• Structural Engineering and Mechanics
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• v.20 no.3
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• pp.293-312
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• 2005

In this paper, free vibration of rotating beam with random properties is studied. The cross-sectional area, elasticity modulus, moment of inertia, shear modulus and density are modeled as random fields and the rotational speed as a random variable. To study uncertainty, stochastic finite element method based on second order perturbation method is applied. To discretize random fields, the three methods of midpoint, interpolation and local average are applied and compared. The effects of rotational speed, setting angle, random property variances, discretization scheme, number of elements, correlation of random fields, correlation function form and correlation length on "Coefficient of Variation" (C.O.V.) of first mode eigenvalue are investigated completely. To determine the significant random properties on the variation of first mode eigenvalue the sensitivity analysis is performed. The results are studied for both Timoshenko and Bernoulli-Euler rotating beam. It is shown that the C.O.V. of first mode eigenvalue of Timoshenko and Bernoulli-Euler rotating beams are approximately identical. Also, compared to uncorrelated random fields, the correlated case has larger C.O.V. value. Another important result is, where correlation length is small, the convergence rate is lower and more number of elements are necessary for convergence of final response.

• Korean Journal of Applied Biomechanics
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• v.15 no.4
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• pp.13-24
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• 2005

The purpose of this study was to compare kinematic data between experts and novices, and identify difference kinematic parameters changing direction to kick in penalty kick of soccer play. Novice subjects were 5 high school students Who has never been experienced a soccer player, and expert subjects were 5 competitive high school soccer players. The 3-d angle was calculated by Euler's Angle by inertial axis and local axis with three-dimensional cinematography. Kinematic parameters in this study consisted of angles of knee joints, hip joints, lower trunk and upper trunk when the support foot was contacted on ground and kicking foot impacted the ball. The difference of angle of knee joints in the flexion/extension was insignificantly showed below $4{\sim}9^{\circ}$ in groups and directions of ball at the time of support and impact. But the difference of angle of hip joint was significant in groups and directions of ball at the time of support and impact. Specially the right hip joint of experts were more flexed about $12^{\circ}$($43.99{\pm}6.17^{\circ}$ at left side, $31.87{\pm}4.49^{\circ}$ at right side), less abducted about $10^{\circ}$ ($-31.27{\pm}4.49^{\circ}$ at left side, $-41.97{\pm}6.67^{\circ}$ at right side) at impact when they kicked a ball to the left side of goalpost. The difference of amplitude angle in the trunk was significantly shown at upper trunk not lower trunk. The upper trunk was external rotated about $30^{\circ}$ (novice' angle was $-16.3{\pm}17.08^{\circ}$, expert's angle was $-43.73{\pm}12.79^{\circ}$) at impact. Therefore the significant difference of kinematic characteristics could be found at the right hip joint and the upper trunk at penalty kick depending on the direction of kicking.

• Explosives and Blasting
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• v.36 no.3
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• pp.1-9
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• 2018

This study was conducted to evaluate the influences of the angle of artificial joints, the distance between the artificial joints and the blast hole, and the number of artificial joints on the pressure wave propagation, crack propagation, and blast wave velocity. The evaluation was conducted numerically by use of the Euler-Lagrange solver supported by the AUTODYN, which is a dynamic FEM program. As a result, it was found that the blast wave velocity was decreased most rapidly as either the distance between the artificial joint and the blast hole was decreased or the angle of the artificial joint was increased. In contrast to the case of no artificial joint, the amount of attenuation of the blast wave velocity was considerably large when an artificial joint was present. However, the effect of the number of artificial joint on the attenuation of the blast wave velocity was negligible under the given condition.

• Journal of Advanced Marine Engineering and Technology
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• v.14 no.4
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• pp.46-56
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• 1990

Stress analysis of axi-symetric body with non-symetric loading and non-symetric given displacements is investigated in this paper using the finite element method. As the non-symetric load and non-symetric given displacements of axi-symetric body are generally periodic functions of angle .theta., the nodal forces and nodal displacements can be expanded in cosine and sine series, that is, Fourier series. Furthermore, using Euler's formula, the cosine and sine series can be converted into exponential series and it is prooved that the related calculus become more clear. Substituting the nodal displacements expanded in Fourier series into the strain components of cylindrical coordinates system, the element strains are expressed in series form and by the principal of virtual work, the element stiffness martix and element load vector are obtained for each order. It is also showed that if the non-symetric loads are even or odd functions of angle ${\theta}$ the stiffness matrix and load vector of the system are composed with only real numbers and relatively small capacity fo computer memory is enough for calculation.

• Steel and Composite Structures
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• v.39 no.5
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• pp.543-564
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• 2021

In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.

• International Journal of Fluid Machinery and Systems
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• v.10 no.2
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• pp.154-163
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• 2017

Performance characteristics in pump mode of pump-turbines are vital for the safe and effective operation of pumped storage power plants. However, the head characteristics are different under different guide vane openings. In this paper, 3-D steady simulations were performed under 13mm, 19mm and 25mm guide vane openings. Three groups of operating points under the three GVOs were chosen based on experimental validation to investigate the influence of guide vane setting on flow patterns upstream and downstream. The results reveal that, the guide vane setting will obviously change the flow pattern downstream, which in turn influences the flow upstream. It shows a strong effect on hydraulic loss (power dissipation) in the guide and stay vanes. It is also found that the hydraulic loss mainly comes from the flow separation and vortices. In addition, in some operating conditions, the change of guide vane opening will change the flow angle at the runner inlet and outlet, which will change the Euler momentum (power input). The joint action of Euler momentum and hydraulic loss results in the change of the head characteristics.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.6
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• pp.1994-2004
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• 1996

Numerical calculation was applied to supersonic under-expanded jets, and compared with the results of a linear theory and other experiments. TVD difference scheme was employed to solve 2-dimensional and axisymmetric inviscid Euler equation. This paper aims to explore the effects of angle of divergence and design Mach number of nozzle on the structure of under-expanded jets. The angle of divergence was varied from 0 to 20 deg. The results show that the length of the first cell of the under-expanded jets decreases and Mach disk generates at lower nozzle pressure ratio, if the angle of divergence or design Mach number of nozzle increases. The distance from the nozzle exit to Mach disk in 2-dimensional jets becomes much larger than that of axisymmetric jets, and the widths of the jet boundary and the barrel shock wave are also larger than that of axisymmetric jets. Calculation results indicate that the configuration of the under-expanded jets is strongly dependent on the nozzle pressure ratio.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.12
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• pp.143-152
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• 1997

The deflection of an end mill is very important in machining process and cutting simulation because it affects directly workpiece accuracy, cutting force, and chattering. In this study, the deflection of the end mill was studied both experimentally and by using finite element analysis. And the moment of inertia of cross sections of the helical end mill is calculated for the determination of the relation between geometry of radial cross section and rigidity of the tools. Using the Bernoulli-Euler beam theory and the concept of equivalent diameter, a deflection model is established, which includes most influences from tool geomety parameters. It was found that helix angle attenuates the rigidity of the end mill by the finite element analysis. As a result, the equivalent diameter is determined by tooth number, inscribed diameter ratio, cross sectional geometry and helix angle. Because the relation betweem equivalent diameter and each factor is nonlinear, neural network is used to decide the equivalent diameter. Input patterns and desired outputs for the neural network are obtained by FEM analysis in several case of end milling operations.

• Structural Engineering and Mechanics
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• v.32 no.4
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• pp.501-516
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• 2009

This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on Kirchhoff's rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance ($10^{-5}$). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.

• Transactions of the Korean Society of Automotive Engineers
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• v.24 no.4
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• pp.408-415
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• 2016

The vehicle attitude and sideslip is critical information to control the vehicle to prevent from unintended motion. Many of estimation strategy use bicycle model or IMU integration, but both of them have limits on application. The main purpose of this paper is development of vehicle orientation estimator which is robust to various vehicle state and road shape. The suggested estimator use 3-axis magnetometer, yaw rate sensor and lateral acceleration sensor to estimate three Euler angles of vehicle. The estimator is composed of two individual observers: First, comparing the known magnetic field and gravity with measured value, the TRIAD algorithm calculates optimal rotational matrix when vehicle is in static or quasi-static condition. Next, merging 3-axis magnetometer with inertial sensors, the extended Kalman filter is used to estimate vehicle orientation under dynamic condition. A validation through simulation tools, Carsim and Simulink, is performed and the results show the feasibility of the suggested estimation method.