Investigation of Strain Gradient Theory for the Analysis of Free Linear Vibration of Nano Truncated Conical Shell

Subject Areas : Mechanical Engineering

A.R Sheykhi ¹ (Department of Mechanical Engineering , Science and Research Branch, Islamic Azad University, Tehran, Iran)
Sh Hosseini Hashemi ² (School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran)
A Maghsoudpour ³ (Department of Mechanical Engineering , Science and Research Branch, Islamic Azad University, Tehran, Iran)
Sh Etemadi Haghighi ⁴ (Department of Mechanical Engineering , Science and Research Branch, Islamic Azad University, Tehran, Iran)

Received: 2020-06-26 Accepted : 2020-08-22 Published : 2020-09-30

Keywords:

References:

[1] Firouz-Abadi R.D., Fotouhi M.M., Haddadpour H., 2011, Free vibration analysis of nano cones using a nonlocal continuum model, Physics Letters A 375(41): 3593-3598.
[2] Firouz Abadi R.D., Fotouhi M.M., Haddadpour H., 2012, Stability analysis of nano cones under external pressure and axial compression using nonlocal shell model, Physica E: Low-Dimensional Systems and Nanostructures 44(9): 1832-1837.
[3] Fotouhi M.M., Firouz-Abadi R.D., Haddadpour H., 2013, Free vibration analysis of nano cones embedded in an elastic medium using a nonlocal continuum shell model, International Journal of Engineering Science 64(1): 14-22.
[4] Tadi Beni Y., Soleimani I., 2015, Free torsional vibration and static analysis of the conical nano-shell based on modified couple stress theory, 3rd International Conference on Nanotechnology of Science and Research Pioneers Institute, Istanbul, Turkey.
[5] Zeighampour H., Tadi Beni Y., Mehralian F., 2015, A shear deformable conical shell formulation in the frame work of couple stress theory, Acta Mechanica 226(8): 2607-2629.
[6] Zeighampour H., Tadi Beni Y., 2014, Analysis of conical shells in the framework of coupled stresses, International Journal of Engineering Science 81: 107-122.
[7] Sofiyev A.H., 2013, The non-linear dynamics of FGM truncated conical shells surrounded by an elastic medium, International Journal of Mechanical Sciences 66: 33-44.
[8] Sofiyev A.H., Kuruoglu N., 2011, Natural frequency of laminated orthotropic shells with different boundary conditions and resting on the Pasternak type elastic foundation, Composites: Part B 42(6): 1562-1570.
[9] Sofiyev A.H., Kuruoglu N., 2014, Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium, Thin-Walled Structures 80: 178-191.
[10] Sofiyev A.H., 2014, Large-amplitude vibration of non-homogenous orthotropic composite truncated conical shells, Composites Part B: Engineering 61: 365-374.
[11] Mehri M., Asadi H., Wang Q., 2016, Buckling and vibration analysis of a pressurized CNT reinforced functionally graded truncated conical shell under an axial compression using HDQ method , Computer Methods in Applied Mechanics and Engineering 303: 75-100.
[12] Ansari R., Rouhi H., Rad A.N., 2014, Vibrational analysis of carbon nanocones under different boundary conditions:an analytical approach, Mechanics Research Communications 56: 130-135.
[13] Kamarian S., Salim M., Dimitri R., Tornabene F., 2016, Free vibration analysis of conical shells reinforced with agglomerated carbon nanotubes, International Journal of Mechanical Sciences 108-109: 157-165.
[14] Sofiyev A.H., 2012, Large-amplitude vibration of non-homogenous orthotropic composite truncated conical shells, Composites Part B: Engineering 94(7): 2237-2245.
[15] Tohidi H. , Hosseini-Hashemi S.H., Maghsoudpour A., Etemadi S., 2017, Strain gradient theory for vibration analysis of embedded CNT-reinforced micro Mindlin cylindrical shells considering agglomeration effects, Structural Engineering and Mechanics 62(5):551-565.
[16] Zeighampour H., Tadi Beni Y., 2014, Cylindrical thin-shell model based on modified strain gradient theory, International Journal of Engineering Science 78: 27-47.
[17] Tadi Beni Y., Mehralian F., Razavi H., 2014, Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Composite Structures 111: 349-353.
[18] Gholami R., Darvizeh A., Ansari R., Sadeghi F., 2016, Vibration and buckling of first-order shear deformable circular cylindrical micro-/nano-shells based on Mindlinʼs strain gradient elasticity theory, European Journal of Mechanics A/Solids 58: 76-88.
[19] Zhang B., He Y., Liu D., Shen L., Lei J., 2015, Free vibration analysis of four-unknown shear deformable functionally graded cylindrical micro shells based on the strain gradient elasticity theory, Composite Structures 119: 578-597.
[20] Bakhtiari M., Lakis A., Kerboua Y., 2018, Nonlinear vibration of truncated conical shells: Donnell, sanders and nemeth theories, Rapport Technique n°EPM-RT 01.
[21] Tohidi H., Hosseini-Hashemi Sh., Maghsoudpour A., Etemadi Haghighi Sh., 2017, Dynamic stability of FG-CNT-reinforced viscoelastic micro cylindrical shells resting on nonhomogeneous orthotropic viscoelastic medium subjected to harmonic temperature distribution and 2D magnetic field, Wind and Structures 25(2): 131-156.
[22] Ghadiri M., Shafiei N., 2015, Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen’s theory using differential quadrature method, Microsystem Technologies 22(12): 2853-2867.
[23] Malekzadeh P., Golbahar Haghighi M.R., Shojaee M., 2014, Nonlinear free vibration of skew nano plates with surface and small scale effects, Thin-Walled Structures 78: 48-56.
[24] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51(8): 1477-1508.
[25] Reddy J.N., 2002, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, USA.