• 한국소음진동공학회논문집
• /
• 제13권1호
• /
• pp.26-32
• /
• 2003

The vibrational system of this study is consisted of a rotating cantilever pipe and the flow in the pipe. The equation of motion is derived by using Lagrange equation. The influences of the rotating angular velocity and the velocities of fluid flow in the pipe have been studied on the dynamic characteristics of a rotating cantilever pipe by numerical method. The tip-amplitude of axial vibration and maximum tip-deflection of axial direction of cantilever pipe are directly proportional to the velocity of fluid and rotating angular velocity of pipe In the steady state. respectively The bending tip-amplitude of cantilever pipe is inversely proportional to the velocity of fluid in the steady state. When the rotating angular velocity is 5 rad/s, the velocity of fluid increase with increasing the natural frequency of axial vibration at second mode and third mode, but the natural frequency axial direction of first mode is decreased. The natural frequency of lateral direction is decreased due to increase of the rotating angular velocity. It identifies that the Influence of velocity of fluid give much variation lower mode of vibration in lateral direction. And the Influence of velocity of fluid give much variation higher mode of vibration in axial direction.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2012년도 추계학술대회 논문집
• /
• pp.792-798
• /
• 2012

This study shows the vibration characteristics of an actuator with six wire-suspensions, used in optical pickups of optical disc drives (ODDs). In this paper, the vibration characteristics of this beam structure is induced mathematically. To obtain vibration modes of focusing direction, the vibration analysis is achieved in lateral and longitudinal directions of the structure. The accuracy of induced vibration characteristics is proved by comparing mode frequencies with a finite element analysis. Finally, it is shown that mode shapes can be modified by changing design parameters in mathematical expressions.

• 한국소음진동공학회논문집
• /
• 제22권11호
• /
• pp.1128-1136
• /
• 2012

This paper analyzes the vibration characteristics of an optical pickup actuator, which has six wire-suspensions and is used in optical disc drives(ODDs). The vibration characteristics of the actuator is mathematically described by analyzing its beam configuration and motion condition confined to lateral and longitudinal directions of the beams. The accuracy of the vibration characteristics is proved by comparing mode frequencies with a finite element analysis. Finally, it is shown that mode frequencies and shapes can be modified by changing design parameters in mathematical expressions.

• Structural Engineering and Mechanics
• /
• 제53권3호
• /
• pp.537-573
• /
• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• 한국소음진동공학회논문집
• /
• 제25권6호
• /
• pp.399-405
• /
• 2015

In this work we use the mode decomposition technique employing chirplet transform, which is able to separate the individual modes from dispersive and multimodal waveform measured with the magnetostrictive sensor. The mode decomposition technique is also used to estimate the time-frequency centers and individual energies of the reflection, which would be used to locate and characterize axial defects. The arrival times of the separated modes are calculated and the axial defect lengths can be evaluated by using the estimated arrival time. Results from an experiment on a carbon steel pipe are presented and it is shown that the accurate and quantitative defect characterization could become enabled using the proposed technique.

• Advances in nano research
• /
• 제15권5호
• /
• pp.411-422
• /
• 2023

In the present study, the axial vibration of the nanorods is investigated in the framework of the doublet mechanics theory. The equations of motion and boundary conditions of nanorods are derived by applying the Hamilton principle. A finite element method is developed to obtain the vibration frequencies of nanorods for different boundary conditions. A two-noded higher order rod finite element is used to solve the vibration problem. The natural frequencies of nanorods obtained with the present finite element analysis are validated by comparing the results of classical doublet mechanics and nonlocal strain gradient theories. The effects of rod length, mode number and boundary conditions on the axial vibration frequencies of nanorods are examined in detail. Mode shapes of the nanorods are presented for the different boundary conditions. It is shown that the doublet mechanics model can be used for the dynamic analysis of nanotubes, and the presented finite element formulation can be used for mechanical problems of rods with unavailable analytical solutions. These new results can also be used as references for the future studies.

• Advances in nano research
• /
• 제14권6호
• /
• pp.521-525
• /
• 2023

This paper concerned with the vibration of double walled carbon nanotubes (CNTs) as continuum model based on Timoshenko-beam theory. The vibration solution obtained from Timoshenko-beam theory provides a better presentation of vibration structure of carbon nanotubes. The natural frequencies of double-walled CNTs against half axial wave mode are investigated. The frequency decreases on decreasing the half axial wave mode. The shape of frequency arcs is different for various lengths. It is observed that model has produced lowest results for C-F and highest for C-C. A large parametric study is performed to see the effect of half axial wave mode on frequencies of CNTs. This numerically vibration solution delivers a benchmark results for other techniques. The comparison of present model is exhibited with previous studies and good agreement is found.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2004년도 춘계학술대회논문집
• /
• pp.942-947
• /
• 2004

The differential equations governing free, in-plane vibrations of stepped non-circuiar arches are derived as nondimensional forms including the effects of rotatory inertia, shear deformation and axial deformation. The governing equations are solved numerically to obtain frequencies and mode shapes. The lowest four natural frequencies and mode shapes are calculated for the stepped parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of arch rise to span length ratios, slenderness ratios, section ratios, and discontinuous sector ratios are considered. The effect of rotatory inertia and shear deformation on natural frequencies is reported. Typical mode shapes of vibrating arches are also presented.

• 소음진동
• /
• 제7권2호
• /
• pp.331-345
• /
• 1997

A theoretical formulation for the analysis of free vibration of clamped-free cylindrical shells with plates attached at arbitrary axial position(s) was completed and it was programed to get the numerical results which yield natural frequencies and mode shape of the combined system of the plate and the shells. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS. In order to validate the theory, modal test was also performed by impact test and FFT analysis. The results shows good agreement with those of ANSYS and test results in frequencies and mode shapes. The method developed herein is likely to be used for the analysis of the free vibration of the clamped-free circular cylindrical shells with any kinds of lids such as hollow circular plates, conical shells, spherical shells, or semi-spherical shells.

• 한국농공학회지
• /
• 제34권1호
• /
• pp.57-65
• /
• 1992

The main purpose of this paper is to present both the natural frequencies and mode shapes of tapered beams under tensile axial force. The differential equation governing planar free vibration for tapered beams under tensile axial force is derived as nondimensional form. The three kinds of cross sectional shape are considered in differential equation. The Runge-Kutta method and Determinant Search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped, clamped-clamped and constraints are applied in numerical examples. The lowest four nondimensional natural frequencies are reported as the function of nondimensional tensile axial force. The fundamental natural frequencies are presented when section ratios and nondimensional axial forces are varied. The effects of cross sectional shapes are reported and some typical mode shapes are also presented.