• Proceedings of the Korean Society of Machine Tool Engineers Conference
• /
• 1999.05a
• /
• pp.99-104
• /
• 1999

In this paper, dynamic behavior of a two stage gear train system is analyzed. This system consists of three shafts supported by ball bearing at the ends of them and two pairs of spur gear sets. For exact analysis, the meshing tooth pair of gears is modeled as spring having time-dependent meshing stiffness and damping. The result of this analysis is compared to that of analysis using other model of spring having mean mesh stiffness. The effect of the excitation force by the imbalance of a rotor of a motor on the vibration of a gear train system is also analyzed. Finally, the change of a natural frequency of the whole system due to the change of an angle between three shafts is compared in each case, and from this analysis, the avoiding angle for design is advised.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.9 no.3
• /
• pp.1-12
• /
• 1989

The nonlinearity of a cable-stayed bridge results from the large displacement of main girder due to a long span, the catenary action of cables and the flexural stiffness reduced by large axial forces. The dynamic behaviour of a cable-stayed bridge plays an important role in determining its safety. Especially, when the eccentrically moving load is applied to a cable-stayed bridge, the torsional vibration and vertical vibration are coupled and moreover the variation of cable tensions shows important dynamic characteristics. This dissertation presents a theoretical study and a finite element procedure for analysis of a cable-stayed bridge under a eccentrically moving load. Attention is focused on the dynamic behaviours such as dynamic increments of cable tensions and nodal displacements, with the variety of velocities and eccentricities of moving load. It is found that a moving load with eccentricity can have significant effects upon the responses; the torsion of bridge deck and the increments of cable tensions, according to the present results in this study.

• Structural Engineering and Mechanics
• /
• v.62 no.6
• /
• pp.759-769
• /
• 2017

The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton‟s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.11 no.2
• /
• pp.15-26
• /
• 1991

The lateral forces such as the earthquake and wind my cause the torsion to be coupled with the lateral bending in the gider, the cross-section of wich has only one axis of symmetry. This induces additional stresses especially in cables arranged in double-planes. Since this effect cannot be considered by using the conventional frame elements, the stiffness and the mass matrices of the geometrically nonlinear thin-walled frame element are developed in this study to model the girder. The equivalent modulus of elasticity proposed by Ernst is used for the cable elements. Verification of the present theory is made through a numerical example. Then, the free vibration of a three dimensional cable-stayed bridge is analyzed to study the coupled flexural-torsional behavior.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.11 no.5
• /
• pp.89-100
• /
• 2001

The Ritz method Is applied In a three-dimensional (3-D) analysis to obtain accurate frequencies for thick. linearly tapered. annular plates. The method is formulated for annular plates haying any combination of free or fixed boundaries at both Inner and outer edges. Admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co-ordinate. and a1gebraic polynomials in the radial and thickness co-ordinates. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant figures is demonstrated. Comparisons of results for annular plates with linearly varying thickness are made with ones obtained by others using 2-D classical thin place theory. Extensive and accurate ( four significant figures ) frequencies are presented 7or completely free. thick, linearly tapered annular plates haying ratios of average place thickness to difference between outer radius (a) and inner radius (b) radios (h$_{m}$/L) of 0.1 and 0.2 for b/L=0.2 and 0.5. All 3-D modes are included in the analyses : e.g., flexural, thickness-shear. In-plane stretching, and torsional. Because frequency data liven is exact 7o a\ulcorner least four digits. It is benchmark data against which the results from other methods (e.g.. 2-D 7hick plate theory, finite element methods. finite difference methods) and may be compared. Throughout this work, Poisson\`s ratio $\upsilon$ is fixed at 0.3 for numerical calculations.s.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.13 no.3 s.55
• /
• pp.101-109
• /
• 2009

An algorithm is proposed for estimating dynamic displacements of a bridge by using FBG sensors and by superposing some measurable low modes. Modal displacements are obtained from the beam theory and the generalized coordinates are deduced from the strains measured by FBG sensors. By considering flexural and torsional modes occurred in bridges only as flexural modes of a simply supported beam by separating a bridge into multiple girders or parts, the proposed algorithm can be applied to various types of bridges. Guidelines are provided theoretically for determining the number of modes and the number of strain gages to be used. The proposed algorithm has been examined through simulation studies on various types of bridges, laboratory experiments on a model bridge, and field tests on a simple span PC Box girder bridge. Through the simulation study, the effects of the error in the vibration modes and measurement noise on estimating the dynamic displacements are analyzed.

• Journal of Korean Society of Steel Construction
• /
• v.10 no.1 s.34
• /
• pp.47-61
• /
• 1998

The behavior of horizontally curved I-girder bridges is complex because the flexural and torsional behavior of curved girders are coupled due to their initial curvature. Also, the behavior is affected by cross beams. To investigate the behavior of horizontally curved I-girder bridges, it is necessary to consider curved girders with cross beams. In order to perform free vibration analyses of horizontally curved I-girder bridges, a finite element formulation is presented here and a finite element analysis program is developed. The formulation that is presented here consists of curved and straight beam elements, including the warping degree of freedom. Based on the theory of thin-walled curved beams, the shape functions of the curved beam elements are derived from homogeneous solutions of the static equilibrium equations. Third-order hermits polynomials are used to form the shape functions of the straight beam elements. In the finite element analysis program, global stiffness and mass matrix are composed, based on the Cartesian coordinate system. The Gupta method is used to efficiently solve the eigenvalue problem. Comparing the results of several examples here with those of previous studies, the formulation presented is verified. The validity of the program developed is shown by comparing results with those analyzed by the shell element.