Journal of Computational Applied Mechanics

Transverse Sensing of Simply Supported Truncated Conical Shells

Document Type : Research Paper

Authors

Khaje Nasir University of Technology, Mechanical Engineering Department, Tehran, Iran

Abstract

Modal signals of transverse sensing of truncated conical shells with simply supported boundary condition at both ends are investigated. The embedded piezoelectric layer on the surface of conical shell is used as sensors and output voltages of them in considered modes are calculated. The Governing sensing signal displacement equations are derived based on the Kirchhoff theory, thin-shell assumption, piezoelectric direct effect, the Gauss theory and the open circuit assumption. A conical shell with fully covered piezoelectric layer is considered as a case study and the layer is segmented into 400 patches. Modal voltages of the considered model are calculated and evaluated. The ideal locations for sensor patches are in the middle of conical shell surface in the longitudinal direction and locations near the ends of the conical shell are not recommended. The longitudinal membrane strain signal has a leading role on the total signal in comparison with other strain signal components. The output signals of the sensor can be used as a controller input for later active vibration control or structural health monitoring.

Keywords

Main Subjects

1.   Thakkar, D. and R. Ganguli, Induced shear actuation of helicopter rotor blade for active twist control. Thin-Walled Structures, 2007. 45(1): p. 111-121.
2.   Li, F.-M., K. Kishimoto, and W.-H. Huang, The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh–Ritz method. Mechanics Research Communications, 2009. 36(5): p. 595-602.
3.   Lam, K.Y. and L. Hua, Vibration analysis of a rotating truncated circular conical shell. International Journal of Solids and Structures, 1997. 34(17): p. 2183-2197.
4.   Li, H., Z.B. Chen, and H.S. Tzou, Torsion and transverse sensing of conical shells. Mechanical Systems and Signal Processing, 2010. 24(7): p. 2235-2249.
5.   Tzou, H.S., W.K. Chai, and D.W. Wang, Modal voltages and micro-signal analysis of conical shells of revolution. Journal of Sound and Vibration, 2003. 260(4): p. 589-609.
6.   Chai, W.K., P. Smithmaitrie, and H.S. Tzou, Neural potentials and micro-signals of non-linear deep and shallow conical shells. Mechanical Systems and Signal Processing, 2004. 18(4): p. 959-975.
7.   Li, F.-M., Z.-G. Song, and Z.-B. Chen, Active vibration control of conical shells using piezoelectric materials. Journal of Vibration and Control, 2011. 18(14): p. 2234-2256.
8.   Safarabadi, M., et al., Effect of surface energy on the vibration analysis of rotating nanobeam. Journal of Solid Mechanics, 2015. 7(3): p. 299-311.
9.   Mohammadi, M., et al., Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment. Acta Mechanica, 2016. 227(8): p. 2207-2232.
10. Danesh, M., A. Farajpour, and M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method. Mechanics Research Communications, 2012. 39(1): p. 23-27.
11. Goodarzi, M., et al., Thermo-Mechanical Vibration Analysis of FG Circular and Annular Nanoplate Based on the Visco-Pasternak Foundation. Journal of Solid Mechanics, 2016. 8(4): p. 788-805.
12. Mohammadi, M., M. Ghayour, and A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version of differential quadrature method. 2011.
13. Goodarzi, M., et al., Investigation of the Effect of Pre-Stressed on Vibration Frequency of Rectangular Nanoplate Based on a Visco-Pasternak Foundation. Journal of Solid Mechanics, 2014. 6(1): p. 98-121.
14. Farajpour, M.R., et al. Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory. Micro & Nano Letters, 2016. 11, 302-307.
15. Mohammadi, M., et al., Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial in-plane pre-load via nonlocal elasticity theory. Journal of Solid Mechanics, 2012. 4(2): p. 128-143.
16. Asemi, H., et al., Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads. Physica E: Low-dimensional Systems and Nanostructures, 2015. 68: p. 112-122.
17. Farajpour, A., et al., A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mechanica, 2016. 227(7): p. 1849-1867.
18. Farajpour, A., et al., Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics. Composite Structures, 2012. 94(5): p. 1605-1615.
19. Farajpour, A., M. Danesh, and M. Mohammadi, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics. Physica E: Low-dimensional Systems and Nanostructures, 2011. 44(3): p. 719-727.
20. Asemi, S., et al., Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM. Physica E: Low-dimensional Systems and Nanostructures, 2014. 63: p. 169-179.
21. Farajpour, A., et al., Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates. Composite Structures, 2016. 140: p. 323-336.
22. Asemi, S.R., M. Mohammadi, and A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory. Latin American Journal of Solids and Structures, 2014. 11(9): p. 1515-1540.
23. Mohammadi, M., et al., Temperature effect on vibration analysis of annular graphene sheet embedded on visco-pasternak foundation. J. Solid Mech, 2013. 5: p. 305-323.
24. Mohammadi, M., et al., Levy type solution for nonlocal thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium. Journal of Solid Mechanics, 2013. 5(2): p. 116-132.
25. Mohammadi, M., et al., Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium. Latin American Journal of Solids and Structures, 2014. 11(3): p. 437-458.
26. Mohammadi, M., et al., Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium. Latin American Journal of Solids and Structures, 2014. 11(4): p. 659-682.
27. Mohammadi, M., A. Farajpour, and M. Goodarzi, Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium. Computational Materials Science, 2014. 82: p. 510-520.
28. Mohammadi, M., M. Ghayour, and A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model. Composites Part B: Engineering, 2013. 45(1): p. 32-42.
29. Mohammadi, M., et al., Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory. Composites Part B: Engineering, 2013. 51: p. 121-129.
30. Mohammadi, M., et al., Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment. Composites Part B: Engineering, 2014. 56: p. 629-637.
31. Farajpour, A., et al., Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model. Physica E: Low-dimensional Systems and Nanostructures, 2011. 43(10): p. 1820-1825.
32. Farajpour, A., A. Rastgoo, and M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment. Physica B: Condensed Matter, 2017. 509: p. 100-114.
33. Farajpour, A., A. Rastgoo, and M. Mohammadi, Surface effects on the mechanical characteristics of microtubule networks in living cells. Mechanics Research Communications, 2014. 57: p. 18-26.
34. Asemi, S., A. Farajpour, and M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory. Composite Structures, 2014. 116: p. 703-712.
35. Moosavi, H., et al., Vibration analysis of nanorings using nonlocal continuum mechanics and shear deformable ring theory. Physica E: Low-dimensional Systems and Nanostructures, 2011. 44(1): p. 135-140.
Journal of Computational Applied Mechanics
Volume 49, Issue 2
December 2018
Pages 212-230
  • Receive Date: 27 July 2017
  • Revise Date: 04 November 2017
  • Accept Date: 07 November 2017