• Title/Summary/Keyword: Vibration Gradient

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Optimization of Piezoceramic Sensor/Actuator Placement for Vibration Control Using Gradient Method (구배법을 이용한 진동제어용 압전 감지기/작동기의 위치 최적화)

  • 강영규
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.11 no.6
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    • pp.169-174
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    • 2001
  • Optimization of the collocated piezoceramic sensor/actuator placement is investigated numerically and verified experimentally for vibration control of laminated composite plates. The finite element method is used for the analysis of dynamic characteristics of the laminated composite plates with the piezoceramic sensor/actuator. The structural damping index(SDI) is defined from the modal damping(2$\omega$ζ) . It is chosen as the objective function for optimization. Weights for each vibrational mode are taken into account in the SDI calculation. The gradient method is used for the optimization. Optimum location of the piezoceramic sensor/actuator is determined by maximizing the SDI. Numerical simulation and experimental results show that the optimum location of the piezoceramic sensor/actuator is dependent upon the outer layer fiber orientations of the plate, and location and size of the piezoceramic sensor/actuator.

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Wave propagation and vibration of FG pipes conveying hot fluid

  • Zhang, Yi-Wen;She, Gui-Lin
    • Steel and Composite Structures
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    • v.42 no.3
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    • pp.397-405
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    • 2022
  • The existing researches on the dynamics of the fluid-conveying pipes only focus on stability and vibration problems, and there is no literature report on the wave propagation of the fluid-conveying pipes. Therefore, the purpose of this paper is to explore the propagation characteristics of longitudinal and flexural waves in the fluid-conveying pipes. First, it is assumed that the material properties of the fluid-conveying pipes vary based on a power function of the thickness. In addition, it is assumed that the material properties of both the fluid and the pipes are closely depended on temperature. Using the Euler-Bernoulli beam equation and based on the linear theory, the motion equations considering the thermal-mechanical-fluid coupling is derived. Then, the exact expressions of phase velocity and group velocity of longitudinal waves and bending waves in the fluid-conveying pipes are obtained by using the eigenvalue method. In addition, we also studied the free vibration frequency characteristics of the fluid-conveying pipes. In the numerical analysis, we successively studied the influence of temperature, functional gradient index and liquid velocity on the wave propagation and vibration problems. It is found that the temperature and functional gradient exponent decrease the phase and group velocities, on the contrary, the liquid flow velocity increases the phase and group velocities. However, for vibration problems, temperature, functional gradient exponent parameter, and fluid velocity all reduce the natural frequency.

Investigating vibrational behavior of graphene sheets under linearly varying in-plane bending load based on the nonlocal strain gradient theory

  • Shariati, Ali;Barati, Mohammad Reza;Ebrahimi, Farzad;Singhal, Abhinav;Toghroli, Ali
    • Advances in nano research
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    • v.8 no.4
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    • pp.265-276
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    • 2020
  • A study that primarily focuses on nonlocal strain gradient plate model for the sole purpose of vibration examination, for graphene sheets under linearly variable in-plane mechanical loads. To study a better or more precise examination on graphene sheets, a new advance model was conducted which carries two scale parameters that happen to be related to the nonlocal as well as the strain gradient influences. Through the usage of two-variable shear deformation plate approach, that does not require the inclusion of shear correction factors, the graphene sheet is designed. Based on Hamilton's principle, fundamental expressions in regard to a nonlocal strain gradient graphene sheet on elastic half-space is originated. A Galerkin's technique is applied to resolve the fundamental expressions for distinct boundary conditions. Influence of distinct factors which can be in-plane loading, length scale parameter, load factor, elastic foundation, boundary conditions, and nonlocal parameter on vibration properties of the graphene sheets then undergo investigation.

Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory

  • Barati, Mohammad Reza
    • Structural Engineering and Mechanics
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    • v.64 no.6
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    • pp.683-693
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    • 2017
  • According to a generalized nonlocal strain gradient theory (NSGT), dynamic modeling and free vibrational analysis of nanoporous inhomogeneous nanoplates is presented. The present model incorporates two scale coefficients to examine vibration behavior of nanoplates much accurately. Porosity-dependent material properties of the nanoplate are defined via a modified power-law function. The nanoplate is resting on a viscoelastic substrate and is subjected to hygro-thermal environment and in-plane linearly varying mechanical loads. The governing equations and related classical and non-classical boundary conditions are derived based on Hamilton's principle. These equations are solved for hinged nanoplates via Galerkin's method. Obtained results show the importance of hygro-thermal loading, viscoelastic medium, in-plane bending load, gradient index, nonlocal parameter, strain gradient parameter and porosities on vibrational characteristics of size-dependent FG nanoplates.

Nonlinear resonances of nonlocal strain gradient nanoplates made of functionally graded materials considering geometric imperfection

  • Jia-Qin Xu;Gui-Lin She;Yin-Ping Li;Lei-Lei Gan
    • Steel and Composite Structures
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    • v.47 no.6
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    • pp.795-811
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    • 2023
  • When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

Unidirectional Solidification of $Al-CuAl_2$ Eutectic Composites under Forced Convection by Vibration (진동하에서 일방향응고 시킨 $Al-CuAl_2$ 공정복합재료의 응고에 관한 연구)

  • Lee, Hyun-Kyu;Lee, Kil-Hong
    • Journal of Korea Foundry Society
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    • v.18 no.3
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    • pp.234-239
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    • 1998
  • Unidirectional solidification of $Al-CuAl_2$ eutectic composites was studied under the condition of forced convection by vibration. It has been shown that thermal gradient for solid is different from that for liquid during solidification under force convection by vibration. With increase of vibration, mobility of liquid increases, but decreases with decreasing vibration. The rate of solidification is very high initially, and decreases suddenly. For further solidification, the rate of solidification decrceases slowly, and shows a L-type behavior. The mechanical vibration during solidification effects efficiently on nucleation, and induces a forced convection in liquid. By the forced convection, great thermal gradient of liquid interface between solid and liquid can be obtained. The amount of solute near the interface also decreases as solute distribution is improved by the forced convection.

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Development of electronic shearography for vibration analysis (진동해석을 위한 전자전단간섭계의 개발)

  • Kang, Young-June;Kwon, Yong-Ki
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.12
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    • pp.2047-2054
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    • 1997
  • This paper describes a measuring method of vibration mode shapes by the Electronic Shearography. This method called the speckle interferometer has many merits in practical use, such as low sensitivity to environmental noise, low limit of coherent-length and simple optical configuration. In this study, we developed Michelson-type shearing interferometer provided with a phase stepping mirror and with a bias modulation mirror to quantify the vibration gradient fields. Results of application to a simple cantilever plate show that the vibration amplitude fields obtained are in good agreement with those of the electronic speckle pattern interferometry (ESPI).

Vibration of elastically supported bidirectional functionally graded sandwich Timoshenko beams on an elastic foundation

  • Wei-Ren Chen;Liu-Ho Chiu;Chien-Hung Lin
    • Structural Engineering and Mechanics
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    • v.91 no.2
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    • pp.197-209
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    • 2024
  • The vibration of elastically supported bidirectional functionally graded (BDFG) sandwich beams on an elastic foundation is investigated. The sandwich structure is composed of upper and lower layers of BDFG material and the core layer of isotropic material. Material properties of upper and lower layers are assumed to vary continuously along the length and thickness of the beam with a power-law function. Hamilton's principle is used to deduce the vibration equations of motion of the sandwich Timoshenko beam. Then, the partial differential equation of motion is spatially discretized into a time-varying ordinary differential equation in terms of Chebyshev differential matrices. The eigenvalue equation associated with the free vibration is formulated to study the influence of various slenderness ratios, material gradient indexes, thickness ratios, foundation and support spring constants on the vibration frequency of BDFG sandwich beams. The present method can provide researchers with deep insight into the impact of various geometric, material, foundation and support parameters on the vibration behavior of BDFG sandwich beam structures.

Forced vibration response in nanocomposite cylindrical shells - Based on strain gradient beam theory

  • Shokravi, Maryam
    • Steel and Composite Structures
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    • v.28 no.3
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    • pp.381-388
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    • 2018
  • In this paper, forced vibration of micro cylindrical shell reinforced by functionally graded carbon nanotubes (FG-CNTs) is presented. The structure is subjected to transverse harmonic load and modeled by beam model. The size effects are considered based on strain gradient theory containing three small scale parameters. The mixture rule is used for obtaining the effective material properties of the structure. Based on sinusoidal shear deformation theory of beam, energy method and Hamilton's principle, the motion equations are derived. Applying differential quadrature method (DQM) and Newmark method, the frequency curves of the structure are plotted. The effect of different parameters including, CNTs volume percent and distribution type, boundary conditions, size effect and length to thickness ratio on the frequency curves of the structure is studied. Numerical results indicate that the dynamic deflection of the FGX-CNT-reinforced cylindrical is lower with respect to other type of CNT distribution.

Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities

  • Barati, Mohammad Reza
    • Advances in nano research
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    • v.5 no.4
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    • pp.393-414
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    • 2017
  • Forced vibration behavior of porous metal foam nanoplates on elastic medium is studied via a 4-variable plate theory. Different porosity distributions called uniform, symmetric and asymmetric are considered. Nonlocal strain gradient theory (NSGT) containing two scale parameters is employed for size-dependent modeling of porous nanoplates. The present plate theory satisfies the shear deformation effect and it has lower field variables compared with first order plate theory. Hamilton's principle is employed to derive the governing equations. Obtained results from Galerkin's method are verified with those provided in the literature. The effects of nonlocal parameter, strain gradient, foundation parameters, dynamic loading, porosity distributions and porosity coefficient on dynamic deflection and resonance frequencies of metal foam nanoscale plates are examined.