Bubnov-Galerkin Method

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Z.w. Zhong - One of the best experts on this subject based on the ideXlab platform.

  • The thermo-mechanical vibration of a single-walled carbon nanotube studied using the Bubnov–Galerkin Method
    Physica E: Low-dimensional Systems and Nanostructures, 2010
    Co-Authors: K.b. Mustapha, Z.w. Zhong
    Abstract:

    Abstract The subject of this study is the application of the Bubnov–Galerkin Method to the multi-parameter thermo-mechanical vibration of a single-walled carbon nanotube (SWCNT) embedded in a Winkler-type elastic medium. The studies are carried out on the basis of the nonlocal continuum mechanics modeling of the SWCNT. The independent and combined effects of the small scale coefficient (nonlocal parameter), the thermal loading, and the elastic foundation on the fundamental natural frequencies of the SWCNT are extensively investigated. Different boundary configurations of the SWCNT are considered. Validation of special cases of the model with results available in the literature shows good agreement. It is observed that in the presence of the thermally induced axial force, the variation in the fundamental frequencies with the scale coefficient does not follow the same trend for all the boundary conditions. The results also show that for all the boundary configurations, the influence of the elastic foundation on the natural frequencies of the SWCNT is small when compared to the influence of the thermally induced axial force and the nonlocal parameter.

Isaac Elishakoff - One of the best experts on this subject based on the ideXlab platform.

  • Buckling of a Clamped-Free Double-Walled Carbon Nanotube by the Bubnov-Galerkin Method
    Journal of Applied Mechanics, 2012
    Co-Authors: Isaac Elishakoff, Simon Bucas
    Abstract:

    This study deals with the Bubnov-Galerkin Method applied to the buckling of clamped-free double-walled carbon nanotubes (DWCNTs) subjected to a concentrated compressive load at the free end. It was found that at least four comparison functions are needed in order to obtain accurate results.

  • A NEW VIEW OF THE Bubnov-Galerkin Method IN THE LINEARIZATION CONTEXT
    Vietnam Journal of Mechanics, 2012
    Co-Authors: Nguyen Dong Anh, Isaac Elishakoff
    Abstract:

    In the study an extension of the Bubnov-Galerkin Method in terms of the equivalent linearization Method is presented. It is combined with sequential linearization and nonlinear procedure to yield a new Method for solving nonlinear equations which can improve the accuracy when the nonlinearity is strong. For illustration the Duffing oscillator is considered to show the effectiveness of the proposed Method.

  • clamped free single walled carbon nanotube based mass sensor treated as bernoulli euler beam
    Journal of Nanotechnology in Engineering and Medicine, 2011
    Co-Authors: Isaac Elishakoff, Claudia Versaci, N Maugeri, G Muscolino
    Abstract:

    In this study, we investigate the vibrations of the cantilever single-walled carbon nanotube (SWCNT) with attached bacterium on the tip in view of developing the sensor. This sensor will be able to help to identify the bacterium or virus that may be attached to the SWCNT. Two cases are considered: These are light or heavy bacteria attached to the nanotube. The problem is solved by the exact solution, the finite difference Method, and the Bubnov-Galerkin Method.

  • Clamped-Free Single-Walled Carbon Nanotube-Based Mass Sensor Treated as Bernoulli–Euler Beam
    Journal of Nanotechnology in Engineering and Medicine, 2011
    Co-Authors: Isaac Elishakoff, Claudia Versaci, N Maugeri, G Muscolino
    Abstract:

    In this study, we investigate the vibrations of the cantilever single-walled carbon nanotube (SWCNT) with attached bacterium on the tip in view of developing the sensor. This sensor will be able to help to identify the bacterium or virus that may be attached to the SWCNT. Two cases are considered: These are light or heavy bacteria attached to the nanotube. The problem is solved by the exact solution, the finite difference Method, and the Bubnov-Galerkin Method.

  • Effective Stiffness and Effective Mass of the Double-Walled Carbon Nanotube Sensor
    Journal of Nanotechnology in Engineering and Medicine, 2011
    Co-Authors: Isaac Elishakoff, Claudia Versaci, G Muscolino
    Abstract:

    In this study, the effective stiffness of the double-walled carbon nanotube sensor is determined by both the Bubnov―Galerkin Method and the finite difference technique. It is shown that in addition to the familiar expression of the effective stiffness of the clamped-free beam, there is an additional term for the double-walled carbon nanotube's effective stiffness. Additionally, it is demonstrated that there are two effective stiffness expressions, depending on where the load is applied, at the inner tube or at the outer tube. Additionally, effective mass is evaluated in the context of the Galerkin Method.

K.b. Mustapha - One of the best experts on this subject based on the ideXlab platform.

  • The thermo-mechanical vibration of a single-walled carbon nanotube studied using the Bubnov–Galerkin Method
    Physica E: Low-dimensional Systems and Nanostructures, 2010
    Co-Authors: K.b. Mustapha, Z.w. Zhong
    Abstract:

    Abstract The subject of this study is the application of the Bubnov–Galerkin Method to the multi-parameter thermo-mechanical vibration of a single-walled carbon nanotube (SWCNT) embedded in a Winkler-type elastic medium. The studies are carried out on the basis of the nonlocal continuum mechanics modeling of the SWCNT. The independent and combined effects of the small scale coefficient (nonlocal parameter), the thermal loading, and the elastic foundation on the fundamental natural frequencies of the SWCNT are extensively investigated. Different boundary configurations of the SWCNT are considered. Validation of special cases of the model with results available in the literature shows good agreement. It is observed that in the presence of the thermally induced axial force, the variation in the fundamental frequencies with the scale coefficient does not follow the same trend for all the boundary conditions. The results also show that for all the boundary configurations, the influence of the elastic foundation on the natural frequencies of the SWCNT is small when compared to the influence of the thermally induced axial force and the nonlocal parameter.

G Muscolino - One of the best experts on this subject based on the ideXlab platform.

  • Clamped-Free Single-Walled Carbon Nanotube-Based Mass Sensor Treated as Bernoulli–Euler Beam
    Journal of Nanotechnology in Engineering and Medicine, 2011
    Co-Authors: Isaac Elishakoff, Claudia Versaci, N Maugeri, G Muscolino
    Abstract:

    In this study, we investigate the vibrations of the cantilever single-walled carbon nanotube (SWCNT) with attached bacterium on the tip in view of developing the sensor. This sensor will be able to help to identify the bacterium or virus that may be attached to the SWCNT. Two cases are considered: These are light or heavy bacteria attached to the nanotube. The problem is solved by the exact solution, the finite difference Method, and the Bubnov-Galerkin Method.

  • clamped free single walled carbon nanotube based mass sensor treated as bernoulli euler beam
    Journal of Nanotechnology in Engineering and Medicine, 2011
    Co-Authors: Isaac Elishakoff, Claudia Versaci, N Maugeri, G Muscolino
    Abstract:

    In this study, we investigate the vibrations of the cantilever single-walled carbon nanotube (SWCNT) with attached bacterium on the tip in view of developing the sensor. This sensor will be able to help to identify the bacterium or virus that may be attached to the SWCNT. Two cases are considered: These are light or heavy bacteria attached to the nanotube. The problem is solved by the exact solution, the finite difference Method, and the Bubnov-Galerkin Method.

  • Effective Stiffness and Effective Mass of the Double-Walled Carbon Nanotube Sensor
    Journal of Nanotechnology in Engineering and Medicine, 2011
    Co-Authors: Isaac Elishakoff, Claudia Versaci, G Muscolino
    Abstract:

    In this study, the effective stiffness of the double-walled carbon nanotube sensor is determined by both the Bubnov―Galerkin Method and the finite difference technique. It is shown that in addition to the familiar expression of the effective stiffness of the clamped-free beam, there is an additional term for the double-walled carbon nanotube's effective stiffness. Additionally, it is demonstrated that there are two effective stiffness expressions, depending on where the load is applied, at the inner tube or at the outer tube. Additionally, effective mass is evaluated in the context of the Galerkin Method.

Hoang Thi Thiem - One of the best experts on this subject based on the ideXlab platform.