the great dependence of damper performance on the support stiffness, this model is inevitable for reliable modelling of structures with visco-elastic dampers. It is shown that the governing equation of free vibration of this model is reduced to a third-order differential equation and the conventional method for defining the critical damping for second-order differential equations cannot be applied to the present model. It is demonstrated that the region of overdamped vibration is finite in contrast to that (semi-infinite) for second-order differential equations and multiple critical damping coefficients exist. However, it turns out that the smaller one is practically meaningful. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Numerical simulation of the unsteady flow over an elliptic cylinder at different orientations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2001
H. M. Badr
Abstract A numerical method is developed for investigating the two-dimensional unsteady viscous flow over an inclined elliptic cylinder placed in a uniform stream of infinite extent. The direction of the free stream is normal to the cylinder axis and the flow field unsteadiness arises from two effects, the first is due to the flow field development following the start of the motion and the second is due to vortex shedding in the wake region. The time-dependent flow is governed by the full conservation equations of mass and momentum with no boundary layer approximations. The parameters involved are the cylinder axis ratio, Reynolds number and the angle of attack. The investigation covers a Reynolds number range up to 5000. The minor,major axis ratio of the elliptic cylinder ranges between 0.5 and 0.6, and the angle of attack ranges between 0° and 90°. A series truncation method based on Fourier series is used to reduce the governing Navier,Stokes equations to two coupled infinite sets of second-order differential equations. These equations are approximated by retaining only a finite number of terms and are then solved by approximating the derivatives using central differences. The results reveal an unusual phenomenon of negative lift occurring shortly after the start of motion. Various comparisons are made with previous theoretical and experimental results, including flow visualizations, to validate the solution methodology. Copyright © 2001 John Wiley & Sons, Ltd. [source]

A stabilized Hermite spectral method for second-order differential equations in unbounded domains

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2007
Heping Ma
Abstract A stabilized Hermite spectral method, which uses the Hermite polynomials as trial functions, is presented for the heat equation and the generalized Burgers equation in unbounded domains. In order to overcome instability that may occur in direct Hermite spectral methods, a time-dependent scaling factor is employed in the Hermite expansions. The stability of the scheme is examined and optimal error estimates are derived. Numerical experiments are given to confirm the theoretical results.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source]