• Smart Structures and Systems
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• v.15 no.5
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• pp.1311-1327
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• 2015

In this paper, we have applied a new class of approximate analytical methods called Variational Approach (VA) for high nonlinear vibration equations. Three examples have been introduced and discussed. The effects of important parameters on the response of the problems have been considered. Runge-Kutta's algorithm has been used to prepare numerical solutions. The results of variational approach are compared with energy balance method and numerical and exact solutions. It has been established that the method is an easy mathematical tool for solving conservative nonlinear problems. The method doesn't need small perturbation and with only one iteration achieve us to a high accurate solution.

• Structural Engineering and Mechanics
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• v.28 no.1
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• pp.107-127
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• 2008

Wind turbine blades are increasing in magnitude without a proportional increase of stiffness for which reason geometrical and inertial nonlinearities become increasingly important. Often these effects are analysed using a nonlinear truncated expansion in undamped fixed base mode shapes of a blade, modelling geometrical and inertial nonlinear couplings in the fundamental flap and edge direction. The purpose of this article is to examine the applicability of such a reduced-degree-of-freedom model in predicting the nonlinear response and stability of a blade by comparison to a full model based on a nonlinear co-rotating FE formulation. By use of the reduced-degree-of-freedom model it is shown that under strong resonance excitation of the fundamental flap or edge modes, significant energy is transferred to higher modes due to parametric or nonlinear coupling terms, which influence the response and stability conditions. It is demonstrated that the response predicted by such models in some cases becomes instable or chaotic. However, as a consequence of the energy flow the stability is increased and the tendency of chaotic vibrations is reduced as the number of modes are increased. The FE model representing the case of infinitely many included modes, is shown to predict stable and ordered response for all considered parameters. Further, the analysis shows that the reduced-degree-of-freedom model of relatively low order overestimates the response near resonance peaks, which is a consequence of the small number of included modes. The qualitative erratic response and stability prediction of the reduced order models take place at frequencies slightly above normal operation. However, for normal operation of the wind turbine without resonance excitation 4 modes in the reduced-degree-of-freedom model perform acceptable.

• The KSFM Journal of Fluid Machinery
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• v.15 no.2
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• pp.36-40
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• 2012

Pitch control of wind turbine is activated above rated wind speed for the purpose of rated power regulation. When we design pitch controller, its gain-scheduling is essential due to nonlinear characteristics of aerodynamic torque. In this study, 2-mass model including a vibration mode of drive-train for a 2 MW wind turbine is considered and pitch control with gain-scheduling using a linearization analysis of the nonlinear aerodynamic torque is applied. Some simulation results for the pitch gain-scheduling under step wind speed are presented and investigated. It is shown that gain-scheduling in pitch control is important especially in the region of high wind speeds when there exists a vibration mode of drive-train.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.2 s.245
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• pp.135-140
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• 2006

In tapping mode atomic force microscopy (TM-AFM), the vibro-contact response of a resonating tip is used to measure the nanoscale topology and other properties of a sample surface. However, the nonlinear tipsurface interactions can affect the tip response and destabilize the tapping mode control. Especially it is difficult to obtain a good scanned image of high adhesion surfaces such as polymers and biomolecules using conventional tapping mode control. In this study, theoretical and experimental investigations are made on the nonlinear dynamics and control of TM-AFM. Also we report the surface adhesion is an additional important parameter to determine the control stability of TM-AFM. In addition, we proved that it was adequate to use Johnson-Kendall-Roberts (JKR) contact model to obtain a reasonable tapping response in AFM for the soft and high adhesion samples.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1266-1271
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• 2007

General coil spring has linearity. However, disc spring has non-linearity so that using this non-linearity disc spring can be designed to do shock-absorbing in cases we need because shock response also has non-linearity. By changing the shape and stacking number, it is satisfactory with response of displacement, velocity and acceleration. Conventionally, disc spring was used to control the vibration against huge load and limited space. However, it is limitedly used because of difficulty of the designing guidance. Therefore, disc spring is needed to study further in order to apply it widely. Response of disc spring is compared to response of coil spring by changing ho/t radio with computer simulation and the usage of disc spring is increased through analysis of effect of design factors. The purpose of this paper is that the shock response of disc spring is calculated through numerical simulation and effect of ho/t and stiffness is analyzed to broad usage so that design factor of disc spring is presented.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.2
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• pp.153-159
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• 2008

General coil spring has linearity. However, disc spring has non-linearity so that using this non-linearity disc spring can be designed to do shock-absorbing in cases we need because shock response also has non-linearity. By changing the shape and stacking number, it is satisfactory with response of displacement, velocity and acceleration. Conventionally, disc spring was used to control the vibration against huge load and limited space. However, it is limitedly used because of difficulty of the designing guidance. Therefore, disc spring is needed to study further in order to apply it widely. Response of disc spring is compared to response of coil spring by changing $h_o/t$ ratio with computer simulation and the usage of disc spring is increased through analysis of effect of design factors. The purpose of this paper is that the shock response of disc spring is calculated through numerical simulation and effect of $h_o/t$ and stiffness is analyzed to broad usage so that design factor of disc spring is presented.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.2
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• pp.193-199
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• 1988

The forced vibrations of nondissipative nonlinear two-degree-of-freedom system, subjected to periodic forcing functions, are investigated by use of the method of slowly changing phase and amplitude. The first order differential equations are derived for nonrationally solutions and the coupled nonlinear algebraic equations for stationary solutions. Through investigating the response curves of the system, which are obtained numerically by using Newton-Raphson method, it is found that the resonances can occur at more than the number of degree-of-freedom of the system depending on the relation between the nonlinear spring parameters, which has no counterpart in linear systems.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.399-406
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• 1998

An investigation into the stochastic bifurcation and response statistits of an autoparameteric system under broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. In view of equilibrium solutions of this system and their stability we examine the stochastic bifurcation and response statistics. The analytical results are compared with results obtained by Monte Carlo simulation.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.7 s.100
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• pp.813-820
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• 2005

A deployable missile control fin has some structural nonlinearities because of the worn or loose hinges and the manufacturing tolerance. The structural nonlinearity cannot be eliminated completely, and exerts significant effects on the static and dynamic characteristics of the control fin. Thus, It is important to establish the accurate deployable missile control fin model. In the present study, the nonlinear dynamic model of 4he deployable missile control fin is developed using a substructure synthesis method. The deployable missile control fin can be subdivided Into two substructures represented by linear dynamic models and a nonlinear hinge with structural nonlinearities. The nonlinear hinge model is established by using a system identification method, and the substructure modes are improved using the Frequency Response Method. A substructure synthesis method Is expanded to couple the substructure models and the nonlinear hinge model, and the nonlinear dynamic model of the fin is developed. Finally, the established nonlinear dynamic model of the deployable missile control fin is verified by dynamic tests. The established model is In good agreement with test results, showing that the present approach is useful in aeroelastic stability analyses such as time-domain nonlinear flutter analysis.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.350-355
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• 2008

A Rubber mount is widely used for mechanical parts or engineering materials. Especially, it plays an important role in reducing mechanical vibration due to cyclic loading. But, rubber mount is damaged due to the cyclic loading and resonance. Therefore, it is necessary to investigate evaluation of fatigue life considering vibration characteristics for rubber. In this study, a vibration fatigue analysis was performed and based on Power Spectral Density(PSD) and the stress-life curve and a result of frequency response analysis in the finite element method. The measured load history in experiment was transformed to PSD curve. The stress-life curve was obtained by nonlinear static analysis and fatigue test. In addition, frequency response analysis was conducted for mechanical part. In order to evaluate fatigue life of rubber mount, vibration fatigue test was conducted at the constant acceleration-level as well. Fatigue life was determined when the load capacity is reduced to 60% of its initial value. As a result, predicted fatigue life of rubber mount agreed fairly well with the experimental fatigue life.