• Structural Engineering and Mechanics
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• v.71 no.5
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• pp.485-502
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• 2019

In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton's principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.69-78
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• 1997

Main sources of the vibration in gear driving system are transmission error and backlash. Transmission error is the difference of the rotation between driving and driven gear due to tooth deformation and profile error. Vibro-impacts induced by backlash between meshing gears lead to excessive vibration and noise in many geared rotation systems. Nonlinear dynamic characteristics of the gear driving system due to transmi- ssion error and backlash are investigated. Transmission error is calculated for spur gear. Nonlinear equation of motion for the gear driving system is developed with the calculated transmission error and backlash. Numerical analysis of the equation and the experimental results show the existence of meshing frequency, superharmonic compon- ents. Instability of the gear driving motion is found on the basis of Mathieu equation. Rattle vibration due to backlash is also discussed on the basis if nonlinear jump phenomenon.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.431-454
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• 2016

In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton's principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.10a
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• pp.113-118
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• 2009

A designer regards the vibration system as a linear system. However, in real world, nonlinearity of a vibration system should exist caused by various factors like manufacturing conditions or uncertain material properties. So, properties of a spring and a damper which are consisting the vibration system have statistical distribution. Therefore, a designer needs to analyze the statistical nonlinearity in a vibration system. In this paper, $1^{st}$ Taylor series expansion method and univariate dimension reduction method apply to a performance measure of nonlinear vibration system, and compare each result. And then, merits and demerits of each method are discussed. For apply more actual problem, a performance measure population is estimated based on design variable samples like properties of spring or damper.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.31-36
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• 2002

Even through the problem of misalignment is of great importance, not much work has been reported in the literature on the effect of misalignment on the vibrations of the gear-bearing systems. Therefore, the nonlinear dynamic characteristics of the gear drive system due to misalignment are investigated in this work. Transmission error for helical gear and bearing nonlinear stiffness is calculated. The equation of motion of the gear drive system is modelled using the time-varying gear meshing stiffness, bearing nonlinear stiffness, and bearing pre-load due to the housing deformation. Numerical analysis lot the gear drive system show the result of misalignment effect - sub-harmonic component, bearing pre-load effect, and another nonlinear phenomenon. And the numerical analysis are verified by the experimental result.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.05a
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• pp.417-418
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• 2012

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.9
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• pp.731-737
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• 2002

Nonlinear vibration of the CRT shadow mask with impact damping wires is analyzed in consideration of the mask tension distribution and the effect of wire impact damping. A reduced order FEM model of the shadow mask is obtained from dynamic condensation of the mass and stiffness matrices, and damping wire is modeled using the lumped parameter method to effectively describe its contact interactions with the shadow mask. 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. The analysis model of the shadow mask with damping wires is experimentally verified through impact tests of shadow masks performed in a vacuum chamber.

• 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.

• Geomechanics and Engineering
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• v.36 no.2
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• pp.99-109
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• 2024

Studying the dynamic behavior of axially moving cylindrical shells in hygro-thermal environments has important theoretical and engineering value for aircraft design. Therefore, in this paper, considering hygro-thermal effect, the nonlinear forced vibration of an axially moving cylindrical shell made of functionally graded materials (FGM) is studied. It is assumed that the material properties vary continuously along the thickness and contain pores. The Donnell thin shell theory is used to derive the motion equations of FGM cylindrical shells with hygro-thermal loads. Under the four sides clamped (CCCC) boundary conditions, the Gallekin method and multi-scale method are used for nonlinear analysis. The effects of power law index, porosity coefficient, temperature rise, moisture concentration, axial velocity, prestress, damping and external excitation amplitude on nonlinear forced vibration are explored through parametric research. It can be found that, the changes in temperature and humidity have a significant effect. Increasing in temperature and humidity will cause the resonance position to shift to the left and increase the resonance amplitude.