• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.250-251
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• 2014

This paper investigates the stick-slip phenomena on spinning shaft. The modeling of the shaft is considered only torsional direction with nonlinear friction. The friction is adopted a negative friction-velocity slope. Based on the model, a nonlinear equation of motion is derived and analyze the stick-slip phenomena. In order to analyze the time dependent response, the nonlinear formulations are numerically solved by nonlinear Newmark method. The numerical results reveal the stick-slip phenomena on the spinning shaft system.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.9
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• pp.813-819
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• 2011

This paper predicted nonlinear dynamic responses of a cantilevered carbon nanotube(CNT) resonator incorporating the electrostatic forces and van der Waals interactions between the CNT cantilever and ground plane. The structural model of CNT includes geometric and inertial nonlinearities to investigate various phenomena of nonlinear responses of the CNT due to the electrostatic excitation. In order to solve this problem, we used Galerkin's approximation and the numerical integration techniques. As a result, the CNT nano-resonator shows the softening effect through saddle-node bifurcation near primary resonance frequency with increasing the applied AC and DC voltages. Also we can predict nonlinear secondary resonances such as superharmonic and subharmonic resonances. The superharmonic resonance of the nano-resonator is influenced by applied AC voltage. The period-doubling bifurcation leads to the subharmonic resonance which occurs when the nano-resonator is actuated by electrostatic forces as parametric excitation.

• Journal of KSNVE
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• v.7 no.1
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• pp.55-60
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• 1997

In order to examine the validity of an asymptotic solution obtained from the method of multiple scales, we investigate a third-order subharmonic resonance response of a bar constrained by a nonlinear spring to a harmonic excitation. The motion of the bar is governed by a linear partial differential equation with a nonlinear boundary condition. The nonlinear boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution.

• Advances in nano research
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• v.9 no.4
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• pp.277-294
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• 2020

In current paper, nonlocal (NLT), nonlocal strain gradient (NSGT) and Gurtin-Murdoch surface/interface (GMSIT) theories with classical theory (CT) are utilized to investigate vibration and stability analysis of Double Walled Piezoelectric Nanosensor (DWPENS) based on cylindrical nanoshell. DWPENS simultaneously subjected to direct electrostatic voltage DC and harmonic excitations, structural damping, two piezoelectric layers and also nonlinear van der Waals force. For this purpose, Hamilton's principle, Galerkin technique, complex averaging and with arc-length continuation methods are used to analyze nonlinear behavior of DWPENS. For this work, three nonclassical theories compared with classical theory CT to investigate Dimensionless Natural Frequency (DNF), pull-in voltage, nonlinear frequency response and stability analysis of the DWPENS considering the nonlocal, material length scale, surface/interface (S/I) effects, electrostatic and harmonic excitation.

• Structural Monitoring and Maintenance
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• v.5 no.1
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• pp.15-38
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• 2018

Negative stiffness dampers (NSDs) have been proven an efficient solution to vibration control of stay cables. Although previous studies usually assumed a linear negative stiffness behavior of NSDs, many negative stiffness devices produce negative stiffness with nonlinear behavior. This paper systematically evaluates the impact of nonlinearity in negative stiffness on vibration control performance for stay cables. A linearization method based on energy equivalent principle is proposed, and subsequently, the impact of two types of nonlinear stiffness, namely, displacement hardening and softening stiffness, is evaluated. Through the Hilbert transform (HT) of free vibration responses, the effects of nonlinear stiffness of an NSD on the modal frequencies, damping ratios and frequency response functions of a stay cable is also investigated. The HT analysis results validate the accuracy of the linearization method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.11
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• pp.1743-1750
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• 2001

This paper presents an analysis of nonlinear response of the seismically isolated structure against earthquake excitation to evaluate isolation performances of a rubber bearing. In the analysis of the vibration of building, the building is modeled by lumped mass system where the restoring force is considered as linear, bilinear and trilinear. Fundamental equations of motion are derived for the base isolated structure, and hysteretic and nonlinear-elastic characteristics are considered for a numerical calculation. The excitation levels are magnified fur the recorded strong earthquake motions in order to examine dynamic stability of the structure. Seismic responses (of the building are compared fur the each restoring force type. As a result, it is shown that the effect of the motion by the nonlinear response of the building is comparatively not so large from a seismic design standpoint. The responses of the isolated structures reduce sufficiently and controled the motion of the building well in a practical range. By increasing the acceleration of the earthquake, the yielding of the farce was occurred in the concrete and steel frame, which shows the necessity of the exact nonlinear dynamic analysis.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.623-637
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• 2019

This paper analyzes the non-stationary vibration and super-harmonic resonances in nonlinear dynamic motion of viscoelastic nano-resonators. For this purpose, a new coupled size-dependent model is developed for a plate-shape nano-resonator made of nonlinear viscoelastic material based on modified coupled stress theory. The virtual work induced by viscous forces obtained in the framework of the Leaderman integral for the size-independent and size-dependent stress tensors. With incorporating the size-dependent potential energy, kinetic energy, and an external excitation force work based on Hamilton's principle, the viscous work equation is balanced. The resulting size-dependent viscoelastically coupled equations are solved using the expansion theory, Galerkin method and the fourth-order Runge-Kutta technique. The Hilbert-Huang transform is performed to examine the effects of the viscoelastic parameter and initial excitation values on the nanosystem free vibration. Furthermore, the secondary resonance due to the super-harmonic motions are examined in the form of frequency response, force response, Poincare map, phase portrait and fast Fourier transforms. The results show that the vibration of viscoelastic nanosystem is non-stationary at higher excitation values unlike the elastic ones. In addition, ignoring the small-size effects shifts the secondary resonance, significantly.

• Journal of the Korean Society of Safety
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• v.14 no.4
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• pp.3-12
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• 1999

This research concentrates on the influence of non-linearities associated with impact for the nonlinear rocking behavior of rigid block subjected to one dimensional sinusoidal excitation of horizontal direction. The transition of two governing rocking equations, the abrupt reduction in the kinetic energy associated with impact, and sliding motion of block. In this study, two type of rocking vibration system are considered. One is the undamped rocking vibration system, disregarding energy dissipation at impact and the other is the damped rocking system, including energy dissipation and sliding motion. The response analysis using non-dimensional rocking equation is carried out for the change of excitation parameters and friction coefficient. The chaos responses were discovered in the wide response region, particularly, for the case of high excitation amplitude and their chaos characteristics were examined by the time history, Poincare map, power spectra and Lyapunov Exponent of rocking responses. The complex behavior of chaos response, in the phase space, were illustrated by Poincare map. The bifurcation diagram and Poincare map were shown to be effective in order to understand chaos of rocking system.

• Wind and Structures
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• v.9 no.5
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• pp.397-412
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• 2006

This paper presents the wind excited acceleration responses of a 50 m guyed mast under the action of Typhoon Dujuan. The response of the structure is reconstructed from using a full finite element model and an equivalent beam-column model. The wind load is modelled based on the measured wind speed and recommendations for high-rise structures. The nonlinear time response analysis is conducted using the Newton Raphson iteration procedure. Comparative studies on the measured and computed frequencies and acceleration responses show that the torsional vibration of the structure is significant particularly in the higher vibration modes after the first few bending modes. The equivalent model, in general, gives less accurate amplitude predictions than the full model because of the omission of torsional stiffness of the mast in the vibration analysis, but the root-mean-square value is close to the measured value in general with an error of less than 10%.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.62-65
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• 2006

In this paper, nonlinear nonplanar vibration of a flexible rectangular cantilever beam is analyzed when one-to-one resonance occurs to the beam. The planar and nonplanar motions of the beam are analyzed in time and frequency domains. In frequency domain, FFT analyzer is used to perform autospectrum and cepstrum analyses for nonlinear response of the beam. In time domain, an oscilloscope is used to investigate the phase difference between the planar and nonplanar motions and to perform Torus analysis in the phase space. Through those analyzing process, the main frequencies of superharmonic, subharmonic, and super-subharmonic motions are investigated in the nonplanar motion due to one-to-one resonance. Analyzing the phase difference between the planar and nonplanar motions, it is observed that the phase difference varies in time.