Geometrically Non-Linear Vibration of a Cantilever Interacting with Rarefied Gas Flow

Shterev, Kiril; Manoach, Emil

doi:10.2478/cait-2020-0067

Abstract

The work is devoted to study 2D pressure driven rarefied gas flow in a microchannel having an elastic obstacle. The elastic obstacle is clamped at the bottom channel wall and its length is half of the channel height. The gas flow is simulated by Direct Simulation Monte Carlo (DSMC) method applying the advanced Simplified Bernoulli Trial (SBT) collision scheme. The elastic obstacle is modelled as geometrically nonlinear Euler Bernoulli beam. A reduced 3 modes reduction model of the beam is created. The influence of the gas flow on the beam vibration is studied, considering the linear and nonlinear beam theories.

References

1. Paidoussis, M. Fluid-Structure Interactions. Second Edition. 2013.10.1016/B978-0-12-397312-2.00001-6
Search in Google Scholar Back to article
2. Martin, J. M., H. K. Fathy, B. H. Houston. Dynamic Simulation of Atomic Force Microscope Cantilevers Oscillating Inliquid. – J. Appl. Phys., Vol. 104, 2008, 044316.10.1063/1.2970154
Search in Google Scholar Back to article
3. Cole, D. G., R. L Clark. Fluid-Structure Interaction in Atomic Force Microscope Cantilever Dynamics and Thermal Response, 6. – J. Appl. Phys.,Vol. 101, 2007. 10.1063/1.242972.10.1063/1.2429726
Search in Google Scholar Back to article
4. Green, C. P., J. E. Sader. Frequency Response of Cantilever Beams Immersed in Viscous Fluids near a Solid Surface with Applications to the Atomic Force Microscope. – J. Appl. Phys., Vol. 98, 2005, 114913.10.1063/1.2136418
Search in Google Scholar Back to article
5. Cornelis, A., E. Van, J. E. Sader. Frequency Response of Cantilever Beams Immersed in Viscous Fluids with Applications to the Atomic Force Microscope: Arbitrary Mode Order. – J. Appl. Phys., Vol. 101, 2007, 044908.10.1063/1.2654274
Search in Google Scholar Back to article
6. Van Rij, J., T. Harman, T. Ameel. Slip Flow Fluid-Structure Interaction. – International Journal of Thermal Sciences, Vol. 58, 2012, pp. 9-19.10.1016/j.ijthermalsci.2012.03.001
Search in Google Scholar Back to article
7. Chakraborty, D., et al. Fluid-Structure Interaction in Deformable Microchannels. – Physics of Fluids, Vol. 24, 2012, No 10, p. 102002.10.1063/1.4759493
Search in Google Scholar Back to article
8. Pan, F., J. Kubi, J. Chen. Numerical Simulation of Fluid-Structure Interaction in a MEMS Diaphragm Drop Ejector. – J. Micromech. Microeng., Vol. 12, 2002, No 1, 70.10.1088/0960-1317/12/1/311
Search in Google Scholar Back to article
9. Baudille, R., M. E. Biancolini. A General Approach for Studying the Motion of a Cantilever Beam Interacting with a 2D Fluid Flow. – Interact. Multisc. Mech., Vol. 1, 2008, pp. 449-465.10.12989/imm.2008.1.4.449
Search in Google Scholar Back to article
10. Shterev, K., E. Manoach, S. Stefanov. Hybrid Numerical Approach to Study the Interaction of the Rarefied Gas Flow in a Microchannel with a Cantilever. – International Journal of Non-Linear Mechanics, Vol. 117, 2019, 103239.10.1016/j.ijnonlinmec.2019.103239
Search in Google Scholar Back to article
11. Meirovitch, L. Fundamentals of Vibrations. McGraw-Hill, 2001.10.1115/1.1421112
Search in Google Scholar Back to article
12. Gear, C. W. Numerical Initial Value Problems in Ordinary Differential Equations. Upper Saddle River, NJ, USA, Prentice Hall PTR. 1971.
Search in Google Scholar Back to article
13. Bird, G. A. Molecular, Gas Dynamics and the Direct Simulation of Gas Flows. Oxford, Clarendon Press, 1994.
Search in Google Scholar Back to article
14. Roohi, E., S. Stefanov. Collision Partner Selection Schemes in DSMC: From Micro/Nano Flows to Hypersonic Flows. – In: Physics Reports. Vol. 656. 2016, pp. 1-38.10.1016/j.physrep.2016.08.002
Search in Google Scholar Back to article
15. Stefanov, S. K. On DSMC Calculations of Rarefied Gas Flows with Small Number of Particles in Cells. – SIAM Journal on Scientific Computing, Vol. 33, 2011, No 2, pp. 677-702.10.1137/090751864
Search in Google Scholar Back to article
16. Taheri, E., E. Roohi, S. Stefanov. On the Convergence of the Simplified Bernoulli Trial Collision Scheme in Rarefied Fourier Flow. – Physics of Fluids, Vol. 29, 2017, 062003.10.1063/1.4985712
Search in Google Scholar Back to article
17. Roohi, E., et al. A Generalized Form of the Bernoulli Trial Collision Scheme in DSMC: Derivation and Evaluation. – Journal of Computational Physics, Vol. 354, 2018, pp. 476-492.10.1016/j.jcp.2017.10.033
Search in Google Scholar Back to article
18. Bird, G. A. Visual DSMC Program for Two-Dimensional and Axially Symmetric Flows. – In: The DS2V Program User’S Guide. Version 3.8. 2006. Sydney NSW 2000, Australia, G. A. B. Consulting Pty. Ltd.
Search in Google Scholar Back to article
19. Geuzaine, C., J.-F. Remacle. Gmsh: A 3-D Finite Element Mesh Generator with Built-in Pre- and Post-Processing Facilities. – International Journal for Numerical Methods in Engineering, Vol. 79, 2009, No 11, pp. 1309-1331.10.1002/nme.2579
Search in Google Scholar Back to article
20. Arkilic, E. B., M. A. Schmidt, K. S. Breuer. Gaseous Slip Flow in Long Microchannels. – Journal of Microelectromechanical Systems, Vol. 6, 1997, pp. 167-178.10.1109/84.585795
Search in Google Scholar Back to article
21.Shterev, K. S., S. K. Stefanov. Pressure Based Finite Volume Method for Calculation of Compressible Viscous Gas Flows. – Journal of Computational Physics, Vol. 229, 2010, pp. 461-480.10.1016/j.jcp.2009.09.042
Search in Google Scholar Back to article

Geometrically Non-Linear Vibration of a Cantilever Interacting with Rarefied Gas Flow

Abstract

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