Vibration Analysis and Sensitivity Analysis of Semi-Submerged Multilayer Piezoelectric Microcantilever
Subject Areas :
micro and nano mechanics
Mohamadreza Khosravi
1
,
Reza Ghaderi
2
1 - Department of Mechanical Engineering,
Faculty of Technical and Engineering,
Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
2 - Department of Mechanical Engineering,
Faculty of Technical and Engineering,
Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
Received: 2021-02-18
Accepted : 2021-06-22
Published : 2021-12-01
Keywords:
Piezoelectric Microcantilever,
Hydrodynamic Force,
Sensitivity analysis,
Semi-Submerged,
Abstract :
The growing development of nanobiotechnology and its applicability resulted in a wider range of use of Microcantilevers (MCs) in liquid. Considering the applications of piezoelectric MCs in the microelectromechanical systems and Atomic Force Microscope (AFM), as well as the high performance of these beams, this article investigates the vibrating behavior of multilayer piezoelectric MCs with geometric discontinuity in liquid environment. Due to the extreme complexity of hydrodynamic forces introduced to MCs, this force may reduce their accuracy. As a result, the MC was considered to be semi-submerged in the liquid medium to reduce the effect of hydrodynamic force. In addition, to reduce the effect of hydrodynamic force on vibrating behavior of the MC, sensitivity analysis was performed on its geometric dimensions to obtain the optimal dimensions, aiming at minimizing the effect of this force. The differential equation of motion was derived using the Euler–Bernoulli theory and the Lagrange method. The hydrodynamic force was exerted on the MC through the sphere string model. The Simulation results indicated that due to reducing resonance frequency variations in the third vibrating mode, the effect of hydrodynamic force on vibrating motion is minimized in this mode and considered as the optimal vibrating mode among the first three modes. The sensitivity analysis results showed that the MC length and piezoelectric layer were geometric parameters with the greatest effect on frequency sensitivity of MC, which should be considered in semi-submerged piezoelectric MC design.
References:
Raman, A., Melcher, J., and Tung, R., Cantilever Dynamics in Atomic Force Microscopy, Nano Today, Vol. 3, No. 1-2, 2008, pp. 20-27.
Sader, J. E., Frequency Response of Cantilever Beams Immersed in Viscous Fluids with Applications to the Atomic Force Microscope, Journal of Applied Physics, Vol. 84, No. 64, 1998.
Maali, A., Hurth, C., Boisgard, R., Jai, C., Cohen-Bouhacina, T., and Aimé, J. P., Hydrodynamics of Oscillating Atomic Force Microscopy Cantilevers in Viscous Fluids, Journal of Applied Physics, Vol. 97, 2005, DOI:1063/1.1873060.
Kahrobaiyan, M., Asghari, M., Rahaeifard, M., Ahmadian, M., Investigation of the Size-Dependent Dynamic Characteristics of Atomic Force Microscope Microcantilevers Based On the Modified Couple Stress Theory, International Journal of Engineering Science, Vol. 48, No. 12, 2010, pp. 1985-1994, DOI:10.1016/j.ijengsci.2010.06.003.
Dufour, I., Lemaire, E., Caillard, B., Debéda, H., Lucat, C., Heinrich, S. M., Josse, F., and Brand, O., Effect of Hydrodynamic Force On Microcantilever Vibrations: Applications to Liquid-Phase Chemical Sensing, Sensors and Actuators B: Chemical, Vol. 192, 2014, pp. 664-672, DOI:10.1016/j.snb.2013.10.106.
Karimpour, M., Ghaderi, R., and Raeiszadeh, F., Vibration Response of Piezoelectric Microcantilever as Ultrasmall Mass Sensor in Liquid Environment, Micron, Vol. 101, 2017, pp. 213-220, DOI: 10.1016/j.micron.2017.07.009.
Wang, Y., Zu, J., Analytical Analysis for Vibration of Longitudinally Moving Plate Submerged in Infinite Liquid Domain, Applied Mathematics and Mechanics, Vol. 38, No. 5, 2017, DOI: 10.1007/s10483-017-2192-9
Ivaz, K., Abdollahi, D., and Shabani, R., Analyzing Free Vibration of a Cantilever Microbeam Submerged in Fluid with Free Boundary Approach, Journal of Applied Fluid Mechanics, Vol. 10, No. 6, 2017.
Van Eysden, C. A., Sader, J. E., Small Amplitude Oscillations of a Flexible Thin Blade in a Viscous Fluid: Exact Analytical Solution, Physics of Fluids, Vol. 18, No. 12, 2006.
Penedo, M., Hormeño, S., Prieto, P., Alvaro, R., Anguita, J., Briones, F., and Luna, M., Selective Enhancement of Individual Cantilever High Resonance Modes, Nanotechnology, Vol. 26, No. 48, 2015.
Agostini, M., Greco, G., and Cecchini, M., A Rayleigh Surface Acoustic Wave (R-Saw) Resonator Biosensor Based On Positive and Negative Reflectors with Sub-Nanomolar Limit of Detection, Sensors and Actuators B: Chemical, Vol. 254, 2018.
Faegh, S., Jalili, N., Sridhar, S., Ultrasensitive Piezoelectric-Based Microcantilever Biosensor: Theory and Experiment, IEEE/ASME Transactions on Mechatronics, Vol. 20, No. 1, 2015.
Ahmadi, M., Ansari, R., Darvizeh, M., Rouhi, H., Effects of Fluid Environment Properties on the Nonlinear Vibrations of AFM Piezoelectric Microcantilevers, Journal of Ultrafine Grained and Nanostructured Materials, Vol. 50, No. 2, 2017.
Weckman, N. E., Seshia, A. A., Reducing Dissipation in Piezoelectric Flexural Microplate Resonators in Liquid Environments, Sensors and Actuators A: Physical, Vol. 267, 2017.
Fischeneder, M., Kucera, M., Hofbauer, F., Pfusterschmid, G., Schneider, M., and Schmid, U. Q., Factor Enhancement of Piezoelectric Mems Resonators in Liquids with Active Feedback, Sensors and Actuators B: Chemical, 2018.
Yuan, Y., Du, H., Xia, X., and Wong, Y. R., Analytical Solutions to Flexural Vibration of Slender Piezoelectric Multilayer Cantilevers, Smart Materials and Structures, Vol. 23, No. 9, 2014.
Yu, G. L., Zhang, H. W., Li, Y. X., and Li, J., Equivalent Circuit Method for Resonant Analysis of Multilayer Piezoelectric-Magnetostrictive Composite Cantilever Structures, Composite Structures, Vol. 125, 2015.
Moory-Shirbani, M., Sedighi, H. M., Ouakad, H. M., and Najar, F., Experimental and Mathematical Analysis of a Piezoelectrically Actuated Multilayered Imperfect Microbeam Subjected to Applied Electric Potential, Composite Structures, Vol. 184, 2018.
Yi, J. W., Shih, W. Y., and Shih, W. H., Effect of Length, Width, and Mode On the Mass Detection Sensitivity of Piezoelectric Unimorph Cantilevers, Journal of Applied Physics, Vol. 91, No. 3, 2002.
Zhou, W., Khaliq, A., Tang, Y., Ji, H., Selmic, R. R., Simulation and Design of Piezoelectric Microcantilever Chemical Sensors, Sensors and Actuators A: Physical, Vol. 125, No. 1, 2005.
Korayem, M., Razazzadeh, S., Korayem, A., and Ghaderi, R., Effect of Geometrical and Environmental Parameters On Vibration of Multi-Layered Piezoelectric Microcantilever in Amplitude Mode, Applied Physics A, Vol. 121, No. 1, 2015.
Salehi-Khojin, A., Bashash, S., Jalili, N., Müller, M., and Berger, R., Nanomechanical Cantilever Active Probes for Ultrasmall Mass Detection, Journal of Applied Physics, Vol. 105, No. 1, 2009.
Korayem, A. H., Abdi, M., 3D Simulation of AFM Non-Uniform Piezoelectric Micro-Cantilever with Various Geometries Subjected to the Tip-Sample Forces, The European Physical Journal Applied Physics, Vol. 77, No. 2, 2017.
Mahmoodi, S. N., Jalili, N., Piezoelectrically Actuated Microcantilevers: An Experimental Nonlinear Vibration Analysis, Sensors and actuators A: physical, Vol. 150, No. 1, 2009.
Maraldo, D., Mutharasan, R., Detection and Confirmation of Staphylococcal Enterotoxin B in Apple Juice and Milk Using Piezoelectric-Excited Millimeter-Sized Cantilever Sensors at 2.5 fg/mL, Analytical Chemistry, Vol. 79, No. 20, 2007.
Johnson, B. N., Mutharasan, R., The Origin of Low-Order and High-Order Impedance-Coupled Resonant Modes in Piezoelectric-Excited Millimeter-Sized Cantilever (PEMC) Sensors: Experiments and Finite Element Models, Sensors and Actuators B: Chemical, Vol. 155, No. 2, 2011.
Korayem, H., Ghaderi, R., Sensitivity Analysis of Nonlinear Vibration of AFM Piezoelectric Microcantilever in Liquid, International Journal of Mechanics and Materials in Design, Vol. 10, No. 2, pp. 121-131, 2014.
Saltelli, K. Chan, E. M. Scott, Sensitivity Analysis, Wiley, New York, Vol. 1, 2000, pp. 112-115.
