Abstract
In this paper, we estimated the hydrodynamic force in an array of cantilever beams separated by a distance \(\bar{s}\) oscillating in a viscous fluid. The beam is assumed to be sufficiently long to consider 2D flow and has symmetric as well as asymmetric shape morphing curvature while oscillating in a fluid. The fluid-structure interaction problem is modelled by considering the unsteady Stokes equation. The resulting 1D boundary integral problem is solved by the boundary element method (BEM) numerically in MATLAB to obtain the desired pressure distribution on the beam. It is found that as the frequency oscillation of the rigid beam is increased, both the damping as well as added mass effects are decreased at different rates due to the gradual decrease in unsteady viscous layer. Finally, the hydrodynamic coupling effect on the beam is demonstrated at \(\beta =0.1\). However, for increase in the symmetric and asymmetric shape morphing parameters, the hydrodynamic decoupling appears lower than the gap ratio 5. The cantilever beam with optimal shape morphing parameter can be useful for the optimal designs of atomic force microscopy (AFM).
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References
Sader, J.E.: Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J. Appl. Phys. 84(1), 64–76 (1998)
Sader, J.E., Chon, J.W., Mulvaney, P.: Calibration of rectangular atomic force microscope cantilevers. Rev. Sci. Instrum. 70(10), 3967–3969 (1999)
Ahsan, S.N., Aureli, M.: Nonlinear oscillations of shape-morphing submerged structures: Control of hydrodynamic forces and power dissipation via active flexibility. J. Fluids Struct. 74, 35–52 (2017)
Ahsan, S.N., Aureli, M.: Three-dimensional analysis of hydrodynamic forces and power dissipation in shape-morphing cantilevers oscillating in viscous fluids. Int. J. Mech. Sci. 149, 436–451 (2018)
Ahsan, S.N., Aureli, M.: Finite amplitude oscillations of flanged laminas in viscous flows: vortex-structure interactions for hydrodynamic damping control. J. Fluids Struct. 59, 297–315 (2015)
Hu, L., Yan, H., Zhang, W.M., Zou, H.X., Peng, Z.K., Meng, G.: Theoretical and experimental study on dynamic characteristics of V-shaped beams immersed in viscous fluids: from small to finite amplitude. J. Fluids Struct. 82, 215–244 (2018)
Basak, S., Raman, A.: Hydrodynamic coupling between micromechanical beams oscillating in viscous fluids. Phys. Fluids 19(1), 017105 (2007)
Ande, R., Gutschmidt, S., Sellier, M.: Fluid dynamics investigation of a large array. Phys. Fluids 33(7), 073608 (2021)
Li, C., Ma, X., Guan, Y., Tang, J., Zhang, B.: Microcantilever array biosensor for simultaneous detection of carcinoembryonic antigens and \(\alpha \)-fetoprotein based on real-time monitoring of the profile of cantilever. ACS Sens. 4(11), 3034–3041 (2019)
Manickavasagam, A.K.: Hydrodynamic coupling of arrays in fluids (2020)
Hosaka, H., Itao, K.: Coupled vibration of microcantilever array induced by airflow force. J. Vib. Acoust. 124(1), 26–32 (2002)
Green, C.P., Sader, J.E. Small amplitude oscillations of a thin beam immersed in a viscous fluid near a solid surface. Phys. Fluids 17(7), 073102 (2005)
Tuck, E.O.: Calculation of unsteady flows due to small motions of cylinders in a viscous fluid. J. Eng. Math. 3(1), 29–44 (1969)
Landau, L.D., Lifshitz, E.M.: Fluid Mechanics: Landau and Lifshitz: Course of Theoretical Physics, vol. 6. Elsevier (2013)
Lang, H.P., Hegner, M., Gerber, C.: Cantilever array sensors. Mater. Today 8(4), 30–36 (2005)
Kimber, M., Garimella, S.V., Raman, A.: An experimental study of fluidic coupling between multiple piezoelectric fans. In: Thermal and Thermomechanical Proceedings 10th Intersociety Conference on Phenomena in Electronics Systems, 2006. ITHERM 2006, pp. 333–340. IEEE (2006)
Lang, H.P., Hegner, M., Gerber, C.: Nanomechanical cantilever array sensors. In: Springer Handbook of Nanotechnology, pp. 457–485. Springer, Berlin, Heidelberg (2017)
Amiri, I.S., Addanki, S.: Simulation fabrication and characterization of micro-cantilever array based ozone sensor. Results Phys. 10, 923–933 (2018)
Akarapu, A., Nighot, R.P., Devsoth, L., Yadav, M., Pal, P., Pandey, A.K.: Experimental and theoretical analysis of drag forces in micromechanical-beam arrays. Phys. Rev. Appl. 13(3), 034003 (2020)
Ashok, A., Kumar, P.M., Singh, S.S., Raju, P., Pal, P., Pandey, A.K.: Achieving wideband micromechanical system using coupled non-uniform beams array. Sens. Actuators A: Phys. 273, 12–18 (2018)
Meirovitch, L., Parker, R.G.: Fundam. Vibr. Appl. Mech. Rev. 54(6), B100–B101 (2001)
Kreyszig, E., Stroud, K., Stephenson, G.: Advanced engineering mathematics. Integration, 9(4) (2008)
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The author would like to acknowledge the fellowship provided by the Ministry of Education, New Delhi, the Government of India.
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Devsoth, L., Pandey, A.K. (2023). Two-Dimensional Hydrodynamic Forces in an Array of Shape-Morphed Cantilever Beams. In: Pandey, A.K., Pal, P., Nagahanumaiah, Zentner, L. (eds) Microactuators, Microsensors and Micromechanisms. MAMM 2022. Mechanisms and Machine Science, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-031-20353-4_18
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DOI: https://doi.org/10.1007/978-3-031-20353-4_18
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