• Steel and Composite Structures
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• v.21 no.2
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• pp.395-409
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• 2016

Nonlinear vibration characteristics of composite laminated trapezoidal plates are studied. The geometric nonlinearity of the plate based on the von Karman's large deformation theory is considered, and the finite element method (FEM) is proposed for the present nonlinear modeling. Hamilton's principle is used to establish the equation of motion of every element, and through assembling entire elements of the trapezoidal plate, the equation of motion of the composite laminated trapezoidal plate is established. The nonlinear static property and nonlinear vibration frequency ratios of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results published in the open literatures. Moreover, the effects of the ply angle and the length-high ratio on the nonlinear vibration frequency ratios of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are analyzed for the different ply angles and harmonic excitation forces.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.8 s.113
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• pp.814-821
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• 2006

A structural coupling method is developed for the dynamic analysis of a nonlinear structure with concentrated nonlinear hinge joints or sliding lines. The component mode synthesis method is extended to couple substructures and the nonlinear models. In order to verify the improved coupling method, a numerical plate model consisting of two substructures and torsional springs, is synthesized by using the proposed method and its modal parameters are compare with analysis data. Then the coupling method is applied to a three-substructure-model with the nonlinearity of sliding lines between the substructures. The coupled structural model is verified from its dynamic analysis. The analysis results show that the improved coupling method is adequate for the structural nonlinear analyses with the nonlinear hinge and sliding mode condition.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.311.2-311
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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 driving system due to misalignment are investigated in this work. Transmission error for helical gear and bearing nonlinear stiffness is calculated. (omitted)

• Steel and Composite Structures
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• v.48 no.3
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• pp.293-303
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• 2023

In this paper, geometrically nonlinear free vibration analysis of Mindlin viscoelastic plates with various geometrical and material properties is studied based on the Von-Karman assumptions. A novel solution is proposed in which the nonlinear frequencies of time-dependent plates are predicted according to the nonlinear frequencies of plates not dependent on time. This method greatly reduces the cost of calculations. The viscoelastic properties obey the Boltzmann integral law with constant bulk modulus. The SHPC meshfree method is employed for spatial discretization. The Laplace transformation is used to convert equations from the time domain to the Laplace domain and vice versa. Solving the nonlinear complex eigenvalue problem in the Laplace-Carson domain numerically, the nonlinear frequencies, the nonlinear viscous damping frequencies, and the nonlinear damping ratios are verified and calculated for rectangular, skew, trapezoidal and circular plates with different boundary conditions and different material properties.

• Smart Structures and Systems
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• v.18 no.5
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• pp.1029-1062
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• 2016

In this research, the nonlinear free vibration analysis of boron-nitride micro ribbon (BNMR) on the Pasternak elastic foundation under electrical, mechanical and thermal loadings using modified strain gradient theory (MSGT) is studied. Employing the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear geometry theory, the nonlinear equations of motion for the graphene micro ribbon (GMR) using Euler-Bernoulli beam model with considering attached mass and size effects based on Hamilton's principle is obtained. These equations are converted into the nonlinear ordinary differential equations by elimination of the time variable using Kantorovich time-averaging method. To determine nonlinear frequency of GMR under various boundary conditions, and considering mass effect, differential quadrature element method (DQEM) is used. Based on modified strain MSGT, the results of the current model are compared with the obtained results by classical and modified couple stress theories (CT and MCST). Furthermore, the effect of various parameters such as material length scale parameter, attached mass, temperature change, piezoelectric coefficient, two parameters of elastic foundations on the natural frequencies of BNMR is investigated. The results show that for all boundary conditions, by increasing the mass intensity in a fixed position, the linear and nonlinear natural frequency of the GMR reduces. In addition, with increasing of material length scale parameter, the frequency ratio decreases. This results can be used to design and control nano/micro devices and nano electronics to avoid resonance phenomenon.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.4
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• pp.87-93
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• 2002

In this study, basic concepts of magnet were introduced, and dynamic characteristics of magnet coupling were explored. Based on these characteristics, it was proposed how to analyze transverse and torsional vibrations of a spindle system with magnet coupling. Proposed theoretical approaches were applied to a precision power transmission system machined for this study, and the transverse and torsional vibrations were simulated. The force on magnet coupling was shown as a form of nonlinear function of the gap and the eccentricity. Also, the form of torque transmitted by magnet coupling was considered as a sinusoidal function. Main spindle connected to a coupling of a follower part was assumed to be a rigid body. Nonlinear partial differential equation was derived to be as a function of angular displacement. By using the equation, torsional vibration analysis of a spindle system with magnet coupling was performed. Free and forced vibration analyses of a spindle system with magnetic coupling were explored by using FEM.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.8
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• pp.747-756
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• 2007

The hydropneumatic suspension units, which have applied to the tracked vehicles, have the spring and damping function in the unit. The nonlinear characteristics such as roadwheel rotation effects, gas behavior changes, hydraulic damping characteristics, hysterisis, and frictional forces have been ignored or simplified to analyze the mathematical models in many areas. This study describes the dynamic characteristics and the nonlinear behaviors of hydropneumatic suspension unit considering the nonlinear effects such as the nonlinear spring and nonlinear damping through the simulation and the experiment. The utility of nonlinear analysis through the higher-order spectral analysis is also presented.

• The KSFM Journal of Fluid Machinery
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• v.13 no.5
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• pp.35-42
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• 2010

This paper deals with the development of analytical model of a turbocharger and its detail rotordynamic analysis. Two analytical models, which are verified by experimental modal testing, are proposed and the analytical model including rotor shaft extended to compressor and turbine wheel end side is chosen. A rotordynamic analysis includes the critical map, Campbell diagram, stability, and unbalance response, especially nonlinear transient response considering nonlinear fluid film force at bearings. Although the linearized analysis accurately predicts the critical speeds, stability limit, and stability threshold speed, the predicted vibration results are not valid for speeds above the stability threshold speed since the rotor vibrates with a subsynchronous component much larger than the one synchronous with rotor speed. Hence, for operating speed above the stability threshold, a nonlinear transient analysis considering nonlinear fluid film force must be performed in order to accurately predict vibration responses of rotor and guarantee results of analysis.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.746-757
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• 2021

To investigate the mechanism of friction-induced vibration and noise of ship water lubricated stern bearings, a two-degree-of-freedom (2-DOF) nonlinear self-excited vibration model is established. The novelty of this work lies in the detailed analysis of influence of different parameters on the stability and nonlinear vibration characteristics of the system, which provides a theoretical basis for the various friction vibration and noise phenomenon and has a very important directive meaning for low noise design of water lubricated stern bearings. The results reveal that the change of any parameter, such as rotating speed of shaft, contact pressure, friction coefficient, system damping and stiffness, has an important influence on the stability and nonlinear response of the system. The vibration amplitudes of the system increase as (a) rotating speed of shaft, contact pressure, and the ratio of static friction coefficient to dynamic friction coefficient increase and (b) the transmission damping between motor and shaft decreases. The frequency spectrum of the system is modulated by the first mode natural frequency, which is continuous multi-harmonics of the first mode natural frequency. The response of the system presents a quasi-periodic motion.

• 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.