Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory |
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Authors: | F Daneshmand M Rafiei SR Mohebpour M Heshmati |
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Institution: | 1. Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6;2. Department of Bioresource Engineering, McGill University, 21111 Lakeshore Road, Sainte-Anne-de-Bellevue, Quebec, Canada H9X 3V9;3. School of Mechanical Engineering, Shiraz University, Shiraz, Iran;4. Department of Mechanical Engineering, School of Engineering, Persian Gulf University, Bushehr 75168, Iran;5. Department of Mechanical Engineering, Kermanshah University of Technology, Kermanshah, Iran |
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Abstract: | A gradient-enriched shell formulation is introduced in the present study based on the first order shear deformation shell model and the stress gradient and strain-inertia gradient elasticity theories are used for dynamic analysis of single walled carbon nanotubes. It provides extensions of the first order shear deformation shell formulation with additional higher-order spatial derivatives of strains and stresses. The higher-order terms are introduced in the formulation by using the Laplacian of the corresponding lower-order terms. The proposed shell formulation includes two length scale size parameters related to the strain gradients and inertia gradients. The effects of the transverse shear, aspect ratio, circumferential and half-axial wave numbers and length scale parameters on different vibration modes of the single-walled carbon nanotubes are elucidated. The results are also compared with those obtained from a classical shell theory with Sanders–Koiter strain-displacement relationships. |
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Keywords: | Gradient elasticity Carbon nanotubes Shell theory Vibration analysis |
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