Sayyid H. Hashemi Kachapi

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In the present work, surface/interface energy effects for pull-in instability analysis on dimensionless natural frequency (DNF) and nonlinear dynamics response (NDR) of piezoelectric nanosensor (PENS) subjected to nonlinear electrostatic excitation and harmonic force are studied using Gurtin–Murdoch (GM) surface/interface energy approach. To achieve this purpose, the Hamilton’s approach, assumed mode and Lagrange–Euler’s theories and also arc-length continuation and complex averaging methods are used to investigate influences of surface/interface parameters of PENS such as Lame’s constants, residual stress, piezoelectric constants and mass density for analysis of pull-in instability voltage.


Pull-in instability, Nonlinear dynamic response, Piezoelectric nanosensor, Surface/interface effects, Arc-length continuation, Nonlinear electrostatic excitation

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Tzou, H., 2019, Piezoelectric Shells: Sensing, Energy Harvesting, and Distributed Control, Springer, USA.

Wang, L., Chen, W., Liu, J., Deng, J., Liu, Y., 2011, A review of recent studies on non-resonant piezoelectric actuators, Mechanical Systems and Signal Processing, 11(4), pp. 187-96.

Nayfeh, A.H., Ouakad, H.M., Najar, F., Choura, S., Abdel-Rahman, E.M., 2010, Nonlinear dynamics of a resonant gas sensor, Nonlinear Dynamics, 59, pp. 607–618.

Farokhi, H., Païdoussis, M. P., Misra, A., 2018, Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model, Journal of Sound and Vibration, 49, pp. 604-629.

Prasanth, C.S.R., Harsha, C.S., Pratiher, B., 2018, Electrostatic pull-in analysis of a nonuniform micro-resonator undergoing large elastic deflection, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 18(232), pp. 3337-3350.

Pourkiaee, S. M., Khadem, S. E., Shahgholi, M., Bab, S., 2017, Nonlinear modal interactions and bifurcations of a piezoelectric nanoresonator with three-to-one internal resonances incorporating surface effects and van der Waals dissipation forces, Nonlinear Dynamics, 88, pp. 1785–1816.

Karimipour, I., Tadi Beni, Y., Zeighampour, H., 2018, Nonlinear size-dependent pull-in instability and stress analysis of thin plate actuator based on enhanced continuum theories including nonlinear effects and surface energy, Microsystem Technologies, 24, pp. 1811–1839.

Nikpourian, A. R., Ghazavi, M. R., Azizi, S., 2018, On the nonlinear dynamics of a piezoelectrically tuned micro-resonator based on non-classical elasticity theories, International Journal of Mechanics and Materials in Design, 14, pp. 1–19.

Zhang, W.M., Yan, H., Peng, Z.K., Meng, G., 2014, Electrostatic pull-in instability in MEMS/NEMS: A review, Sensors and Actuators A: Physical, 214, pp. 187–218.

Sedighi, H.M., 2014, Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory, Acta Astronautica, 95, pp. 111-123.

Sedighi, H.M., Koochi, A., Daneshmand, F., Abadyan, M., 2015, Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow, International Journal of Non-Linear Mechanics, 77, pp. 96-106.

Y. Tadi Beni, I. Karimipour, M. Abadyan, 2014, Modeling the instability of electrostatic nano-bridges and nano-cantilevers using modified strain gradient theory. Applied Mathematical Modelling. 39, 2633-2648.

Tadi Beni, Y., Karimipour, I., Abadyan, M., 2014, Modeling the effect of intermolecular force on the size-dependent pull-in behavior of beam-type NEMS using modified couple stress theory, Journal of Mechanical Science and Technology, 28, pp. 3749-3757.

Tadi Beni, Y., 2016, Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling, Mechanics Research Communications, 75, pp. 67–80.

Tajalli, S. A., Tajalli, S. M., 2019, Wavelet based damage identification and dynamic pull-in instability analysis of electrostatically actuated coupled domain microsystems using generalized differential quadrature method, Mechanical Systems and Signal Processing, 133, 106256.

Farokhi, H., Misra, A. K., Païdoussis, M. P., 2017, A new electrostatic load model for initially curved carbon nanotube resonators: pull-in characteristics and nonlinear resonant behaviour, Nonlinear Dynamics, 88, pp. 1187–1211.

Amabili, M., 2008, Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, New York.

Bornassi, S., Haddadpour, H., 2017, Nonlocal vibration and pull-in instability analysis of electrostatic carbon-nanotube based NEMS devices, Sensors and Actuators A: Physical, 266, pp. 185-196.

Gurtin, M.E., Murdoch, A.I., 1975, A continuum theory of elastic material surface, Archive for Rational Mechanics and Analysis, 57, pp. 291–323.

Gurtin, M.E., Murdoch, A.I., 1978, Surface stress in solids, International Journal of Solids and Structures, 14, pp. 431–40.

Fang, X.Q., Zhu, C.S., Liu, J.X., Liu, X.L., 2018, Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures, Physica B: Condensed Matter, 529, pp. 41-56.

Fang, X.Q., Zhu, C.S., Liu, J.X., Zhao, J., 2018, Surface energy effect on nonlinear buckling and postbuckling behavior of functionally graded piezoelectric cylindrical nanoshells under lateral pressure, Materials Research Express, 5.4, 045017.

Hashemi Kachapi, Sayyid H., Dardel, M., Mohamadi daniali, H., Fathi, A., 2019, Effects of surface energy on vibration characteristics of double-walled piezo-viscoelastic cylindrical nanoshell, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 15(233), pp. 5264-5279.

Hashemi Kachapi, Sayyid H., 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 Structures. 143, 106210.

Hashemi Kachapi, Sayyid H., Dardel, M., Mohamadi daniali, H., Fathi, A., 2019, Nonlinear dynamics and stability analysis of piezo-visco medium nanoshell resonator with electrostatic and harmonic actuation, Applied Mathematical Modelling, 75, pp. 279-309.

Hashemi Kachapi, Sayyid H., Dardel, M., Mohamadi daniali, H., Fathi, A., 2019, Nonlinear vibration and stability analysis of double-walled piezoelectric nanoresonator with nonlinear van der Waals and electrostatic excitation, Journal of Vibration and Control, 9-10(26), pp. 680-700.

Hashemi Kachapi, Sayyid H., Mohamadi daniali, H., Dardel, M., Fathi, A., 2020, The effects of nonlocal and surface/interface parameters on nonlinear vibrations of piezoelectric nanoresonator, Journal of Intelligent Material Systems and Structures, 31(6), pp. 818–842.

Hashemi Kachapi, Sayyid H., 2020, Nonlinear and nonclassical vibration analysis of double walled piezoelectric nano-structure, Advances in Nano Research, An International Journal, 9(4).

Fan, T., 2015, Nano-scale energy harvester of piezoelectric/piezomagnetic structures with torsional mode, Mechanical Systems and Signal Processing, 26, pp. 1150–1163.

Manevitch, A.I., Manevitch, L.I., 2005, The mechanics of Nonlinear Systems with Internal Resonance, Imperial College Press, London.


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