Vibration Sensitivity Analysis of Nano-mechanical Piezo-Laminated Beams with Consideration of Size Effects

Subject Areas : micro and nano mechanics

mostafa  nazemizadeh ¹ (Faculty of Mechanics, Malek Ashtar Univeristy of Technology, Iran)
Firooz  Bakhtiari-Nejad ² (Department of Mechanical Engineering, University of Maryland, Maryland, USA Department of Mechanical Engineering, Amirkabir University of Technology, Iran)
Behrooz  Shahriari ³ (Faculty of Mechanics, Malek Ashtar University of Technology, Iran)

Received: 2020-05-04 Accepted : 2020-07-22 Published : 2020-12-01

Keywords: Size effects, Vibration, Sensitivity, Nano-mechanical Beam, Piezoelectric,

Abstract :

The presented article investigates vibration sensitivity analysis of Nano-mechanical piezo-laminated beams with consideration of size effects. To do this, the vibration governing equation of the stepped Nano-mechanical piezo-laminated beam is firstly derived by implementation of the nonlocal elasticity theory. The nonlocal formulation is considered for both of the beam and the piezoelectric layer and the obtained equation is solved analytically. Moreover, there is a need to recognize the importance and relative effects of the beam parameters on the natural frequencies and resonant amplitudes of the nonlocal beam. Therefore, the Sobol sensitivity analysis is utilized to investigate the relative effects of geometrical and the nonlocal parameters on the natural frequencies and the resonant amplitude of the nanobeam. The obtained results show that the length and the thickness of the piezoelectric layer have prominent effects on the vibration characteristics of the beam. Moreover, it is indicated that nonlocal parameter effect on the resonant amplitudes is more than resonant frequency. Also, the effect of the nonlocal term is more important at higher modes of vibration. Therefore, the nonlocal size effects cannot be ignored in vibration analysis of the nanobeam especially at higher modes.

References:

[1]     Bakhtiari-Nejad, F., Nazemizadeh, M., Size-Dependent Dynamic Modeling and Vibration Analysis of MEMS/NEMS-Based Nano-Mechanical Beam Based On the Nonlocal Elasticity Theory, Acta Mechanica, Vol. 227, No. 5, 2016, pp. 1363-1379.

[2]     Pak, A., Determination of Material Properties Components used in FEM Modeling of Ultrasonic Piezoelectric Transducer, ADMT Journal, Vol. 12, No. 2, 2019, pp. 75-81.

[3]     Norouzi, A., Tahmasebipour, M., Effect of AFM Cantilever Geometry on the DPL Nanomachining Process, ADMT Journal, Vol. 9, No. 4, 2016, pp. 75-80.

[4]     Taghizade, M., Korayem, A., and Korayem, M., Modelling of Non-Uniform Piezoelectric Micro-Cantilever in Different Environments, ADMT Journal, Vol. 12, No. 1, 2019, pp. 23-29.

[5]     Nazemizadeh, M., Bakhtiari-Nejad, F., A General Formulation of Quality Factor for Composite Micro/Nano Beams in The Air Environment Based On the Nonlocal Elasticity Theory, Composite Structures, Vol. 132, 2015, pp. 772-783.

[6]     Feng, C., Jiang, L., and Lau, W. M., Dynamic Characteristics of a Dielectric Elastomer-Based Microbeam Resonator with Small Vibration Amplitude, Journal of Micromechanics and Microengineering, Vol. 21, No. 9, 2011, pp. 95-102.

[7]     M. Taheri, Using of SphericalContact Models in 3D ManipulationModelingof Au Nanoparticles using Atomic Force Microscopyto Calculate the Critical Force and Time, Modares Mechanical Engineering, Vol. 48, No. 2, 2018, pp. 184-175.

[8]     Korayem, M. H., Badkoobeh, H. H., and Taheri, M., Dynamic Modeling and Simulation of Rough Cylindrical Micro/Nanoparticle Manipulation with Atomic Force Microscopy, Microscopy and microanalysis: the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada, 2014, pp. 1-16.

[9]     Souayeh, S., Kacem, N., Najar, F., and Foltête, E., Nonlinear Dynamics of Parametrically Excited Carbon Nanotubes for Mass Sensing Applications, ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete Island, Greece, 25–27 May 2015.

[10]  Zhu, H. T., Zbib, H. M., and Aifantis, E. C., Strain Gradients and Continuum Modeling of Size Effect in Metal Matrix Composites, Acta Mechanica, Vol. 121, No. 1, 1997, pp. 165-176.

[11]  Jalali, M. H., Zargar, O., and Baghani, M., Size-Dependent Vibration Analysis of Fg Microbeams in Thermal Environment Based On Modified Couple Stress Theory, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, Vol. 43, No. 1, 2019, pp. 761-771.

[12]  Akgöz, B., Civalek, Ö, Free Vibration Analysis of Axially Functionally Graded Tapered Bernoulli–Euler Micro Beams Based On the Modified Couple Stress Theory, Composite Structures, Vol. 98, 2013, pp. 314-322.

[13]  Demir, C., Mercan, K., Numanoglu, H. M., and Civalek, O., Bending Response of Nanobeams Resting On Elastic Foundation, Journal of Applied and Computational Mechanics, Vol. 4, No. 2, 2018, pp.105-114.

[14]  Nazemizadeh, M., Bakhtiari-Nejad, F., Size-Dependent Free Vibration of Nano/Microbeams with Piezo-Layered Actuators, Micro & Nano Letters, Vol. 10, No. 2, 2015, pp. 93-98

[15]  Eftekhari, S. A., Hashemian, M. and Toghraie, D., Optimal Vibration Control of Multi-Layer Micro-Beams Actuated by Piezoelectric Layer Based On Modified Couple Stress and Surface Stress Elasticity Theories, Physica A: Statistical Mechanics and its Applications, 2020, pp. 123998

[16]  Tong, C., Self-Validated Variance-Based Methods for Sensitivity Analysis of Model Outputs, Reliability Engineering & System Safety, Vol. 95, No. 3, 2010, pp. 301-309

[17]  Sobol, I. M., Sensitivity Estimates for Nonlinear Mathematical Models, Math Model Computation Experiments, Vol. 14, 1993, pp. 407-414

[18]  Eringen, A. C., Linear Theory of Nonlocal Elasticity and Dispersion of Plane Waves, International Journal of Engineering Science, Vol. 10, No. 5, 1972, pp. 425-435

[19]  Zhou, Z. G., Wu, L. Z., and Du, S. Y., Non-local Theory Solution for A Mode I Crack in Piezoelectric Materials, European Journal of Mechanics-A/Solids, Vol. 25, No. 5, 2006, pp. 793-807

[20]  Matviykiv, O., Lobur, M., Design Principles and Sensitivity Analysis of MEMS Cantilever Sensors, International Conference on Perspective Technologies and Methods in MEMS Design (MEMSTECH), 2010, pp. 230-232.

[21]  Korayem, M. H., Taheri, M., and Zakeri, M., Sensitivity Analysis of Nanoparticles Manipulation Based On Different Friction Models, Applied Surface Science, Vol. 258, No. 18, 2012, pp. 6713-6722.

[22]  Wang, C. M., Zhang, Y. Y., and He, X. Q., Vibration of Nonlocal Timoshenko Beams, Nanotechnology, Vol. 18, No. 10, 2007, pp. 105401.