• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.731-738
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• 2001

The conventional techniques for the prediction of natural frequency are often used to estimate the floor vibration. However. the predicted frequency differs significantly from the measured one since the predicted equation is not able to proper1y treat various material type. Transformation of slab section is necessary to predict natural frequency of composite deck plate, and this effort is complicated due to the various shape of each deck plate. In this study, a new simplified methodology to transform slab section is proposed, which treats effective depth as the distance from the top of a concrete topping to neutral axis of each deck plate. Finally proposed equation with fairly reasonable result compared to the measured values is obtained. based on the modification of vibration equation from LRFD theory. This efforts enhance errors in predicting frequency up to 15％.

• 한국안전학회지
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• 제4권1호
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• pp.47-58
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• 1989

This paper treats the vibration analysis of a simply supported rectangular plate stiffened with viscoelastic beams. The effect of viscoelastic beams on the vibration of the plate is analyzed by using Dirac delta function and the equation of motion can be expressed only one equation. The frequency equation is obtained by applying Laplace transformation. The effect of volumes, numben and aspect ratios of beam on the frequency of the plate is analyzed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 추계학술대회논문집; 한국과학기술회관, 8 Nov. 1996
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• pp.288-294
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• 1996

In this paper, Chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which have the parametric and external excitation. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Poincare maps numerically demonstrate theoretical results and show transverse homoclinic orbit of the chaotic motion.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.911-914
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• 2005

The vibrational characteristics of the piezoelectric disc for a torsional vibration transducer is theoretically studied in this paper. The characteristic equation of the piezoelectric annular disc has been derived from Newton's End law and Gibb's free energy equations. With an anisotropic material property of the disc, the characteristic equation has yielded resonance frequencies. Numerically-calculated results were compared with the values obtained by finite element analysis and experiments

• 한국소음진동공학회논문집
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• 제21권1호
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• pp.9-17
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• 2011

In this paper, the general equation of motion of damped sandwich beam with multi-viscoelastic material layer was derived based on the equation presented by Mead and Markus. The viscoelastic layer, which has characteristics of complex shear modulus, was assumed to be dominantly under shear deformation. The equation of motion of n-layered damped sandwich beam in bending could be represented by (n+3)th order ordinary differential equation. Finite element model for the n-layered damped sandwich beam was formulated and programmed using higher order shape functions. Several numerical examples were implemented to show the effects of damped material.

• Steel and Composite Structures
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• 제26권5호
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• pp.649-662
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• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

• Structural Engineering and Mechanics
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• 제8권3호
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• pp.243-256
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• 1999

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 추계학술대회논문집
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• pp.802-808
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• 2000

This paper characterizes the electromechanical parameters due to the fault of rotor bars in a squirrel cage induction motor. Simulation is performed to investigate how broken rotor bars have effect on them by solving the time-stepping finite element equation coupled with magnetic field equation, circuit equation and mechanical equation of motion. It shows that the asymmetry of magnetic flux due to the broken rotor bar introduces the beating phenomenon in time domain and the sideband frequencies in frequency spectra, respectively, to the stator current, torque, speed, magnetic force and vibration of a rotor. However, vibration of a rotor would be the most effective monitoring parameters to detect the faults of rotor bars.

• Structural Engineering and Mechanics
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• 제24권5호
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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.

• 한국소음진동공학회논문집
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• 제12권5호
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• pp.330-337
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• 2002

A frequency equation of beam subjected to the axial load and having ηthrough-the-width-splits is developed. The beam comprises of beam elements that are split into the upper and the lower part, and non-split beam elements. Equations of motion of each beam element are non-dimensionalized with respect to length. The frequency equation of beam is derived from that of each beam element, which satisfies the displacement of the longitudinal and transverse vibration and the boundary conditions between the beam elements. Numerical simulation and experimental work for the beam having several split beam elements are carried out to demonstrate the analytical development and its validity. The experimental results are in good agreement with those of the present frequency equation. The relationships between the split beam width and natural frequencies, and also the relationships between number of split and natural frequencies, in case that the total beam split length is same. are discussed.