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Steel and Composite Structures Volume 36, Number 3, August10 2020 , pages 293-305 DOI: https://doi.org/10.12989/scs.2020.36.3.293 |
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Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models |
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Emad E. Ghandourah and Azza M. Abdraboh
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| Abstract | ||
| This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials. | ||
| Key Words | ||
| free vibration; functionally graded nanobeam; porosity models; nonlocal elasticity theory; finite element method | ||
| Address | ||
| Emad E. Ghandourh: Nuclear Engineering Dept., Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia Azza M. Abdraboh: Physics Department, Faculty of Science, Banha University, Banha, Egypt | ||