• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.29 no.1A
• /
• pp.31-43
• /
• 2009

In this study, the numerical method is presented, which can consider the various train types and can solve the equations of motion for a vehicle-bridge interaction analysis by non-iteration procedure through formulating the coupled equations of motion. The coupled equations of motion for the vehicle-bridge interaction are solved by the Newmark ${\beta}$ of a direct integration method, and by composing the effective stiffness matrix and the effective force vector according to a analysis step, those can be solved with the same manner of the solving procedure of equilibrium equations in static analysis. Also, the effective stiffness matrix is reconstructed by the Skyline method for increasing the analysis effectiveness. The Cholesky's matrix decomposition scheme is applied to the analysis procedure for minimizing the numerical errors that can be generated in directly calculating the inverse matrix. The equations of motion for the conventional trains are derived, and the numerical models of the conventional trains are idealized by a set of linear springs and dashpots with 16 degrees of freedom. The bridge models are simplified by the 3 dimensional space frame element which is based on the Euler-Bernoulli theory. The rail irregularities of vertical and lateral directions are generated by the PSD functions of the Federal Railroad Administration (FRA). The results of the vehicle-bridge interaction analysis are verified by the experimental results for the railway plate girder bridges of a span length with 12 m, 18 m, and the experimental and analytical data are applied to the low pass filtering scheme, and the basis frequency of the filtering is a 2 times of the 1st fundamental frequency of a bridge bending.

• Journal of the Korean Society for Precision Engineering
• /
• v.32 no.5
• /
• pp.405-413
• /
• 2015

This paper presents the motion accuracy simulation considering loads such as workpiece weight, cutting force, cogging force of a linear motor, and force caused by misalignment and runout error of a ballscrew in linear motion units. The transfer function method is basically utilized to estimate 5-DOF motion errors, together with the equilibrium equations of force and moment on the table. The transfer function method is modified in order to consider clearance changed according to the loads in the double sided hydrostatic/aerostatic bearings. Then, the analytic model for predicting the 5-DOF motion errors is proposed with the modified transfer function method. Motion errors were simulated under different loading conditions in the linear motion units using hydrostatic, aerostatic, and linear motion bearings, respectively. And the proposed analytic model was verified by comparing the estimated and measured motion errors.

• Journal of the Society of Naval Architects of Korea
• /
• v.40 no.1
• /
• pp.20-27
• /
• 2003

The FPSO is moored by mooring lines to keep the position of it. The nonlinear motion analysis of the moored FPSO must be carried out in the initial design stage because sea environments affect motion of it. In this paper, the mathematical model is based on the slow motion maneuvering equations in the horizontal plane considering wave, current and wind forces. The direct integration method is employed to estimate wave loads. The current forces are calculated by using mathematical model of MMG. The turret mooring forces are quasi-statically evaluated by using the catenary equation. The coefficients of a model for wind forces are calculated from Isherwood's experimental data and the variation of wind speed is estimated by wind spectrum according to the guidelines of API-RP2A. The nonlinear motions of FPSO are simulated under external forces due to wave, current, wind including mooring forces in time domain.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.25 no.5
• /
• pp.866-873
• /
• 2001

The governing partial differential equations of a helical spring with a circular section were derived from Frenet formulas and Timoshenko beam theory. These were solved to give the dispersion relationship between wave number and frequency along with wave form. Wave motions of helical springs are categorized by 4 regimes. In the first regime, the lower frequency area, the torsional and extensional waves of the spring are predominant and two waves are composite wave motions involving lateral motion of the coils and rotation of the coils about a horizontal axis. All waves are propagating in the second regime. The wave of the extensional motion of the spring and one wave of transverse motion of a wire change from travelling waves to near field waves in the third regime. Both waves excited by both axial and transverse motion are predominant in the fourth regime.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.9 s.180
• /
• pp.2266-2273
• /
• 2000

Equations of motion of a multi-beam system undergoing overall rigid body motion are derived by employing finite element method. An orientation angle is employed to allow the arbitrary orientation o f the beam element. Modal coordinate reduction technique, which has been successfully utilized in the conventional linear modeling method, is employed for the present modeling method to reduce the computational effort. Different from the conventional linear modeling method, the present modeling method captures the motion-induced stiffness variations which are important for the dynamic analysis of structures undergoing overall rigid body motion. The numerical results are compared to those of a commercial program to verify the reliability of the present method.

• Structural Engineering and Mechanics
• /
• v.35 no.2
• /
• pp.217-240
• /
• 2010

A semi-analytical method is presented for accurately prediction of the free vibration behavior of generally laminated composite plates with arbitrary boundary conditions. The method employs the technique of separation of spatial variables within Hamilton's principle to obtain the equations of motion, including two systems of coupled ordinary homogeneous differential equations. Subsequently, by applying the laminate constitutive relations into the resulting equations two sets of coupled ordinary differential equations with constant coefficients, in terms of displacements, are achieved. The obtained differential equations are solved for the natural frequencies and corresponding mode shapes, with the use of the exact state-space approach. The formulation is exploited in the framework of the first-order shear deformation theory to incorporate the effects of transverse shear deformation and rotary inertia. The efficiency and accuracy of the present method are demonstrated by obtaining solutions to a wide range of problems and comparing them with finite element analysis and previously published results.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.7
• /
• pp.1751-1758
• /
• 1994

A new set of governing equations is derived for the dynamic analysis of the Free-Piston Stirling Engines(EPSE). Equations from the ideal adiabatic model for the thermodynamic analysis of the working fluid are incoporated with the equations of motion for the moving masses of the system, resulting in a set of nonlinear differential equations. The coupled set of equations are numerically integrated with proper intial conditions to obtain a steady state response of the engine. The proposed method is compared with the conventional method of analyzing EPSE based mainly on the ideal isothermal model. The results clearly shows the limitationsl of the conventional methods and the relative advantages of the method proposed in the present study.

• Journal of Mechanical Science and Technology
• /
• v.19 no.spc1
• /
• pp.377-387
• /
• 2005

The equations of motion of two-wheeled vehicles, e.g. bicycles or motorcycles, are developed by using Lagrange's equations for quasi-coordinates. The pure rolling constraints between the ground and the two wheels are considered in the dynamical equations of the system. For each wheel, two nonholonomic and two holonomic constraints are introduced in a set of differential-algebraic equations (DAE). The constraint Jacobian matrix is obtained by collecting all the constraint equations and converting them into the velocity form. Equilibrium, an algorithm for searching for equilibrium points of two-wheeled vehicles and the associated problems are discussed. Formulae for calculating the radii of curvatures of ground-wheel contact paths and the reference point are also given.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.9
• /
• pp.2339-2348
• /
• 1994

The objective of this paper is to develop a solution method for the differential-algebraic equation(DAE) derived from constrained muti-body dynamic systems. Mechanical systems are often modeled as bodies and joints. Differential equations of motion are formulated for bodies. Since the bodies are connected by joint, the differential variables must satisfy the kinematic constraint equations that come from the joints. Difficulties are arised due to drift of the differential variables off the constraint equations. An optimization method is adopted to correct the drift of the differential variables. To demonstrate the efficiency of the proposed method a slider-crank mechanism is analyzed dynamically. Identical results are obtained as these from the commercial program DADS. Dynamic analysis of a High Mobility Multi-purpose Wheeled. Vehicle(HMMWV) is carried out to show the practicalism of the proposed method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2011.04a
• /
• pp.681-688
• /
• 2011

Structural model of laminated composite plates based on the first order shear deformable plate theory and subjected to a combination of magnetic and thermal fields is developed. Coupled equations of motion are derived via Hamilton's principle on the basis of electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. In order to obtain the implications of a number of geometrical and physical features of the model, one special case is investigated, that is, free vibration of a composite plate immersed in a transversal magnetic field. Special coupling effects between the magnetic and elastic fields are revealed in this paper.