Nonlinear Vibration of Piezoelectric Nano Biological Sensor Based on Non-Classical Mathematical Approach
In this study, nonlinear vibration analysis of a parametrically excited piezoelectric nano beam subjected to DC and AC voltages is investigated for biological sensor applications on the basis of the non-local continuum theory. Equations of the motion and boundary conditions of the nano beam are obtained by implementation of Hamilton’s principle and the Galerkin approach. Hamiltonian solution namely Frequency-Amplitude approach is used for natural frequencies and mode shapes as a function of the piezo-layered nano beam characteristic non-local size scale parameter. The size effects on the vibration behavior (frequency and harmonic response) of the beam are studied and it is found that the non-local parameter has significant effects on the free vibration of system.
Jalili N, Piezoelectric-Based Vibration Control: From Macro to Micro/Nano Scale Systems (Springer, New
York, USA), 2010.
Turner K L & Zhang W, Design and analysis of a dynamic MEM chemical sensor, American Control
Conference -IEEE Xplore, 2 (2001) 1214–1218.
Zhang W, Baskaran R & Turner K L, Effect of cubic nonlinearity on autoparametrically amplified resonant
MEMS mass sensor, Sens Actuators A, 102 (2002) 139–150.
Zhang W M, & Meng G, Nonlinear dynamic analysis of electrostatically actuated resonant MEMS sensors
under parametric excitation, IEEE Sens J , 7 (2007) 370–380.
Zamanian M, Khadem S E & Mahmoodi S N, the effect of a piezoelectric layer on the mechanical behavior of an electrostatic actuated microbeam, Smart Mater Struct, 17(2008) 065024.
Rezaei Kivi A & Azizi S, On the dynamics of a micro-gripper subjected to electrostatic and piezoelectric excitations, Int J Non-Linear Mech, 77 (2015) 183–192.
Ghazavi M R, Rezazadeh G & Azizi S, Pure parametric excitation of the micro cantilever beam actuated by piezoelectric layer, Appl Math Modell, 34(2010) 4196–4207.
Saeedi Vahdat A, Rezazadeh G & Ahmadi G, Thermoelastic damping in a micro-beam resonator tunable with piezoelectric layers, Acta Mech Solida Sin, 25(2012) 73–81.
Azizi S, Rezaei Kivi A, Marzbanrad J, Mass detection based on pure parametric excitation of a micro beam actuated by piezoelectric layers, Microsyst Technol, (2015) DOI 10.1007/s00542-016-2813-7.
Jiang L Y & Yan Z, Timoshenko beam model for static bending of nanowires with surface effects, Physica E, 42 (2010), 2274–2279.
Eringen A C & Edelen D G B, On nonlocal elasticity, Int J Eng Sci, 10 (1972), 233–248.
Eringen A C, Screw dislocation in non-local elasticity, J Phys D: Appl Phys, 10 (1977).
Reddy J N, Nonlocal theories for bending, buckling and vibration of beams, Int J Eng Sci, 45 (2007), 288–307.
Civalek Ö, Demir C & Akgöz B, Free vibration and bending analyses of cantilever microtubules based on nonlocal continuum model, Math Comput Appl, 15 (2010), 289–298.
Zhou Z G, Wu L Z, Du S Y, Non-local theory solution for a mode I crack in piezoelectric materials, Eur J Mech A-Solid, 25, (2006), 793–807.
Hashemi Kachapi S H & Ganji D, Dynamics and Vibration: Progress in Nonlinear Sciences, (Springer, Series: Solid Mechanics and Its Applications), 2014.
Ganji D & Hashemi Kachapi S H, Application of Nonlinear Systems in Nanomechanics and Nanofluids: Analytical Methods and Applications-Micro and Nano Technologies (Elsevier), 2015.
Hashemi Kachapi S H & Ganji D, Nonlinear Differential Equations: Analytical Methods and Application (Cambridge International Science Publishing Ltd, Cambridge, United Kingdom), 2013.
Hashemi Kachapi S H & Ganji D, Analytical and Numerical Methods in Engineering and Applied Sciences (Asian Academic Publisher Limited, Progress in Nonlinear Science, Hong Kong, Chine), 2011.
Copyright (c) 2019 Sayyid H. Hashemi Kachapi, S.GH. Hashemi Kachapi
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain the copyright of their manuscripts, and all Open Access articles are distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.