Comparison of nonclassical controllers on piezoelectric nanoresonator: nonlinear ‎frequency response and stability analysis

Authors

1 Assistant Professor, Department of Mechanical Engineering, University of Mazandaran, Babolsar, Islamic Republic of ‎Iran

2 Ph.D. Student, Department of Physics, University of Kashan, Kashan, Islamic Republic of Iran

10.22044/jsfm.2024.14369.3851

Abstract

In current study, nonlinear vibrations and stability analysis of piezoelectric nanoresonator (PENR) ‎considering with the effects of non-‎classical controllers such as strain gradient (SGT), nonlocal (NLT) and ‎Gurtin–Murdoch surface/interface ‎‎(GMSIT) theories are presented in comparison with the classical theory ‎‎(CT). PENR subjected to nonlinear ‎electrostatic excitation with direct (DC) and alternative (AC) voltages ‎and also visco-pasternak medium. For ‎this work, Hamilton’s principle and Galerkin technique are used to ‎obtain the governing ‎equations and boundary conditions and also to solve the equation of motion. Complex ‎averaging method ‎combined with arc-length continuation is used to investigate nonlinear frequency response ‎and stability ‎analysis of PENR. The results show that ignoring small-scale and surface/interface effects give ‎inaccurate ‎predictions of vibrational response of the PENR. It is indicated that in different boundary ‎condition, material ‎length scale and nonlocal scale parameters respectively lead to decreasing and increasing ‎of PENR stiffness ‎and also the amplitude of oscillation and the range of instability of non-classic theories of ‎NLT and SGT are ‎greater than that of the classical one. Also changes of surface/interface parameters lead to ‎decreasing or ‎increasing of the resonant frequency, resonance amplitude, nonlinear behavior and the ‎system's instability of ‎PENR.‎

Keywords

Main Subjects

References

  • Oliveira OJ, Marystela FLG, Lima LFd, Róz ALD (2017) Nanoscience and its Applications (Micro and Nano Technologies). William Andrew. Elsevier. New York. USA.
  • Ganji DD, Hashemi Kachapi SH (2015) Application of Nonlinear Systems in Nanomechanics and Nanofluids: Analytical Methods and Applications (Micro and Nano Technologies). Elsevier. New York. USA.
  • Rupitsch SJ (2018) Piezoelectric Sensors and Actuators: Fundamentals and Applications. Springer. Springer Berlin Heidelberg. German.
  • Tzou H (2019) Piezoelectric Shells: Sensing, Energy Harvesting, and Distributed Control. Springer. New York. USA.
  • Gurtin ME, Murdoch AI (1978) Surface stress in solids. Int. J. Solids Struct. 14(6): 431–
  • Eringen AC (2002) Nonlocal Continuum Field Theories. Springer. New York. USA.
  • Lim CW, Zhang G, Reddy JN (2015) A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids. 78: 298–
  • Farajpour A, Yazdi MRH, Rastgoo A, Loghmani M, Mohammadi M (2016) Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates. Compos. Struct. 140: 323–
  • Ebrahimi F, Barati MR (2016) Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field. J. Intell. Mater. Syst. Struct. 11(28).
  • Najafi M, Ahmadi I (2022) Free Vibration Analysis of Piezoelectric Nanobeam Based on a 2D-formulation and Nonlocal Elasticity Theory. J. Solid Fluid Mech. 12(4): 59–72 (In Persian).
  • Arefi M (2018) Analysis of a doubly curved piezoelectric nano shell: Nonlocal electro-elastic bending solution. Eur. J. Mech. A. Solids. 70: 226–
  • Ebrahimi F, Barati MR (2017) Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory. Compos. Struct. 159: 433–
  • Mehralian F, Tadi Beni Y, Karimi Zeverdejani M (2017) Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes. Physica B. 514: 61–69.
  • Karamad H, Andakhshideh A‚ Maleki S (2020) Study of Primary and Secondary Nonlinear Resonances of Nanobeam Based on Nonlocal Strain Gradient Theory. Physica B. 10(2): 163–
  • Fang XQ, Zhu CS, Liu JX, Zhao J (2018) Surface energy effect on nonlinear buckling and postbuckling behavior of functionally graded piezoelectric cylindrical nanoshells under lateral pressure. Mater. Res. Express. 5.4: 045017.
  • Fang XQ, Zhu CS, Liu JX, Liu XL (2018) Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures. Physica B. 529: 41–
  • Hashemi Kachapi SH, Dardel M, Mohamadi daniali H, Fathi A (2019) Effects of surface energy on vibration characteristics of double-walled piezo-viscoelastic cylindrical nanoshell. P I Mech. Eng. C-J Mec. 233: 5264–
  • Hashemi Kachapi SH, Dardel M, Mohamadi daniali H, Fathi A (2019) Pull-in instability and nonlinear vibration analysis of electrostatically piezoelectric nanoresonator with surface/interface effects. Thin Walled Struct. 143: 106210.
  • Hashemi Kachapi SH, Dardel M, Mohamadi daniali H, Fathi A (2019) Nonlinear dynamics and stability analysis of piezo-visco medium nanoshell resonator with electrostatic and harmonic actuation. Math. Modell. 75: 279–309.
  • Hashemi Kachapi Sayyid H (2020) Nonlinear vibration and stability analysis of piezo-harmo-electrostatic nanoresonator based on surface/interface and nonlocal strain gradient effects. J. Braz. Soc. Mech. Sci. 42(107).
  • Hashemi Kachapi Sayyid H (2020) Nonlinear and nonclassical vibration analysis of double walled piezoelectric nano-structure. Adv. Nano Res. 9(4).

 

  • Hashemi Kachapi SH, Dardel M, Mohamadi daniali H, Fathi A (2020) Nonlinear vibration and stability analysis of double-walled piezoelectric nanoresonator with nonlinear van der Waals and electrostatic excitation. J. Vib. Control. 26(9-10): 680–700.
  • Hashemi Kachapi SH, Mohamadi daniali H, Dardel M, Fathi A (2020) The effects of nonlocal and surface/interface parameters on nonlinear vibrations of piezoelectric nanoresonator. J. Intell. Mater. Syst. Struct. 31(6): 818–842.
  • Hashemi Kachapi Sayyid H (2020) Fluid-conveying piezoelectric nanosensor: Nonclassical effects on vibration-stability analysis, Struct. Eng. Mech. 76(5): 619–629.
  • Sun J, Wang Z, Zhou Z, Xu Xg, Lim CW (2018) Surface effects on the buckling behaviors of piezoelectric cylindrical nanoshells using nonlocal continuum model. Appl. Math. Modell. 59: 341–356.
  • Kiani K (2017) Postbuckling scrutiny of highly deformable nanobeams: A novel exact nonlocal-surface energy-based model. J. Phys. Chem. Solids. 110: 327–343.
  • Ghorbanpour Arani A, Kolahchi R, Hashemian M (2014) Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories. P I Mech Eng C-J Mec. 228: 3258–80.
  • Ghorbani K, Mohammad K, Rajabpour i, Ghadiri M (2019) Surface and size-dependent effects on the free vibration analysis of cylindrical shell based on Gurtin-Murdoch and nonlocal strain gradient theories. J. Phys. Chem. Solids. 129: 140–150.
  • Amabili M (2008) Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press. New York.
  • Manevitch AI, Manevitch LI (2005) Themechanics of Nonlinear Systems with Internal Resonance. Imperial College Press. London, UK.
Journal of Solid and Fluid Mechanics
Volume 14, Issue 3
September and October 2024
Pages 125-139

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