• Steel and Composite Structures
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• v.39 no.1
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• pp.95-107
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• 2021

In this work, the dynamic response of functionally graded beams on variable elastic foundations is studied using a novel higher-order shear deformation theory (HSDT). Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. The FG beams were assumed to be supported on Winkler-Pasternak type foundations in which the Winkler modulus is supposed to be variable in the length of the beam. The variable rigidity of the elastic foundation is assumed to be linear, parabolic and sinusoidal along the length of the beam. The material properties of the FG porous beam vary according to a power law distribution in terms of the volume fraction of the constituents. The equations of motion are determined using the virtual working principle. For the analytical solution, Navier method is used to solve the governing equations for simply supported porous FG beams. Numerical results of the present theory for the free vibration of FG beams resting on elastic foundations are presented and compared to existing solutions in the literature. A parametric study will be detailed to investigate the effects of several parameters such as gradient index, thickness ratio, porosity factor and foundation parameters on the frequency response of porous FG beams.

• Journal of Korean Association for Spatial Structures
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• v.22 no.2
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• pp.57-64
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• 2022

In this paper, the physical model and governing equations of a shallow arch with a moving boundary were studied. A model with a moving boundary can be easily found in a long span retractable roof, and it corresponds to a problem of a non-cylindrical domain in which the boundary moves with time. In particular, a motion equation of a shallow arch having a moving boundary is expressed in the form of an integral-differential equation. This is expressed by the time-varying integration interval of the integral coefficient term in the arch equation with an un-movable boundary. Also, the change in internal force due to the moving boundary is also considered. Therefore, in this study, the governing equation was derived by transforming the equation of the non-cylindrical domain into the cylindrical domain to solve this problem. A governing equation for vertical vibration was derived from the transformed equation, where a sinusoidal function was used as the orthonormal basis. Terms that consider the effect of the moving boundary over time in the original equation were added in the equation of the transformed cylindrical problem. In addition, a solution was obtained using a numerical analysis technique in a symmetric mode arch system, and the result effectively reflected the effect of the moving boundary.

• Steel and Composite Structures
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• v.46 no.3
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• pp.367-383
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• 2023

In this investigation, an improved integral trigonometric shear deformation theory is employed to examine the vibrational behavior of the functionally graded (FG) sandwich plates resting on visco-Pasternak foundations. The studied structure is modelled with only four unknowns' variables displacements functions. The simplicity of the developed model being in the reduced number of variables which was made with the help of the use of the indeterminate integral in the formulation. The current kinematic takes into consideration the shear deformation effect and does not require any shear correction factors as used in the first shear deformation theory. The equations of motion are determined from Hamilton's principle with including the effect of the reaction of the visco-Pasternak's foundation. A Galerkin technique is proposed to solve the differentials governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for various clamped and simply supported FG sandwich plates resting on visco-Pasternak foundations. The validity of proposed model is checked with others solutions found in the literature. Parametric studies are performed to illustrate the impact of various parameters as plate dimension, layer thickness ratio, inhomogeneity index, damping coefficient, vibrational mode and elastic foundation on the vibrational behavior of the FG sandwich plates.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.1
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• pp.77-85
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• 1988

A stochchastic analysis procedure of generating floor response spectra for proportionally damped linear systems subject to earthquake loading is presented. Theories of random vibration and mode acceleration method are used in the formulation of governing equations. The structure-oscillator interaction is not considered. It is assumed that the input motions and oscillator responses are stationary Gaussian processes with mean zero. The nonstationary characteristics of earthquake motion are incorporated in the peak factor which is based on Vanmarcke's theory. Floor response spectra for both resonance and non-resonance cases are calculated under the assumption that the peak factors for structure and oscillator are equal to that for ground response spectrum. The validity of this method is demonstrated by comparing the results obtained by proposed method with those by time history analyses. The results obtained by this method are conservative and accurate with tolerable precision. This method saves much computing time compared with time history analysis method.

• Journal of Korean Ophthalmic Optics Society
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• v.4 no.2
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• pp.1-16
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• 1999

Differential equations and its numerical solution program using Turbo-C were formulated to describe the radical distribution and average displacement amplitude of vibrating dehydrated contact lens(HEMA) driven by sinusoidal or rectangular pressure. The natural resonant frequency of the lens diaphram(thickness 0.08mm, diameter 14mm, curvature radius 8mm) was measured to be 5730 Hz from the extrapolation of frequency vs addedmass to the diaphram curve. The Young's modulus of the lens was measured to be $4{\times}10^9$ Pa with altering the original shape. The effect of parameters such as thickness, effective radius, damping coeff., amplitude of driving pressure on the vibration characteristics was illustrated by the computer simulation of the derived program. When the frequency of driving pressure coincides with the integral multiple of fundamental resonance frequency of the lens the wave pattern changes from arc to bell-shape along the radial position of the diaphram. If this happens to the contact lens on the cornea in vivo, it might create the feel of pull of the lens due to the increased rise of central part of the lens.

• Wind and Structures
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• v.26 no.5
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• pp.331-341
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• 2018

A numerical study on the flow over a square cylinder in the vicinity of a wall is conducted for different Couette-Poiseuille-based non-uniform flow with the non-dimensional pressure gradient P varying from 0 to 5. The non-dimensional gap ratio L (=$H^{\ast}/a^{\ast}$) is changed from 0.1 to 2, where $H^{\ast}$ is gap height between the cylinder and wall, and $a^{\ast}$ is the cylinder width. The governing equations are solved numerically through finite volume method based on SIMPLE algorithm on a staggered grid system. Both P and L have a substantial influence on the flow structure, time-mean drag coefficient ${\bar{C}}_D$, fluctuating (rms) lift coefficient ($C_L{^{\prime}}$), and Strouhal number St. The changes in P and L leads to four distinct flow regimes (I, II, III and IV). Following the flow structure change, the ${\bar{C}}_D$, $C_L{^{\prime}}$, and St all vary greatly with the change in L and/or P. The ${\bar{C}}_D$ and $C_L{^{\prime}}$ both grow with increasing P and/or L. The St increases with P for a given L, being less sensitive to L for a smaller P (< 2) and more sensitive to L for a larger P (> 2). A strong relationship is observed between the flow regimes and the values of ${\bar{C}}_D$, $C_L{^{\prime}}$ and St. An increase in P affects the pressure distribution more on the top surface than on bottom surface while an increase in L does the opposite.

• Wind and Structures
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• v.6 no.5
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• pp.387-402
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• 2003

In the past decades, much effort has been made towards the study of single-mode-based vibration controls with dynamic energy absorbers such as single or multiple Tuned Mass Dampers(TMDs). With the increase of bridge span length and the tendency of the bridge cross-section being more slender and streamlined, multi-mode coupled vibrations as well as their controls have become very important for large bridges susceptible to strong winds. As a simple but effective device, the TMD system especially the semi-active one has become a promising option for such coupled vibration controls. However, despite various studies of optimal controls of single-mode-based vibrations with TMDs, research on the corresponding controls of the multi-mode coupled vibrations is very rare so far. For the development of a semi-active control strategy to suppress the multi-mode coupled vibrations, a comprehensive parametric analysis on the optimal variables of this control is substantial. In the present study, a multi-mode control strategy named "three-row" TMD system is discussed and the general numerical equations are developed at first. Then a parametric study on the optimal control variables for the "three-row" TMD system is conducted for a prototype Humen Suspension Bridge, through which some useful information and a better understanding of the optimal control variables to suppress the coupled vibrations are obtained. This information lays a foundation for the design of semi-active control.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.4
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• pp.429-435
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• 2012

An abrasion due to continuous friction between a work roll and strip causes the mass of the work roll to be unbalanced in the rolling process. We developed a mathematical model for the rolling mill considering the unbalanced mass and verified the model experimentally. The work roll was approximated as a rigid rotor with eccentricity, and the effect of the unbalanced mass on chatter vibration was investigated. The joint forces computed by quasistatic analysis were applied to the work roll in the rolling mill. Transient responses were obtained, and frequency analysis was performed by solving equations of motion using a direct integration method. Horizontal vibrations were more strongly affected by eccentricity than vertical vibrations. In the horizontal direction, a small eccentricity of 1% of the work roll radius considerably increased the amplitude of the chatter frequency.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.5
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• pp.346-354
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• 2002

The present study is to investigate the propagation characteristics of the impulse waves discharged from the exit of the convergent and divergent pipes. An experiment is carried out using a shock tube with an open end and is compared to the computation of the axisymmetric, compressible, unsteady Euler equations, which are solved by the second-order total variation diminishing (TVD) scheme. For the computational work, several initial compression waves are assumed inside the pipe so that those are the same to the experimental ones of the shock tube. The results show that the peak pressures of the impulse waves discharged from the exit of convergent and divergent pipes decrease with an increase in the wavelength of the initial compression wave. All of the impulse waves have a strong directivity toward the pipe axis, regardless of the exit type of the pipe employed. The impulse waves discharged from the divergent pipe are stronger than those from the straight pipe, while the impulse waves of the convergent pipe are weaker than those from the straight pipe. It is found that the convergent pipe can play a role of a passive control to reduce the peak pressure of the impulse wave. The present computations represent the experimented impulse waves with a good accuracy.

• Earthquakes and Structures
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• v.19 no.4
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• pp.243-259
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• 2020

This study aims to optimize, design, and predict the MTMDs performance in SDOF systems using spectral analysis, and then apply their results to MDOF structures. Given the importance of spectral analysis in the design of new engineering structures, achieving a method for designing TMDs based on this theory can be of great importance for structural designers. In this study, several convenient combinations of MTMDs in an SDOF system are first considered to minimize the maximum displacement. For calculating the frequency ratios of dampers, an innovative technique is adopted in which the values of different modal responses obtained from the spectral analysis are approached together. This procedure is done using a harmony search (HS) algorithm. Also, using the random vibration theory, the damping ratio of the dampers is obtained. Then, an equation is presented for predicting the performance of MTMDs. For evaluating this equation, three structures with different stories are designed. Some of the presented combinations of dampers are added to them. The time history analyses are employed to analyze the structures under 30 different accelerograms. The findings indicated that the proposed equation could efficiently predict the performance of the MTMDs. Furthermore, four different patterns of damper distribution along the height of the structures are defined. The effect of them on the maximum deformation of the structures in time history analyses is discussed, and an equation is presented to estimate this effect. The results indicated that the average and maximum error percentages of the proposed equations are about three and seven percent, respectively, compared to the time history analyses results, which are negligible values.