• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.703-708
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• 2006

The cantilever beam with nonlinearity has many dynamic characteristics of nonlinear vibration. Nonlinear terms of a flexible cantilever beam include inertia, spring, damping, and warping. When the beam is given basic harmonic excitation, it shows planar and nonplanar vibrations due to one-to-one resonance. And when the one-to-one resonance occurs, the flexible beam shows different behaviors in those vibrations. For the one-to-one resonance occurring in each mode, the phase value of the planar vibration is different from that of the nonlinear vibration. This paper investigates the phase change and the phase difference between such planar and nonplanar vibrations which are caused by one-to-one resonance.

• Journal of Advanced Marine Engineering and Technology
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• v.16 no.5
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• pp.67-76
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• 1992

This paper describes the vibration characteristic of second-order nonlinear systems subjected to parametric excitation. Emphasis is put on the examination of the hydrodynamic nonlinear damping effect on limiting the response amplitudes of parametric vibration. Since the parametric vibration is described by the Mathieu equation, the Mathieu stability chart is examined in this paper. In addition, the steady-state solutions of the nonlinear Mathieu equation in the first instability region are obtained by using a perturbation technique and are compared with those by a numerical integration method. It is shown that the response amplitudes of parametric vibration are limited even in unstable conditions by hydrodynamic nonlinear damping force. The largest reponse amplitude of parametric vibration occurs in the first instability region of Mathieu stability chart. The parametric excitation induces the response of a dynamic system to be subharmonic, superharmonic or chaotic according to their dynamic conditions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.1 s.118
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• pp.48-54
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• 2007

The cantilever beam with nonlinearity has many dynamic characteristics of nonlinear vibration. Nonlinear terms of a flexible cantilever beam include inertia, spring, damping, and warping. When the beam is given basic harmonic excitation, it shows planar and nonplanar vibrations due to one-to-one resonance. And when the one-to-one resonance occurs, the flexible beam shows different behaviors in those vibrations. For the one-to-one resonance occurring in each mode, the phase value of the planar vibration is different from that of the nonlinear vibration. This paper investigates the phase change and the phase difference between such planar and nonplanar vibrations which are caused by one-to-one resonance.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.8
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• pp.639-647
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• 2002

The nonlinear vibration of the thin perforated plate is analyzed in consideration of the V-shaped tension distribution and the effect of wire impact damping. The reduced order FEM model of the tension plate is obtained from dynamic condensation for the mass and stiffness matrices. Tension wire is modeled using the lumped parameter method to effectively describe its contact interactions with the plate. The nonlinear contact-impact model is composed of spring and damper elements, of which parameters are determined from the Hertzian contact theory and the restitution coefficient, respectively. From the evaluation of the computational accuracy and computation time for the deduced impact stiffness and damping coefficient, we determined proper values for the simulation works, accounting for the computational accuracy as well as the computational efficiency. Finally we discussed the results of nonlinear nitration analysis for variations of their design parameters.

• Smart Structures and Systems
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• v.25 no.6
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• pp.643-655
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• 2020

Active control of nonlinear vibration of stiffened functionally graded (SFG) cylindrical shell is studied in this paper. The system is subjected to axial and transverse periodic loads in the presence of thermal uncertainty. The material composition is considered to be continuously graded in the thickness direction, also these properties depend on temperature. The relations of strain-displacement are derived based on the classical shell theory and the von Kármán equations. For modeling the stiffeners on the cylindrical shell surface, the smeared stiffener technique is used. The Galerkin method is used to discretize the partial differential equations of motion. Some comparisons are made to validate the SFG model. For suppression of the nonlinear vibration, the linear and nonlinear control strategies are applied. For control objectives, the piezoelectric actuator is attached to the external surface of the shell and the thin ring piezoelectric sensor is attached to the middle internal surface of shell. The effect of PID, feedback linearization and sliding mode control on the suppression of vibration for SFG cylindrical shell is presented.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.543-560
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• 2006

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

• Smart Structures and Systems
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• v.26 no.5
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• pp.631-640
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• 2020

In this paper, nonlinear vibration behaviors of multi-phase Magneto-Electro-Elastic (MEE) doubly-curved nanoshells have been studied employing Jacobi elliptic function method. The doubly-curved nanoshell has been modeled by using nonlocal elasticity and classic shell theory. An exact estimation of nonlinear vibrational behavior of smart doubly-curved nanoshell has been obtained via Jacobi elliptic function method. This method can incorporate the influences of higher order harmonics leading to an exact estimation of nonlinear vibration frequency. It will be indicated that nonlinear vibrational frequency of doubly-curved nanoshell relies on nonlocal effect, material composition, curvature radius, center deflection and electro-magnetic field.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.603-606
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• 2007

Wind induced vibration of a stay cable with a nonlinear friction damper is investigated. Stay cables are likely to vibrate under several wind-related environments, and cable dampers can be used to suppress the excessive vibrations of stay cables. Conventional design of cable dampers are based on the equivalent modal damping achieved by the cable damper. However, the equivalent modal damping achieved by nonlinear dampers are depend on the vibration characteristics like the amplitude of the vibration. In this paper, not only the achieved equivalent modal damping, but also the vibration levels under gust wind are analyzed through the time domain buffeting analysis. Numerical simulation results show the efficacy of a nonlinear friction damper for suppressing the excessive vibration of a stay cable.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.77-82
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• 2004

There were many researches about the chatter vibration occur in the cutting process of machine tools. But there are in sufficient research parts ; the frequency about the chatter vibration and its characteristics and its nonlinear properties. This paper measured signals of vibration that occur before and immediately after and after the chatter vibration. This signals were analyzed through autospectrum obtained by the Fast Fourier Transform(FFT). And then, the nonlinear characteristis were analyzed by cepstrum analysis through FFT of autospectrun.

• Smart Structures and Systems
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• v.22 no.1
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• pp.105-120
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• 2018

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.