• Advances in aircraft and spacecraft science
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• v.11 no.1
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• 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.620-628
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• 2005

In this paper, we studied about the dynamic behavior of a cracked rotating cantilever beam. The influences of a rotating angular velocity, the crack depth and the crack position on the dynamic behavior of a cracked cantilever beam have been studied by the numerical method. The equation of motion is derived by using the Lagrange's equation. The cracked cantilever beam is modeled by the Euler-Bernoulli beam theory. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The lateral tip-displacement and the axial tip-deflection of a rotating cantilever beam is more sensitive to the rotating angular velocity than the depth and position of crack. Totally, as the crack depth is increased, the natural frequency of a rotating cantilever beam is decreased in the first and second mode of vibration. When the crack depth is constant, the natural frequencies of a rotating cantilever beam are proportional to the rotating angular velocity in the each direction.

• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.551-566
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• 2005

Using two different, but related approaches, an exact dynamic stiffness matrix for a two-part beam-mass system is developed from the free vibration theory of a Bernoulli-Euler beam. The first approach is based on matrix transformation while the second one is a direct approach in which the kinematical conditions at the interfaces of the two-part beam-mass system are satisfied. Both procedures allow an exact free vibration analysis of structures such as a plane or a space frame, consisting of one or more two-part beam-mass systems. The two-part beam-mass system described in this paper is essentially a structural member consisting of two different beam segments between which there is a rigid mass element that may have rotatory inertia. Numerical checks to show that the two methods generate identical dynamic stiffness matrices were performed for a wide range of frequency values. Once the dynamic stiffness matrix is obtained using any of the two methods, the Wittrick-Williams algorithm is applied to compute the natural frequencies of some frameworks consisting of two-part beam-mass systems. Numerical results are discussed and the paper concludes with some remarks.

• Steel and Composite Structures
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• v.23 no.5
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• pp.557-570
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• 2017

In this study, the seismic performance levels of four bridges are determined using finite element modeling based on ambient vibration testing. The study includes finite element modeling, analytical modal analyses, ambient vibration testing and earthquake analyses of the bridges. For the purpose, four prestressed precast I beam bridges that were constructed for the Ankara-Sivas high speed railway line are selected for analytical and experimental studies. In the study, firstly a literature review related to the dynamic behavior of bridges especially precast beam bridges is given and then the formulation part related to ambient vibration testing and structural performance according to Turkish Seismic Code (2007) is presented. Next, 3D finite element models of the bridge are described and modeled using LARSA 4D software, and analytical dynamic characteristics are obtained. Then ambient vibration testing conducted on the bridges under natural excitations and experimental natural frequencies are estimated. Lastly, time history analyses of the bridges under the 1999 Kocaeli, 1992 Erzincan, and 1999 Duzce Earthquakes are performed and seismic performance levels according to TSC2007 are determined. The results show that the damage on the bridges is all under the minimum damage limit which is in the minimum damage region under all three earthquakes.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.4 no.1
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• pp.49-55
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• 2005

This paper presents experiments on the evaluation of characteristics of ER fluids used for vibration control of application in intelligence type process control systems. Dynamic characteristics of the actuator(beam) embedded with the ER fluid can be controlled by changing the strength of the electric field applied on the ER fluids, thus provides a mean to avoid the resonance. In case electric field is supplied to the smart structure with ER fluids, vibration energy is dissipated more than the beam without electric field, because particles in ER fluid form a chain structure in the presence of electric field. The damping and stiffness of the beam with ER fluid are increased when the applied electric field increases. The characteristics of damping and stiffness of the ER fluid with various electric field strength were investigated by conducting a vibration test of the beam with ER fluid. If it applies characteristics of the ER fluids, it will be able to apply in the PLC control system for the vibration which occurs from process system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.959-962
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• 2005

In the semiconductor and optical industry. a new transport system which can replace the conventional transport system is required. The Transport systems are driven by the magnetic field and conveyer belts. The magnetic field may damage semiconductor and the contact force may scratch the optical lens. The ultrasonic wave driven system can solve these problems. In this semiconductor and optical industry, the non-contact system is required for reducing the damages. The ultrasonic transportation is the solution of the problem. In this paper, the ultrasonic levitation system for levitation object are proposed. The 3D vibration profiles of the beam are measured by Laser Scanning Vibrometer for verifying the vibration characteristics of the system and the amplitudes of the beam and the levitation heights of object are measured fore evaluating the performance.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.199-204
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• 1993

Noise and vibration induced by subway operation are one of the major factor that annoying residents living near the. railway. In general, lateral vibration was the major concern when we are considering vibration of the building. Since the energy due to earthquake is enormous it affects wide area. However, the vertical vibration became a major concern in considering the vibration induced by subway because relatively smaller energy affects only nearby areas than that of earthquake. Analysis model of the structure for the vertical vibration should consider the effect of beam vibration. Thus, the model of the structure for the lateral vibration can not be applied. Appropriate analysis model which can consider the inertia force of the beam is necessary when analyzing a structure for the vertical vibration. Modeling technique for the vertical vibration analysis of structures has been studied on this paper. It is recommeneded to use 2 or more elements for columns and to use 3 or more elements for beams when analyzing structures for vertical vibration induced by subway.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.396-400
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• 2006

We studied the influences of open cracks in free vibrating beam with rectangular section using a numerical model. The crack was assumed to be single and always open during the free vibration and equivalent bending stiffness of a cracked beam was calculated based on the strain energy balance. By Galerkin's method, the frequencies of cantilever beam could he obtained with respect to various crack depths and locations. Also, the experiments on the cracked beams were carried out to find natural frequencies. The cracks were initiated at five locations and the crack depths were increased by five steps at each location. The experimental results were compared with the numerical results and the comparison results were discussed.

• Journal of KSNVE
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• v.5 no.4
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• pp.537-542
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• 1995

In this paper the method of modeling and optimization for the joint of the vehicle structure is proposed. First it is described that the method of substituting equivalent beam elements to spring elements for the joint. The stiffnesses of the spring elementsare calculated using the section properties of equivalent beam elements. To get required dynamic characteristics section properties of equivalent beam element are set to design variables and optimized. The study shows that joint stiffnesses can be effectively determined in designing vehicle structure.

• Steel and Composite Structures
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• v.9 no.5
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• pp.473-497
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• 2009

For the spatially coupled free vibration analysis of composite box beams resting on elastic foundation under the axial force, the exact solutions are presented by using the power series method based on the homogeneous form of simultaneous ordinary differential equations. The general vibrational theory for the composite box beam with arbitrary lamination is developed by introducing Vlasov°Øs assumption. Next, the equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Finally, the dynamic stiffness matrix is calculated using force-displacement relationships. In addition, the finite element model based on the classical Hermitian interpolation polynomial is presented. To show the performances of the proposed dynamic stiffness matrix of composite box beam, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the results from other researchers. Particularly, the effects of the fiber orientation, the axial force, the elastic foundation, and the boundary condition on the vibrational behavior of composite box beam are investigated parametrically. Also the emphasis is given in showing the phenomenon of vibration mode change.