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

1. Paidoussis, M. Fluid-Structure Interactions. Second Edition. 2013.10.1016/B978-0-12-397312-2.00001-6Search in Google Scholar

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, 044316.10.1063/1.2970154Search in Google Scholar

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. 10.1063/1.242972.10.1063/1.2429726Search in Google Scholar

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, 114913.10.1063/1.2136418Search in Google Scholar

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, 044908.10.1063/1.2654274Search in Google Scholar

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.2012.03.001Search in Google Scholar

7. Chakraborty, D., et al. Fluid-Structure Interaction in Deformable Microchannels. – Physics of Fluids, Vol. 24, 2012, No 10, p. 102002.10.1063/1.4759493Search in Google Scholar

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, 70.10.1088/0960-1317/12/1/311Search in Google Scholar

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.2008.1.4.449Search in Google Scholar

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.2019.103239Search in Google Scholar

11. Meirovitch, L. Fundamentals of Vibrations. McGraw-Hill, 2001.10.1115/1.1421112Search in Google Scholar

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

13. Bird, G. A. Molecular, Gas Dynamics and the Direct Simulation of Gas Flows. Oxford, Clarendon Press, 1994.Search in Google Scholar

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.2016.08.002Search in Google Scholar

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. 677-702.10.1137/090751864Search in Google Scholar

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, 062003.10.1063/1.4985712Search in Google Scholar

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.2017.10.033Search in Google Scholar

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

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.2579Search in Google Scholar

20. Arkilic, E. B., M. A. Schmidt, K. S. Breuer. Gaseous Slip Flow in Long Microchannels. – Journal of Microelectromechanical Systems, Vol. 6, 1997, pp. 167-178.10.1109/84.585795Search in Google Scholar

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.2009.09.042Search in Google Scholar