• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.333-345
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• 2007

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.10a
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• pp.321-325
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• 2004

Linear motor feed drive systems have been broadly used in machine tools or precision automatic feed systems. Recently, modem machine tools require high speed and high precision feed drive system to achieve high productivity. Unfortunately, a feed drive system, even though it was optimum designed, may experience severe transient vibrations during high-speed operation if its feed rate control is unsuitable. A rough feed rate curve having discontinuity in its acceleration profile causes a serious vibration problem in the feed slides system. This paper presents a feed rate optimization of a machine tool feed slide system, which is driven by a linear motor, for its minimum vibrations. Firstly, a 4-degree-of-freedom lumped parameter model is proposed for the vibration analysis of a linear motor driven machine tool feed drive system. Next, a feed rate optimization of the feed slide is carried out for minimum vibrations. The feed rate curve optimization strategy is to find out the most appropriate acceleration profile with jerk continuity. Of course, the optimized feed rate should approximate to the desired one as possible. A genetic algorithm with variable penalty function was used in this feed rate optimization.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.695-700
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• 2003

This paper dealt with friction-induced vibrations in engineering practice, specifically arising at the moment of counterturn of two friction surfaces. The harshness of the vibrations are attributed to the sharp change of the friction coefficients from kinetic to static near zero relative velocity, which is one of the examples of the stick slip. But the experimental results and numerical analysis of piston and cylinder operation showed that transition of the friction coefficient from kinetic to static is insignificant in vibrations. Dry friction itself dominates the harshness of vibrations. This study shows that how dry friction triggers the vibrations and demonstrates the effect of sharp transition from kinetic to static friction coefficient on the vibrations.

• Journal of the Korean Ceramic Society
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• v.40 no.11
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• pp.1062-1066
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• 2003

Design of a piezoelectric actuator for the ultrasonic motor must ensure that contact point has elliptic trajectory of movement. The new idea of an elliptic trajectory formation of the piezoelectric actuator is investigated in the paper. Shaking beam for the piezoelectric linear ultrasonic motor was introduced to realize this new idea. The principle is based on the excitation of longitudinal and flexural vibrations of the actuator by using two sources of longitudinal mechanical vibrations shifted by $\pi$/2. Mode-frequency and harmonic response analyses of the actuator based on FEM have been carried out. The moving trajectory of the contact point has been defined. Finally, The experimental research of shaking beam has been confirmed an opportunity of the elliptic trajectory reception with the help of one stable mode of the vibrations.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.12
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• pp.1176-1182
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• 2010

Vibrations caused by automobile engine are absorbed mostly by a passive-type engine mount. However, user specifications for automobile vibrations require more stringent conditions and higher standard. Hence, active-type engine mount have been developed to cope with such specifications. The active-type engine mount consists of sensor, actuator and controller where a control algorithm is implemented. The performance of the active engine mount depends on the control algorithm if the sensor and actuator satisfies the specification. The control algorithm should be able to suppress persistent vibrations caused by the engine which are related to engine revolution. In this study, three control algorithms are considered for suppressing persistent vibrations, which are the positive position feedback control algorithm, the strain-rate feedback control algorithm, and the modified higher harmonic control algorithm. Experimental results show that all the control algorithms considered in this study are effective in suppressing resonant vibrations but the modified higher harmonic controller is the most effective controller for non-resonant vibrations.

• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.227-236
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• 2005

Multibody system dynamics is based on classical mechanics and its engineering applications originating from mechanisms, gyroscopes, satellites and robots to biomechanics. Multibody system dynamics is characterized by algorithms or formalisms, respectively, ready for computer implementation. As a result simulation and animation are most convenient. Recent developments in multibody dynamics are identified as elastic or flexible systems, respectively, contact and impact problems, and actively controlled systems. Based on the history and recent activities in multibody dynamics, recursive algorithms are introduced and methods for dynamical analysis are presented. Linear and nonlinear engineering systems are analyzed by matrix methods, nonlinear dynamics approaches and simulation techniques. Applications are shown from low frequency vehicles dynamics including comfort and safety requirements to high frequency structural vibrations generating noise and sound, and from controlled limit cycles of mechanisms to periodic nonlinear oscillations of biped walkers. The fields of application are steadily increasing, in particular as multibody dynamics is considered as the basis of mechatronics.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.281-298
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• 2015

In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

• Coupled systems mechanics
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• v.7 no.5
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• pp.635-647
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• 2018

Dynamic problems arising from the Euler-Bernoulli beam model with inhomogeneous elastic properties are considered. The method of Green's function and perturbation theory are employed to find the deflection in the beam correct to the first-order. Eigenvalue problems appearing from transverse vibrations of inhomogeneous beams in linear and nonlinear cases are also discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.989-993
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• 2001

This paper deals with the free vibrations of horizontally curved beams supported by non-homogeneous elastic foundation. Taking into account the effects of rotatory inertia and shear deformation, differential equations governing the free vibrations of such beams are derived, in which the linear elastic foundation is considered as the non-homogeneous foundation. Differential equations are solved numerically to calculate natural frequencies. In numerical examples, the parabolic curved member is considered. The parametric studies are conducted and the lowest four frequency parameters are reported in tables and figures as the non-dimensional forms.

• Advances in nano research
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• v.15 no.3
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• pp.215-224
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• 2023

Nonlinearity plays an important role in control systems and the application of design. For this reason, in addition to linear vibrations, nonlinear vibrations of the stepped nanobeam are also discussed in this manuscript. This study investigated the vibrations of stepped nanobeams according to Eringen's nonlocal elasticity theory. Eringen's nonlocal elasticity theory was used to capture the nanoscale effect. The nanoscale stepped Euler Bernoulli beam is considered. The equations of motion representing the motion of the beam are found by Hamilton's principle. The equations were subjected to nondimensionalization to make them independent of the dimensions and physical structure of the material. The equations of motion were found using the multi-time scale method, which is one of the approximate solution methods, perturbation methods. The first section of the series obtained from the perturbation solution represents a linear problem. The linear problem's natural frequencies are found for the simple-simple boundary condition. The second-order part of the perturbation solution is the nonlinear terms and is used as corrections to the linear problem. The system's amplitude and phase modulation equations are found in the results part of the problem. Nonlinear frequency-amplitude, and external frequency-amplitude relationships are discussed. The location of the step, the radius ratios of the steps, and the changes of the small-scale parameter of the theory were investigated and their effects on nonlinear vibrations under simple-simple boundary conditions were observed by making comparisons. The results are presented via tables and graphs. The current beam model can assist in designing and fabricating integrated such as nano-sensors and nano-actuators.