• International Journal of Precision Engineering and Manufacturing
• /
• v.3 no.4
• /
• pp.54-63
• /
• 2002

In recent years, mechanical systems such as high speed vehicles and railway trains moving on elastic beam structures have become a very important issue to consider. In this paper, a general approach, which can predict the dynamic behavior of a constrained mechanical system moving on a flexible beam structure, is proposed. Various supporting conditions for the foundation support are considered for the elastic beam structure. The elastic structure is assumed to be a non-uniform and linear Bernoulli-Euler beam with a proportional damping effect. Combined differential-algebraic equation of motion is derived using the multi-body dynamics theory and the finite element method. The proposed equations of motion can be solved numerically using the generalized coordinate partitioning method and predictor-corrector algorithm, which is an implicit multi-step integration method.

• Structural Engineering and Mechanics
• /
• v.45 no.1
• /
• pp.69-93
• /
• 2013

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.

• Structural Engineering and Mechanics
• /
• v.64 no.6
• /
• pp.723-730
• /
• 2017

This paper studies on dynamic and stability behavior of a clamped-elastically restrained nanobeam under the action of a nonconservative force with an emphasis on the influence of surface properties on divergence and flutter instability. Using the Euler-Bernoulli beam theory incorporating surface effects, a governing equation for a clamped-elastically restrained nanobeam is derived according to Hamilton's principle. The characteristic equation is obtained explicitly and the force-frequency interaction curves are displayed to show the influence of the surface effects, spring stiffness of the elastic restraint end on critical loads including divergence and flutter loads. Divergence and flutter instability transition is analyzed. Euler buckling and stability of Beck's column are some special cases of the present at macroscale.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2009.04a
• /
• pp.573-578
• /
• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfies the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfies the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beam.

• 유체기계공업학회:학술대회논문집
• /
• 2001.11a
• /
• pp.76-80
• /
• 2001

Unsteady compressible Euler equation is solved and the high-order, high-resolution numerical solver, physical boundary condition, adaptive nonlinear artificial dissipation model and conformal mapping are applied to computation of steady transonic flow and unsteady acoustics. The acoustic characteristics of axi-symmetric duct and two dimensional straight/S channel are studied and the computation results shows good agreements with linear analysis. In transonic case, local time stepping and canceling-the-residual techniques are used for convergence acceleration. The aspect of flow and acoustics in S-channel and the Pattern of noise radiation is changed by inflow Mach no. and static pressure at fan-face.

• Journal of Mechanical Science and Technology
• /
• v.19 no.9
• /
• pp.1731-1741
• /
• 2005

In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified.

• Journal of computational fluids engineering
• /
• v.4 no.2
• /
• pp.67-73
• /
• 1999

In the present paper, three types of the flow solvers were used to investigate the influence on the airfoil shape optimization. The adopted equations, i.e., Euler, thin layer Navier-Stokes and full Navier-Stokes ones. are solved using implicit LU-ADI decomposition scheme. The gradient projection method with the sinusoidal function was used as an optimization algorithm. The present numerical method was applied to the drag minimization problems under the initial shape of NACA0012 airfoils.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.19 no.6
• /
• pp.591-598
• /
• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfy the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfy the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beams.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.41 no.1
• /
• pp.106-114
• /
• 1999

This paper explores the geometrical non-linear behavior of the simply supported tapered beams subject to the trapezoidal distributed load and end moments. In order to apply the Bernoulli -Euler beam theory to this tapered beam, the bending moment equation on any point of the elastical is obtained by the redistribution of trapezoidal distributed load. On the basis of the bending moment equation and the BErnoulli-Euler beam theory, the differential equations governging the elastical of such beams are derived and solved numerically by using the Runge-Jutta method and the trial and error method. The three kinds of tapered beams (i.e. width, depth and square tapers) are analyzed in this study. The numerical results of non-linear behavior obtained in this study from the simply supported tapered beams are appeared to be quite well according to the results from the reference . As the numerical results, the elastica, the stress resultants and the load-displacement curves are given in the figures.

• Journal of the Ergonomics Society of Korea
• /
• v.16 no.2
• /
• pp.15-27
• /
• 1997

Brain potential is described using the mesocolumnar activity defined by averaged firings of excitatory and inhibitory neuron of neocortex. Lagrangian is constructed based on SMNI(Statistical Mechanics of Neocortical Interaction) and then Euler Lagrange equation is obtained. Excitatory neuron firing is assumed to be amplitude- modulated dominantly by the sum of two modes of frequency .omega. and 2 .omega. . Time series of this neuron firing is calculated numerically by Euler Lagrangian equation. I .omega. L related to low frequency distribution of power spectrum, I .omega. H hight frequency, and Sd(standard deviation) were introduced for the effective extraction of the dynamic property in the simulated brain potential. The relative behavior of I .omega. L, I .omega. H, and Sd was found by parameters .epsilon. and .gamma. related to nonlinearity and harmonics respectively. Experimental I .omega L, I .omega. H, and Sd were obtained from EEG of human in rest state and of canine in deep sleep state and were compared with theoretical ones.