• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.297-303
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• 2001

This research presents an analytical model to characterize the ball bearing vibration due to the waviness in a rigid rotor supported by multi-row ball bearings considering centrifugal force and gyroscopic moment of ball. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. The waviness of ball and races is modeled by the superposition of sinusoidal function and it is introduced to position vectors of race curvature center to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. The accuracy of this research is validated by comparing with the results of the prior researches. It characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing resulting from the waviness interaction.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.526-529
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• 2004

Arches are one of the most important basic structural units as well as the beams, columns and plates. Most complicated structures consist of only these basic units and therefore it is very attractive research subject to analysis both the static and dynamic behavior of such units including the arches. This study deals with the free vibration of arbitrary shaped arches. In order to obtain the exactly arch shape, which surveyed (x, y) of neutral axis of arbitrary shaped arches are compared to various shape of arch: circular, parabolic, sinusoidal, elliptic, spiral and cartenary. The differential equations governing free vibrations of arches are merely adopted in the open literature rather than deriving the equations in this study. The Taylor series method is used as the numerical differential scheme. The Runge-Kutta method and the Regula-Falsi method, respectively, are used to integrate the governing differential equations and to compute the natural frequencies It is expected that results obtained herein can be practically utilized in the fields of vibration control.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.3
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• pp.101-109
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• 1987

The governing differential equations for the free vibration of general arch are derived including the effect of rotary inertia in addition to the usual actions. These differential equations are applied to the sinusoidal arch and the numerical methods are developed to analyze these equations. A trial eigenvalue method and the Runge-Kutta method are used to determine the natural frequencies and to perform the integration of the differential equations, respectively. A detailed studies are made of the lowest three vibration frequencies for hinged arches with the span length equal to 10 m. The effect of the rotary inertia is analyzed. And as the numerical results the frequency versus the rise of arch and the radius of gyration are presented in figures.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.491-504
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• 2018

Because of sandwich structures with low weight and high stiffness have much usage in various industries such as civil and aerospace engineering, in this article, buckling and free vibration analyses of coupled micro composite sandwich plates are investigated based on sinusoidal shear deformation (SSDT) and most general strain gradient theories (MGSGT). It is assumed that the sandwich structure rested on an orthotropic elastic foundation and make of four composite face sheets with temperature-dependent material properties that they reinforced by carbon and boron nitride nanotubes and two flexible transversely orthotropic cores. Mathematical formulation is presented using Hamilton's principle and governing equations of motions are derived based on energy approach and applying variation method for simply supported edges under electro-magneto-thermo-mechanical, axial buckling and pre-stresses loadings. In order to predict the effects of various parameters such as material length scale parameter, length to width ratio, length to thickness ratio, thickness of face sheets to core thickness ratio, nanotubes volume fraction, pre-stress load and orthotropic elastic medium on the natural frequencies and critical buckling load of double-bonded micro composite sandwich plates. It is found that orthotropic elastic medium has a special role on the system stability and increasing Winkler and Pasternak constants lead to enhance the natural frequency and critical buckling load of micro plates, while decrease natural frequency and critical buckling load with increasing temperature changes. Also, it is showed that pre-stresses due to help the axial buckling load causes that delay the buckling phenomenon. Moreover, it is concluded that the sandwich structures with orthotropic cores have high stiffness, but because they are not economical, thus it is necessary the sandwich plates reinforce by carbon or boron nitride nanotubes specially, because these nanotubes have important thermal and mechanical properties in comparison of the other reinforcement.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.399-407
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• 2002

A three-dimensional method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight line generators or constant thickness. The middle surface of the shell may have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components$U_\Phi, U_z, U_\theta$ in the meridional, normal and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in$\theta$, and algebraic polynomials in the$\Phi$and z directions. Potential(strain) and kinetic energies of the entire body are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degrees of the polynomials are increased, frequencies converge to the exact values. Novel numerical results are presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations. Convergence to four digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.

• Structural Engineering and Mechanics
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• v.81 no.6
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• pp.691-703
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• 2022

To obtain the seismic response of lead-cored rubber, shape memory alloy (SMA)-rubber isolation Plate-shell Integrated Concrete Liquid-Storage Structure (PSICLSS), based on a PSICLSS in a water treatment plant, built a scale experimental model, and a shaking table test was conducted. Discussed the seismic responses of rubber isolation, SMA-rubber isolation PSICLSS. Combined with numerical model analysis, the vibration characteristics of rubber isolation PSICLSS are studied. The results showed that the acceleration, liquid sloshing height, hydrodynamic pressure of rubber and SMA-rubber isolation PSICLSS are amplified when the frequency of seismic excitation is close to the main frequency of the isolation PSICLSS. The earthquake causes a significant leakage of liquid, at the same time, the external liquid sloshing height is significantly higher than internal liquid sloshing height. Numerical analysis showed that the low-frequency acceleration excitation causes a more significant dynamic response of PSICLSS. The sinusoidal excitation with first-order sloshing frequency of internal liquid causes a more significant sloshing height of the internal liquid, but has little effect on the structural principal stresses. The sinusoidal excitation with first-order sloshing frequency of external liquid causes the most enormous structural principal stress, and a more significant external liquid sloshing height. In particular, the principal stress of PSICLSSS with long isolation period will be significantly enlarged. Therefore, the stiffness of the isolation layer should be properly adjusted in the design of rubber and SMA-rubber isolation PSICLSS.

• The Journal of the Acoustical Society of Korea
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• v.18 no.3
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• pp.73-78
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• 1999

The paper describes a theoretical study on the flexural vibration of an elastic flat bar with periodically nonuniform material properties. The approximate solution of the natura1 frequency and mode shape has been obtained using the perturbation technique for sinusoidal modulation of the flexural rigidify and mass density. The numerical solution obtained by using the finite element method verifies the trend of the approximate solution. It appears that distributed vibrations exist in the low modes, and this approach can be extended to the vibration analysis of the p1ate in the flat panel speaker.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.5
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• pp.101-107
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• 2001

This paper deals with the free vibrations of horizontally curved beams with mu1tiple elastic springs. Taking into account the effects of rotatory Inertia and shear deformation. differential equations governing the free vibrations of such beams are derived, In which each e1astic spring is modeled as a discrete Winkler foundation with very short longitudinal length. Differential equations are solved numerically to calculate natural frequencies and mode shapes. In numerical examples, the circular, Parabolic. sinusoidal and elliptic curved beams are considered. The parametric studies are conducted and the lowest four frequency parameters are reported In tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.879-889
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• 2003

This research deals with the nonlinearities of rocking vibration associated with impact and sliding on the rocking behavior of rigid block under two dimensional sinusoidal excitation which has different frequencies in two excitation direction. The varied excitation direction influences not only the rocking response but also the sliding motion and the rocking response shape. Chaotic responses are observed in wider excitation amplitude region, when the frequencies in each excitation direction are different. The complex behavior of chaotic response, in the phase space, is related with the trajectory of base excitation and sliding motion.

• Earthquakes and Structures
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• v.18 no.3
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• pp.313-320
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• 2020

The usage of conventional tuned mass damper (TMD) was proved as an effective method for passive mitigating vortex-induced vibration (VIV) of a bridge deck. Although a variety of linear TMD systems have been so far utilized for vibration control of suspension bridges, a sensitive TMD mechanism to wind spectrum frequency is lacking. Here, we introduce a bistable tuned mass damper (BTMD) mechanism which has an exceptional sensitivity to a broadband input of vortex shedding velocity for suppressing VIV in suspension bridge deck. By use of the Monte Carlo simulation, performance of the nonlinear BTMD is shown to be more efficient than the conventional linear TMD under two different wind load excitations of harmonic (sinusoidal) and broadband input of vortex shedding. Consequently, an appropriate algorithm is proposed to optimize the design parameters of the nonlinear BTMD for Kap Shui Mun Bridge, and then the BTMD system is localized for the interior deck of the suspension bridge.