• Title/Summary/Keyword: Vibration Equation

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Effect of the Vibration Modes on the Radiation Sound for Plate (강판의 진동모드를 고려한 방사음 예측에 관한 연구)

  • Kim Chang-Nam;Byun Young-Su;Kim Jeong-Man;Kim Ue-Kan
    • Journal of Advanced Marine Engineering and Technology
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    • v.30 no.1
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    • pp.73-80
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    • 2006
  • In order to compute the radiated sound from a vibrating structure, the Rayleigh's integral equation has to be derived from the Helmholtz equation using Green's function. Generally, the surface velocity in the Rayleigh's integral equation uses the root mean square(rms) velocity. The calculation value is too large, because it's not considered cancelation. On the other hand. using the complex velocity, the sound pressure is calculated too small, because it considers that sound is perfectly canceled out. Therefore, this thesis proposes a correction factor(CF) which considers vibration modes and the method by which to calculate the radiating sound pressure. The theoretical results are compared with the experimental values, and the proposed method can be verified with confluence.

Vibroacoustics of Axisymmetric Cylindrical Elastic Shells : Wall Impedance of the Plane Mode (축대칭 원통 탄성 셸의 진동음향 : 평면 모드의 벽 임피던스)

  • Park, Chan-Il
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.18 no.9
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    • pp.930-936
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    • 2008
  • Fluid loading of a vibrating cylindrical shell has influence on natural frequencies and vibration magnitudes of the shell and the acoustic pressure of fluid. The vibroacoustics of fluid-filled cylindrical shells need the coupled solution of Helmholtz equation and governing equation of a cylindrical shell with boundary conditions. This paper proposed the wall impedance of fluid-filled axisymmetric cylindrical shells, focusing on the inner fluid/shell interaction. To propose the impedance, shell displacements used the linear combination of in vacuo shell modes. Acoustic pressure prediction of fluid used Kirchhoff-Helmholtz integral equation with Green's function of the plane mode. For the demonstration of the proposed results, numerical applications on mufflers were conducted.

Vibration and stability of fluid conveying pipes with stochastic parameters

  • Ganesan, R.;Ramu, S. Anantha
    • Structural Engineering and Mechanics
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    • v.3 no.4
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    • pp.313-324
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    • 1995
  • Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

Analysis of free vibration of beam on elastic soil using differential transform method

  • Catal, Seval
    • Structural Engineering and Mechanics
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    • v.24 no.1
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    • pp.51-62
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    • 2006
  • Differential transform method (DTM) for free vibration analysis of both ends simply supported beam resting on elastic foundation is suggested. The fourth order partial differential equation for free vibration of the beam resting on elastic foundation subjected to bending moment, shear and axial compressive load is obtained by using Winkler hypothesis and small displacement theory. It is assumed that the material is linear-elastic, and that axial load and modulus of subgrade reaction to be constant. In the analysis, shear and axial load effects are considered. The frequency factors of the beam are calculated by using DTM due to the values of relative stiffness; the results are presented in graphs and tables.

Vibroacoustics of Axisymmetric Cylindrical Elastic Shells (축대칭 원통 탄성 쉘의 진동음향)

  • Park, Chan-IL
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2008.04a
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    • pp.160-165
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    • 2008
  • Fluid loading of a vibrating cylindrical shell can change natural frequencies and vibration magnitudes of the shell and a vibrating cylindrical shell can also change acoustic pressure of fluid. The vibroacoustics of fluid-filled cylindrical shells need the coupled solution of Helmholtz equation and governing equation of a cylindrical shell with boundary conditions. This paper proposed the wall impedance of fluid-filled axisymmetric cylindrical shells, focusing on the inner fluid/shell interaction. To propose the impedance, shell displacements used the linear combination of in vacuo shell modes. Acoustic pressure prediction of fluid used Kirchchoff-Helmholtz Integral equation with Green function of the plane mode. For the demonstration of the proposed results, numerical applications on mufflers were conducted.

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Active and Semi-Active Vibration Control of Piezoelectric Smart Structures Using a Pseudo-Sensor-Output-Feedback Method (PSOF 방법을 이용한 압전 지능 구조물의 능동 및 반능동 진동제어)

  • 김영식;김영태;오동영
    • Journal of KSNVE
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    • v.9 no.1
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    • pp.70-76
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    • 1999
  • This paper presents a pseudo-sensor-output-feedback(PSOF) method for the vibration suppression of the flexible piezoelectric smart structures. This method reduces the modeling errors using pseudo sensors in the output equation formulation. It also reduces computation time in practice. since the output equation does not need the state observer required in the state space equation. Experimental works are performed for the validation of theoretical predictions with the piezoelectric sensor and actuator bonded on the cantilever beam. An algorithm based on the sliding mode control theory is developed and analyzed for the robustness to the modeling errors and parameter uncertainties. This study also discusses the characteristics of the active and semi-active systems.

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Chaotic Out-of-Plane Vibration of Curved Pipe Conveying Oscillatory Flow (조화진동유동을 포함한 곡선파이프계의 외평면 혼돈 운동 연구)

  • 홍성철
    • Journal of KSNVE
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    • v.10 no.5
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    • pp.849-858
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    • 2000
  • In this paper the chaotic out-of-plane vibrations of the uniformly curved pipe with pulsating flow are theoretically investigated. The derived equations of motion contain the effects of nonlinear curvature and torsional coupling. The corresponding nonlinear ordinary differential equation is a type of nonhomogenous Hill's equation . this is transformed into the averaged equation by averaging theorem. Bifurcation curves of chaotic motion are obtained by Melnikov's method and plotted in several cases of frequency ratios. The theoretically obtained results are demonstrated by numerical simulation. And strange attractors are shown.

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Vibration Reaponse Analysis of frames with energy absober installed in Beams (보 제진 프레임의 진동응답해석)

  • Lee, Ho
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • 1997.10a
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    • pp.159-166
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    • 1997
  • The purpose of this thesis is to derive a theoretical model of the hysteretic resistance of the visco-elastic damper based on test results of harmonic excitation and to investigate of the basis of theory and experiment the effect of vibration control and response characteristics of portal frames degree vibration systems provided with the damper. The behaviour of a visco-elastic degree under dynamic loading is idealized by a model of the theory of visco-elasticity, i.e. a four-parameter model formed as a parallel combination of Maxwell fluid and Kelvin-Voigh models and its constitutive equation is derived. The model parameters are determined for a tested damper from the datas of harmonic excitation tests. The theoretical model of the damper is incorporated in equation fo motion of single degree of freedom. A computer program for solving the equation is written using Runge-kuttas's numerical integration scheme. Using this analysis program test cases of the earthquake excitation are simulated and the results of the simulation are the results of the simulation are the results of the simulation are compared with the test results.

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Multiobjective State-Feedback Control of Beams with Piezoelectric Device (압전체가 부착된 보의 다목적 상태궤한제어)

  • Park, Chul-Hue;Hong, Seong-Il;Park, Hyun-Chul
    • Proceedings of the KSME Conference
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    • 2004.04a
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    • pp.828-833
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    • 2004
  • The performance of a mixed $H_{\infty}/H_2$ design with pole placement constraints based on robust vibration control for a piezo/beam system is investigated. The governing equation of motion for the piezo/beam system is derived by Hamilton's principle. The assumed mode method is used to discretize the governing equation into a set of ordinary differential equation. A robust controller is designed by $H_{\infty}/H_2$ feedback control law that satisfies additional constraints on the closed-loop pole location in the face of model uncertainties, which are derived for a general class of convex regions of the complex plane. These constraints are expressed in terms of linear matrix inequalities (LMIs) approach for the multiobjective synthesis. The validity and applicability of this approach for vibration suppressions of SMART structural systems are discussed by damping out the multiple vibrational modes of the piezo/beam system.

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A Study on the vibration analysis of 2-phase HB type Linear Stepping Motor using ACSL (ACSL에 의한 2상 HB형 선형 STEPPING 전동기의 진동해석에 관한 연구)

  • Oh H.S;Jung E.N;Lee S.H;Lee B.S;Won K.S;Kim J.K
    • Proceedings of the KIPE Conference
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    • 2001.07a
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    • pp.14-17
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    • 2001
  • In this paper, the vibration characteristics of a 2-phase Hybrid type Linear Stepping Motor(HLSM) are analyzed using the ACSL. A magnetic equivalent circuit is based on the structure of the HLSM, and then the electric equivalent circuit of the HLSM is derived by solving equations for the magnetic equivalent circuit. A normal force is calculated using FEM(Flux2D). And the vibration characteristics of the HLSM are simulated by the ACSL with the voltage equations, the thrust equation, the normal force equation and the kinetic equation.

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