Vibration Suppression of a Micropipe Conveying Fluid via Sliding Mode Technique
AbstractIn this article, derivation of a nonlinear model for a micropipe conveying fluid which is excited with a piezoelectric actuator as well as studynig the control of this system. The governing equations are derived using Hamilton’s principle. The difference between the equations in micro-scales and macro-scales is stablished using modified couple stress theory. The nonlinear terms of equations also arise from mid-plane stretching. After this derivation, a frequency analysis is done on the model. In addition, the effective parameters on the peak value of the response are also studied. Finally a sliding mode controller is designed for the input voltage of the system. Using this type of controller, it has been observed that the behavior of the system can be improved impressively.
 K. E. Petersen, “Petersen, Kurt E. "Dynamic micromechanics on silicon: Techniques and devices,” IEEE Trans. Electron Devices, vol. 25, no. 10, pp. 1241–1250, 1978.
 L. Csepregi, “Micromechanics: A silicon microfabrication technology,” Microelectron. Eng., vol. 3, no. 1–4, pp. 221–234, 1985.
 N. M. Elman and U. M. Upadhyay, “Medical Applications of Implantable Drug Delivery Microdevices Based on MEMS (Micro-Electro-Mechanical-Systems),” Curr. Pharm. Biotechnol., vol. 11, no. 4, pp. 398–406, 2010.
 W. P. Eaton and J. H. Smith, “Micromachined pressure sensors: review and recent developments,” Smart Mater. Struct., vol. 6, no. 5, p. 530, 1997.
 O. Brand, I. Dufour, H. Stephen, and J. Fabien, Resonant MEMS: Fundamentals, Implementation, and Application. John Wiley & Sons, 2015.
 S. K. Park and X. L. Gao, “Bernoulli-Euler beam model based on a modified couple stress theory,” J. Micromechanics Microengineering, vol. 16, no. 11, pp. 2355–2359, 2006.
 A. Arbind and J. N. Reddy, “Nonlinear analysis of functionally graded microstructure-dependent beams,” Compos. Struct., vol. 98, pp. 272–281, 2013.
 H. M. Ma, X. L. Gao, and J. N. Reddy, “A microstructure-dependent Timoshenko beam model based on a modified couple stress theory,” J. Mech. Phys. Solids, vol. 56, no. 12, pp. 3379–3391, 2008.
 B. Akgöz and Ö. Civalek, “Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory,” Compos. Struct., vol. 98, pp. 314–322, 2013.
 R. Vatankhah, A. Najafi, H. Salarieh, and A. Alasty, “Boundary stabilization of non-classical micro-scale beams,” Appl. Math. Model., vol. 37, no. 20–21, pp. 8709–8724, 2013.
 M. K. Kwak, S. Heo, and M. Jeong, “Dynamic modelling and active vibration controller design for a cylindrical shell equipped with piezoelectric sensors and actuators,” J. Sound Vib., vol. 321, no. 3–5, pp. 510–524, 2009.
 V. R. Sonti and J. D. Jones, “Active vibration control of thin cylindrical shells using piezo-electric actuators,” Proc. Conf. Recent Adv. Act. Control Sound Vib. Virginia Polytech. Inst. State Univ. Blacksburg, VA, pp. 21–38, 1991.
 H. C. Lester and S. Lefebvre, “Piezoelectric Actuator Models for Active Sound and Vibration Control of Cylinders,” J. Intell. Mater. Syst. Struct., vol. 4, no. 3, pp. 295–306, 1993.
 R. L. Clark and C. R. Fuller, “Active Control of Structurally Radiated Sound from an Enclosed Finite Cylinder,” J. Intell. Mater. Syst. Struct., vol. 5, no. 3, pp. 379–391, 1994.
 Y. Yildiz, A. Sabanovic, and K. Abidi, “Sliding-Mode Neuro-Controller for Uncertain Systems,” IEEE Trans. Ind. Electron., vol. 54, no. 3, pp. 1676–1685, 2007.
 H. Xu, M. D. Mirmirani, and P. A. Ioannou, “Adaptive Sliding Mode Control Design for a Hypersonic Flight Vehicle,” J. Guid. Control. Dyn., vol. 27, no. 5, p. 829–838., 2004.
 A. Shahraz and R. Bozorgmehry Boozarjomehry, “A fuzzy sliding mode control approach for nonlinear chemical processes,” Control Eng. Pract., vol. 17, no. 5, pp. 541–550, 2009.
 H. Q. T. N. Shin, Jin-Ho, and W.-H. Kim, “Fuzzy sliding mode control for a robot manipulator,” vArtificial Life Robot., vol. 13, no. 1, pp. 124–128, 2008.
 S. K. Park and X. Gao, “Bernoulli – Euler beam model based on a,” vol. 2355, pp. 0–5, 2006.
 Lai, W. M., Rubin, D. H., Krempl, E., & Rubin, D. (2009). Introduction to continuum mechanics. Butterworth-Heinemann.
 A. M. Dehrouyeh-Semnani, M. Nikkhah-Bahrami, and M. R. H. Yazdi, “On nonlinear vibrations of micropipes conveying fluid,” Int. J. Eng. Sci., vol. 117, pp. 20–33, 2017.