• Title/Summary/Keyword: Coupled equations of motion

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Hydrodynamic response of alternative floating substructures for spar-type offshore wind turbines

  • Wang, Baowei;Rahmdel, Sajad;Han, Changwan;Jung, Seungbin;Park, Seonghun
    • Wind and Structures
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    • v.18 no.3
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    • pp.267-279
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    • 2014
  • Hydrodynamic analyses of classic and truss spar platforms for floating offshore wind turbines (FOWTs) were performed in the frequency domain, by considering coupling effects of the structure and its mooring system. Based on the Morison equation and Diffraction theory, different wave loads over various frequency ranges and underlying hydrodynamic equations were calculated. Then, Response Amplitude Operators (RAOs) of 6 DOF motions were obtained through the coupled hydrodynamic frequency domain analysis of classic and truss spar-type FOWTs. Truss spar platform had better heave motion performance and less weight than classic spar, while the hydrostatic stability did not show much difference between the two spar platforms.

Static bending and free vibration of FGM beam using an exponential shear deformation theory

  • Hadji, L.;Khelifa, Z.;Daouadji, T.H.;Bedia, E.A.
    • Coupled systems mechanics
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    • v.4 no.1
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    • pp.99-114
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    • 2015
  • In this paper, a refined exponential shear deformation beam theory is developed for bending analysis of functionally graded beams. The theory account for parabolic variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Contrary to the others refined theories elaborated, where the stretching effect is neglected, in the current investigation this so-called "stretching effect" is taken into consideration. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Analytical solutions for static are obtained. Numerical examples are presented to verify the accuracy of the present theory.

Stochastic micro-vibration response characteristics of a sandwich plate with MR visco-elastomer core and mass

  • Ying, Z.G.;Ni, Y.Q.;Duan, Y.F.
    • Smart Structures and Systems
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    • v.16 no.1
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    • pp.141-162
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    • 2015
  • The magneto-rheological visco-elastomer (MRVE) is used as a smart core to control the stochastic micro-vibration of a sandwich plate with supported mass. The micro-vibration response of the sandwich plate with MRVE core and supported mass under stochastic support motion excitations is studied and compared to evaluate the vibration suppression capability. The effects of the supported mass and localized magnetic field on the stochastic micro-vibration response of the MRVE sandwich plate are taken into account. The dynamic characteristics of the MRVE core in micro-vibration are described by a non-homogeneous complex modulus dependent on vibration frequency and controllable by applied magnetic fields. The partial differential equations for the coupled transverse and longitudinal motions of the MRVE sandwich plate with supported mass are derived from the dynamic equilibrium, constitutive and geometric relations. The simplified ordinary differential equations are obtained for the transverse vibration of the MRVE sandwich plate under localized magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of sandwich plates with supported mass is developed based on the Galerkin method and random vibration theory. The expressions of frequency-response functions, response power spectral densities and root-mean-square velocity responses of the plate in terms of the one-third octave frequency band are obtained for micro-vibration evaluation. Finally, numerical results are given to illustrate the large response reduction capacity of the MRVE sandwich plate with supported mass under stochastic support motion excitations, and the influences of MRVE parameters, supported mass and localized magnetic field placement on the micro-vibration response.

Nonlinear Dynamic Analysis of a Satellite with Tether Conveying Fluid (유체가 이송하는 테더가 있는 인공위성의 동특성 분석)

  • Jung, Won-Young;Lee, Kyu-Ho;Chung, Jin-Tai
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.8
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    • pp.691-697
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    • 2011
  • The purpose of this study is to analyze nonlinear dynamics of a tethered satellite. The coupled non-linear equations of motion are derived by using the extended Hamilton's principle with the polar coordinate system. In order to analyze the response of tethered satellite, time responses are computed by the Newmark's time integration method. We also investigate the dynamic behavior of the system and the effects of length of tether, tip mass and conveyed fluid through the tether with time variation.

Exact Dynamic Stiffness Model for the Pipelines Conveying Internal Unsteady Flow (내부 비정상유동을 갖는 파이프계의 동강성모델링)

  • Park, Jong-Hwan;Lee, U-Sik
    • Proceedings of the KSME Conference
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    • 2003.11a
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    • pp.1666-1671
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    • 2003
  • Exact dynamic stiffness model for a uniform straight pipeline conveying unsteady fluid is formulated from a set of fully coupled pipe-dynamic equations of motion, in which the fluid pressure and velocity of internal flow as well as the transverse and axial displacements of the pipeline are all treated as dependent variables. The accuracy of the dynamic stiffness model formulated herein is first verified by comparing its solutions with those obtained by the conventional finite element model. The spectral element analysis based on the present dynamic stiffness model is then conducted to investigate the effects of fluid parameters on the dynamics and stability of an example pipeline problem.

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Frequency characteristics of a multiferroic Piezoelectric/LEMV/CFRP/Piezomagnetic composite hollow cylinder under the influence of rotation and hydrostatic stress

  • Selvamani, R.;Mahesh, S.;Ebrahimi, F.
    • Coupled systems mechanics
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    • v.10 no.2
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    • pp.185-198
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    • 2021
  • An analytical model is consider to scrutinize axisymmetric wave propagation in multiferroic hollow cylinder with rotating and initial stressed forces, where a piezomagnetic (PM) material layer is bonded to a piezoelectric (PE) cylinder together by Linear elastic materials with voids. Both distinct material combos are taken into account. Three displacement potential functions are introduced to uncouple the equations of motion, electric and magnetic induction. The numerical calculations are carried out for the non-dimensional frequency by fixing wave number and thickness. The arrived outputs are plotted as the dispersion curves for different layers. The results obtained in this paper can offer significance to the application of PE/PM composite hollow cylinder via LEMV and CFRP layers for the acoustic wave and microwave technologies.

EFFECT OF ORIENTATION OF A MAGNETIC FIELD ON MOTION OF AN ELECTRICALLY CONDUCTING FLUID IN A CONFINED ENCLOSURE (자장 방향 변화에 따른 밀폐공간 내 도전성 유체의 거동)

  • Han, C.Y.;Jun, H.Y.;Park, E.S.
    • Journal of computational fluids engineering
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    • v.14 no.3
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    • pp.123-130
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    • 2009
  • Hydromagnetic flow in a confined enclosure under a uniform magnetic field is studied numerically. The thermally active side walls of the enclosure are kept at hot and cold temperatures specified, while the top and bottom walls are insulated. The coupled momentum and energy equations associating with the electromagnetic retarding force as well as the buoyancy force terms are solved by an iterative procedure using the SIMPLER algorithm based on control volume approach. The changes in the flow and thermal field based on the orientation of an external magnetic field, which varies from 0 to $2{\pi}$ radians, are investigated. Resulting heat transfer characteristics are examined too.

Study for the Controller Design of a Direct Drive Servo Valve (직접구동형 서보밸브의 제어기 설계에 관한 연구)

  • 이성래;김종열;김치붕
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.136-136
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    • 2000
  • The direct drive servo valve(DDV) is composed of a DC rotor, link, valve spool and displacement sensor(LVDT) where the spool is directly coupled to the DC motor through the link. Since the DDV is a kind of one-stage valve, the robust controller is required to overcome the flow force effect on the spool motion. The mathematical equations are derived and the stability, accuracy and response speed of a DDV are investigated analytically using a linearized system block diagram. Proportional control, PID control. Time-Delay control, Sliding Mode control, and Proportional control using the load pressure are applied to DDV to find which one shows the best control performance. The digital computer simulation results show that the proportional control using the load pressure satisfies the design requirement of response speed and steady state error regardless of the variation of load pressure,

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Dynamics of a rotating beam with flexible root and flexible hub

  • Al-Qaisia, A.A.
    • Structural Engineering and Mechanics
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    • v.30 no.4
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    • pp.427-444
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    • 2008
  • A mathematical model for the nonlinear dynamics of a rotating beam with flexible root attached to a rotating hub with elastic foundation is developed. The model is developed based on the large planar and flexural deformation theory and the potential energy method to account for axial shortening due to bending deformation. In addition the exact nonlinear curvature is used in the system potential energy. The Lagrangian dynamics and the assumed mode method is used to derive the nonlinear coupled equations of motion hub rotation, beam tip deflection and hub horizontal and vertical displacements. The derived nonlinear model is simulated numerically and the results are presented and discussed for the effect of root flexibility, hub stiffness, torque type, torque period and excitation frequency and amplitude on the dynamic behavior of the rotating beam-hub and on its stability.

Linear Stability Analysis of a Rotating Disc Brake for Squeal Noise (회전 디스크 브레이크의 스퀼소음에 대한 선형안정성 연구)

  • Kang, Jae-Young
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.19 no.10
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    • pp.1092-1098
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    • 2009
  • The squeal propensity of an automotive disc brake system is studied in the theoretical and computational manner. The rotating disc is in contact with two stationary pads and the nonlinear friction is engaged on the contact surface. The friction-coupled equations of motion are derived in the finite element(FE) of the actual brake disc and pad. From the general definition of friction force, the rotation and in-plane mode effects can be included properly in the brake squeal model. The eigenvalue sensitivity analysis and the mode shape visualization at squeal frequencies are also conducted for the detailed investigation. It is found that the squeal propensity is strongly influenced by rotation effect and the in-plane mode can be involved in squeal generation.