• Journal of the Society of Naval Architects of Korea
• /
• v.50 no.4
• /
• pp.224-231
• /
• 2013

The concept of the natural frequency is useful for understanding the characters of oscillating systems. However, when a circular cylinder floating horizontally on the water surface is heaving, due to the hydrodynamic forces, the system is not governed by the equation like that of the harmonic one. In this paper, in order to shed some lights on the more correct use of the concept of the natural frequency, a problem of the heaving circular cylinder is analyzed in the time domain. The equation of motion, an integro-differential equation, was derived following the fashion of Cummins (1962), and its coefficients including the retardation function were obtained using the numerical solution of Lee (2012). The equation was solved numerically, and the experiment was also carried out in the CNU flume. Using our numerical and experimental results, the natural frequency was defined as its average value given by the motion data excluding those of the initial stage. Our results were then compared with those of the existing investigations such as Maskell and Ursell (1970), Ito (1977) and Yeung (1982) as well as the newly obtained results of Lee (2012). Comparison showed that the natural frequency obtained here agrees well with that of Lee (2012), which was found through the frequency domain analysis. It was also shown that the approximation of heaving motion by a damped harmonic oscillation, which was regarded as suitable by most previous investigators, is not physically suitable for the reason that can be clearly shown through comparing the shape of MCFRs(Modulus of Complex Frequency Response). Furthermore, we found that although the previous approximations yield the damping ratio significantly different from our result the magnitude of natural frequency is not much different from our result.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2008.04a
• /
• pp.50-53
• /
• 2008

The differential equations governing free vibrations of the elastic arches with rectangular hollow section are derived in polar coordinates, in which the effect of rotatory inertia is included. Natural frequencies is computed numerically for circular arches with both clamped ends and both hinged ends. The lowest four natural frequency parameters are reported, with the rotatory inertia, as functions of three non-dimensional system parameters: the breadth ratio, the thickness ratio and the shape ratio.

• Computers and Concrete
• /
• v.32 no.3
• /
• pp.303-311
• /
• 2023

An analysis of the Poisson's ratios influence of single walled carbon nanotubes (SWCNTs) based on Sander's shell theory is carried out. The effect of Poisson's ratio, boundary conditions and different armchairs SWCNTs is discussed and studied. The Galerkin's method is applied to get the eigen values in matrix form. The obtained results shows that, the decrease in ratios of Poisson, the frequency increases. Poisson's ratio directly measures the deformation in the material. A high Poisson's ratio denotes that the material exhibits large elastic deformation. Due to these deformation frequencies of carbon nanotubes increases. The frequency value increases with the increase of indices of single walled carbon nanotubes. The prescribe boundary conditions used are simply supported and clamped simply supported. The Timoshenko beam model is used to compare the results. The present method should serve as bench mark results for agreeing the results of other models, with slightly different value of the natural frequencies.

• Computers and Concrete
• /
• v.26 no.1
• /
• pp.31-52
• /
• 2020

This paper investigates the size dependent effect on the vibration analysis of a porous nanocomposite viscoelastic plate reinforced by functionally graded-single walled carbon nanotubes (FG-SWCNTs) by considering nonlocal strain gradient theory. Therefore, using energy method and Hamilton's principle, the equations of motion are derived. In this article, the effects of nonlocal parameter, aspect ratio, strain gradient parameter, volume fraction of carbon nanotubes (CNTs), damping coefficient, porosity coefficient, and temperature change on the natural frequency are perused. The innovation of this paper is to compare the effectiveness of each mentioned parameters individually on the free vibrations of this plate and to represent the appropriate value for each parameter to achieve an ideal nanocomposite plate that minimizes vibration. The results are verified with those referenced in the paper. The results illustrate that the effect of damping coefficient on the increase of natural frequency is significantly higher than the other parameters effect, and the effects of the strain gradient parameter and nonlocal parameter on the natural frequency increase are less than damping coefficient effect, respectively. Furthermore, the results indicate that the natural frequency decreases with a rise in the nonlocal parameter, aspect ratio and temperature change. Also, the natural frequency increases with a rise in the strain gradient parameter and CNTs volume fraction. This study can be used for optimizing the industrial and medical designs, such as automotive industry, aerospace engineering and water purification system, by considering ideal properties for the nanocomposite plate.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.18 no.2
• /
• pp.215-223
• /
• 2008

The differential equations governing free vibrations of the elastic arches with hollow section are derived in polar coordinates, in which the effect of rotatory inertia is included. Natural frequencies is computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and reference are made to validate theories and numerical methods developed herein. The lowest four natural frequency parameters are reported, with the rotatory inertia, as functions of three non-dimensional system parameters: the breadth ratio, the thickness ratio and the rise to span length ratio.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2007.11a
• /
• pp.121-125
• /
• 2007

LCVA has an advantage that its natural frequency can be easily controlled by changing the area ratio of the vertical column and horizontal part. The previous studies investigated the dynamic characteristics of the LCVA under harmonic load. This study experimentally obtained the first and second mode natural frequencies of the LCVA from shaking table tests using white noise and compared the values with the ones by previous study. Test results show that the measured first mode natural frequency of the LCVA is larger than the calculated one when the area ratio is larger than 1. The second mode frequency increases with the increasing area ratio, which is due to the sloshing motion effect resulting from the large area of the vertical column.

• Journal of the Korean Society for Railway
• /
• v.16 no.1
• /
• pp.1-6
• /
• 2013

In this study, the natural frequency and damping ratio of a four-harness satin woven glass/epoxy composite material are evaluated by means of modal tests and a finite element analysis. To achieve this goal, glass/epoxy beam specimens with different lengths and thicknesses were manufactured via autoclave curing. In the test, the maximum damping ratio was found to occur at the lowest test frequency. As the test frequency increased, the damping ratio decreased exponentially to a critical value. After that value, the damping ratio increased gradually to the maximum test frequency.

• Advances in nano research
• /
• v.13 no.3
• /
• pp.207-216
• /
• 2022

In this paper, a novel model is developed for frequency behavior of single walled carbon nanotubes. The governing equation of motion is constructed method based on the Sander theory using Rayleigh-Ritz's method The frequencies enhances on increasing the power law index using simply supported, clamped and clamped free end conditions. The frequency curve for C-F is less than other conditions. It is due to the physical constraints which are applied on the edge of the CNT. It is observed that the C-F boundary condition have less frequencies from the other two conditions. The frequency phenomena for zigzag are insignificant throughout the aspect ratio. Moreover when index of power law is increased then frequencies increases for all boundary conditions. The natural frequency mechanism for the armchair (10, 10) for various values of power law index with different boundary conditions is investigated. Here frequencies decrease on increases the aspect ratio for all boundary conditions. The frequency curves of SS-SS edge condition is composed between the C-C and C-F conditions. The curves of frequency are less significant from small aspect ratio (L/d = 4.86 ~ 8.47) and decreases fast for greater ratios. It is found that the frequencies via aspect ratios, armchair (10, 10) have higher values from zigzag (10, 0). It is due to the material structure which is made by the carbon nanotubes. The power law index have momentous effect on the vibration of single walled carbon nanotubes. The present frequency result is also compared numerically experimentally with Raman Spectroscopy.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.11 no.3
• /
• pp.473-478
• /
• 1987

In this paper the optimum values of natural frequency ratio and damping ratio for damped systems were studied by numerical analysis. The relation between the amplitude ratio and frequency ratio obtained for the non-linear dynamic vibration absorber was found and it was compared with that of linear system. The results shows that the optimum frequency ratio decreases and the optimum damping ratio increases when the mass ratio of the damped system increases. The resonance frequency ratio and amplitude ratio decrease as mass ratio increases for the non-linear spring system.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.4 no.4
• /
• pp.219-223
• /
• 2000

The evaluation of habitability to building vibration is conducted by the values of natural frequency, amplitude displacement, damping ratio. These values can be obtained from test or analytical results. Data acquisition through test may be possible in existing building, however, to estimate the serviceability of the building, it is necessary to evaluate those values at the stage of design. The natural frequency is important and basic factor for the evaluation of the serviceability. Calculation method of the effective stiffness in RC slab is proposed. To prove the efficiency of the proposed method, sample results of the analysis and the test are compared. These results proved that the effective width proposed to calculate the effective stiffness is proper to evaluate the natural frequency.