• Structural Engineering and Mechanics
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• v.88 no.2
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• pp.159-168
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• 2023

Cost-effective high precision hybrid elements are presented in a hierarchical form for dynamic analysis of plates. The costs associated with controlling the vibrations of ferromagnetic plates can be minimized by adequate determination of the amount of electric current and magnetic field. In the present study, the effect of magnetic field and electric current on nonlinear vibrations of ferromagnetic plates is investigated. The general form of Lorentz forces and Maxwell's equations have been considered for the first time to present new relationships for electromagnetic interaction forces with ferromagnetic plates. In order to derive the governing nonlinear differential equations, the theory of third-order shear deformations of three-dimensional plates has been applied along with the von Kármán large deformation strain-displacement relations. Afterward, the nonlinear equations are discretized using the Galerkin method, and the effect of various parameters is investigated. According to the results, electric current and magnetic field have different effects on the equivalent stiffness of ferromagnetic plates. As the electric current increases and the magnetic field decreases, the equivalent stiffness of the plate decreases. This is a phenomenon reported here for the first time. Furthermore, the magnetic field has a more significant effect on the steady-state deflection of the plate compared to the electric current. Increasing the magnetic field and electric current by 10-times results in a reduction of about 350% and an increase of 3.8% in the maximum steady-state deflection, respectively. Furthermore, the nonlinear frequency decreases as time passes, and these changes become more intense as the magnetic field increases.

• Advances in nano research
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• v.9 no.1
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• pp.47-58
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• 2020

The present paper deals with analyzing nonlinear forced vibrational behaviors of nonlocal multi-phase piezo-magnetic beam rested on elastic substrate and subjected to an excitation of elliptic type. The applied elliptic force may be presented as a Fourier series expansion of Jacobi elliptic functions. The considered multi-phase smart material is based on a composition of piezoelectric and magnetic constituents with desirable percentages. Additionally, the equilibrium equations of nanobeam with piezo-magnetic properties are derived utilizing Hamilton's principle and von-Kármán geometric nonlinearity. Then, an exact solution based on Jacobi elliptic functions has been provided to obtain nonlinear vibrational frequencies. It is found that nonlinear vibrational behaviors of the nanobeam are dependent on the magnitudes of induced electrical voltages, magnetic field intensity, elliptic modulus, force magnitude and elastic substrate parameters.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.392-398
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• 1998

In order to check the validity of nonlinear normal modes of continuous, systems by means of the energy-based formulation, we consider a beam with a nonlinear boundary condition. The initial and boundary e c6nsl of a linear partial differential equation and a nonlinear boundary condition is reduced to a linear boundary value problem consisting of an 8th order ordinary differential equations and linear boundary conditions. After obtaining the asymptotic solution corresponding to each normal mode, we compare this with numerical results by the finite element method.

• 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)

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.57-58
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• 2011

• Wind and Structures
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• v.23 no.3
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• pp.253-273
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• 2016

Ice accretions on stay cables may result in the instable vibration of galloping, which would affect the safety of cable-stayed bridges. A large number of studies have investigated the galloping vibrations of transmission lines. However, the obtained aerodynamics in transmission lines cannot be directly applied to the stay cables on cable-stayed bridges. In this study, linear and nonlinear single degree-of-freedom models were introduced to obtain the critical galloping wind velocity of iced stay cables where the aerodynamic lift and drag coefficients were identified in the wind tunnel tests. Specifically, six ice shapes were discussed using section models with geometric scale 1:1. The results presented obvious sudden decrease regions of the aerodynamic lift coefficient for all six test models. Numerical analyses of iced stay cables associated to a medium-span cable-stayed bridge were carried out to evaluate the potential galloping instability. The obtained nonlinear critical wind velocity for a 243-meter-long stay cable is much lower than the design wind velocity. The calculated linear critical wind velocity is even lower. In addition, numerical analyses demonstrated that increasing structural damping could effectively mitigate the galloping vibrations of iced stay cables.

• Wind and Structures
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• v.36 no.3
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• pp.215-220
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• 2023

We study the progressive full-scale wind tunnel tests on a high solidity vertical axis wind turbine (VAWT) for various tip speeds and pitch angles to understand the VAWT shaft system's dynamics using 0-1 Test for chaos. We identify that while varying rotor speed (tip speed) of the turbine, the system's dynamics change from periodic to chaotic through quasiperiodic and strange non-chaotic (SNA) states. The present study is the first experimental evidence for the existence of these states in the VAWT shaft system to the best of our knowledge. Using the asymptotic growth value Kc in 0-1 test, when the turbine operates at the low tip speeds and high pitch angles for low incoming wind speeds, the system behaves periodic (Kc ≈ 0). However, when the incoming wind speed increases further the system's dynamics shift from periodic to chaotic vibrations through quasi-periodic and SNA. This phenomenon is due to the dynamic stalling of blades which induces chaotic vibration in the VAWT shaft system. Further, the singular continuous spectrum method validates the presence of SNA and differentiates the SNA from chaotic vibrations.

• Advances in nano research
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• v.6 no.4
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• pp.323-337
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• 2018

The nonlinear free vibration of a nanorod subjected to finite strain is investigated. The governing equation of motion in material configuration in terms of displacement is determined. By means of Galerkin method, the Fourier series solutions satisfying some typical boundary conditions are determined. The amplitude-frequency relationship and interaction between the modes are studied. The effects of nonlocal elasticity are shown for different length of nanotubes and nonlocal parameter. The results show that nonlocal effects lead to additional internal modal interaction for nanorod vibrations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.295-301
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• 2001

An investigation into asymmetric vibrations of a clamped circular plate under a hannonic excitation is made. We examine a primary resonance, in which the frequency of excitation is near the natural frequency of an asymmetric mode of the plate. We found not only a response having the form of standing wave but also one having the form of traveling wave, which was not observed by Sridhar, Mook and Nayfeh(1978; Journal of Sound and Vibration 59(2), pp. 159-170).

• Steel and Composite Structures
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• v.35 no.6
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• pp.765-777
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• 2020

In the context of classic conical shell formulation, nonlinear forced vibration analysis of truncated conical shells and annular plates made of multi-scale epoxy/CNT/fiberglass composites has been presented. The composite material is reinforced by carbon nanotube (CNT) and also fiberglass for which the material properties are defined according to a 3D Mori-Tanaka micromechanical scheme. By utilizing the Jacobi elliptic functions, the frequency-deflection curves of truncated conical shells and annular plates related to their forced vibrations have been derived. The main focus is to study the influences of CNT amount, fiberglass volume, open angle, fiber angle, truncated distance and force magnitude on forced vibrational behaviors of multi-scale truncated conical shells and annular plates.