• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1360-1365
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• 2006

In this paper the vibration analysis of cantilever beams having a concentrated tip mass and an open crack are performed. The influences of a concentrated tip mass, the crack depth, and the crack position on the natural frequencies of the cracked cantilever beam are investigated by a numerical method. The cracked cantilever beam is modeled based on the Euler-Bernoulli beam theory. The flexibility due to crack is calculated using a fracture mechanics theory. The crack is assumed to be opened during the vibrations. The results obtained by the present method were compared with experimental results to verify the theory. As inspected, as the crack depth and the concentrated tip mass increase, the natural frequencies of the beam decrease. In general, the natural frequencies of the cantilever beam are more sensitive to the depth of the crack than the position of the crack.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.5 s.98
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• pp.586-594
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• 2005

In this paper, we studied about the effects of the rotating cantilever pipe conveying fluid with a moving mass. The influences of a rotating angular velocity, the velocity of fluid flow and moving mass on the dynamic behavior of a cantilever pipe have been studied by the numerical method. The equation of motion is derived by using the Lagrange's equation. The cantilever pipe is modeled by the Euler-Bernoulli beam theory. When the velocity of a moving mass is constant, the lateral tip-displacement of a cantilever pipe is proportional to the moving mass and the angular velocity. In the steady state, the lateral tip-displacement of a cantilever pipe is more sensitive to the velocity of fluid than the angular velocity, and the axial deflection of a cantilever pipe is more sensitive to the effect of a angular velocity. Totally, as the moving mass is increased, the frequency of a cantilever pipe is decreased in steady state.

• Geomechanics and Engineering
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• v.1 no.2
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.

• Journal of KSNVE
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• v.5 no.2
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• pp.169-181
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• 1995

A theoretical model has been studied to describe the sound radiation analysis for structural vibration noise control of tire under the action of random moving line forces. When a tire is analyzed, it has been modeled as a curved beam with distributed springs and dash-pots which represent the radial, tangential stiffness and damping of tire, respectively. The reaction due to fluid loading on the vibratory response of the curved beam is taken into account. The curved beam is assumed to occupy the plane y = 0 and to be axially infinite. The material of curved beam and elastic foundation are assumed to be lossless, and governed by the law of Bernoulli-Euler beam theory. The expression for sound power is integrated numerically and its results examined as a function of Mach number(M), wavenumber ratio(.gamma.) and stiffness factor(.PSI.). The experimental investigation for structural vibration noise of tire under the action of random moving line forces has been made. Based on the STSF(Spatial Transformation of Sound Field) techniques, the sound power and sound radiation are measured. The experimental results show that operating condition, material properties and design factors of the tire have a great effect on the sound power and sound radiation characteristics.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.677-682
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• 2003

The non-linear dynamic characteristics of a semi-circular pipe conveying fluid are investigated when the pipe is clamped at both ends. To consider the geometric non-linearity for the radial and circumferential displacements, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived form the Galerkin method. The natural frequencies varying with the flow velocity are computed fen the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized- method. From these results, we should to describe the non-linear behavior to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.1 s.71
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• pp.85-92
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• 2006

This paper investigates critical loads of the tapered Beck's columns with clamped and spring supports, subjected to a subtangential follower force. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck's columns is derived using the Bemoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter and the spring stiffness.

• Structural Engineering and Mechanics
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• v.23 no.1
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• pp.15-27
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• 2006

A locally varying temperature field or a mixture of two or more different materials can cause local variation of elasticity properties of a beam. In this paper, a new Euler-Bernoulli beam element with varying Young's modulus along its longitudinal axis is presented. The influence of axial forces according to the linearized 2nd order beam theory is considered, as well. The stiffness matrix of this element contains the transfer constants which depend on Young's modulus variation and on axial forces. Occurrence of the polynomial variation of Young's modulus has been assumed. Such approach can be also used for smooth local variation of Young's modulus. The critical loads of the straight slender columns were studied using the new beam element. The influence of position of the local Young's modulus variation and its type (such as linear, quadratic, etc.) on the critical load value and rate of convergence was investigated. The obtained results based on the new beam element were compared with ANSYS solutions, where the number of elements gradually increased. Our results show significant influence of the locally varying Young's modulus on the critical load value and the convergence rate.

• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.997-1017
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• 2014

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

• Wind and Structures
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• v.24 no.3
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• pp.287-306
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• 2017

In the present study, a new assessment simulation of ride safety based on a new wind-traffic-pavement-bridge coupled vibration system is developed considering stochastic characteristics of traffic flow and bridge surface. Compared to existing simulation models, the new assessment simulation focuses on introducing the more realistic three-dimensional vehicle model, stochastic characteristics of traffic, vehicle accident criteria, and bridge surface conditions. A three-dimensional vehicle model with 24 degrees-of-freedoms (DOFs) is presented. A cellular automaton (CA) model and the surface roughness are introduced. The bridge deck pavement is modeled as a boundless Euler-Bernoulli beam supported on the Kelvin model. The wind-traffic-pavement-bridge coupled equations are established by combining the equations of both the vehicles in traffic, pavement, and bridge using the displacement and interaction force relationship at the patch contact. The numerical simulation shows that the proposed method can simulate rationally useful assessment and prevention information for traffic, and define appropriate safe driving speed limits for vulnerable vehicles under normal traffic and bridge surface conditions.

• Structural Engineering and Mechanics
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• v.62 no.2
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• pp.247-258
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• 2017

Beam-like structures such as bridge, high building and tower, pipes, flexible connecting rods and some robotic manipulators are often excited by support motions. These structures are important in machines and structures. So, this study proposes an analytic method to accurately predict the dynamic behaviors of the structures during support motions or an earthquake. Using Timoshenko beam theory which is valid even for non-slender beams and for high-frequency responses, the analytic responses of fixed-fixed beams subjected to a real seismic motions at supports are illustrated to show the principled approach to the proposed method. The responses of a slender beam obtained by using Timoshenko beam theory are compared with the solutions based on Euler-Bernoulli beam theory to validate the correctness of the proposed method. The dynamic analysis for the fixed-fixed beam subjected to support motions gives useful information to develop an understanding of the structural behavior of the beam. The bending moment and the shear force of a slender beam are governed by dynamic components while those of a stocky beam are governed by static components. Especially, the maximal magnitudes of the bending moment and the shear force of the thick beam are proportional to the difference of support displacements and they are influenced by the seismic wave velocity.