# Vibration Suppression of a Micropipe Conveying Fluid via Sliding Mode Technique

• Zahra Jafari Shahbazzadeh PhD student of Shiraz university
• Ramin Vatankhah School of Mechanical Engineering, Shiraz University, Shiraz, Iran
Keywords: MEMS, Micropipe, Piezoelectric, Couple Stress Theorem, Hamilton’s Principle, Sliding Mode Controller

### Abstract

In this article, derivation of a nonlinear model and nonlinear controller design for a micropipe conveying fluid, which is excited with a piezoelectric actuator, are accomplished. The governing equations are derived by using Hamilton’s principle. The difference between the equations in micro-scales and macro-scales is established by using the modified couple stress theory. Unlike the classical Timoshenko beam theory, this new theorem includes a material length scale parameter which could help capturing the size effect. In addition, for thin members, so long as the deformation in the order of thickness, they do not remain in the elastic zone. Therefore, the linear theorem produces error in predicting in-plane movement of the member. In this way, the nonlinear terms are considered in the equations by applying mid-plane stretching theory. After this derivation, a frequency analysis is performed on the model. In addition, the effective parameters on the peak value of the response are studied as well. Finally, a sliding mode controller for the input voltage of the system is designed. It has been observed that by using this type of nonlinear controller, the behavior of the system could be improved significantly.

### References

[1] K. Subramani and W. Ahmed, Emerging nanotechnologies in dentistry: Processes, materials and applications. William Andrew, 2011.
[2] 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.
[3] L. Csepregi, “Micromechanics: A silicon microfabrication technology,” Microelectron. Eng., vol. 3, no. 1–4, pp. 221–234, 1985.
[4] 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.
[5] W. P. Eaton and J. H. Smith, “Micromachined pressure sensors: review and recent developments,” Smart Mater. Struct., vol. 6, no. 5, p. 530, 1997.
[6] O. Brand, I. Dufour, H. Stephen, and J. Fabien, Resonant MEMS: Fundamentals, Implementation, and Application. John Wiley & Sons, 2015.
[7] 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.
[8] A. Arbind and J. N. Reddy, “Nonlinear analysis of functionally graded microstructure-dependent beams,” Compos. Struct., vol. 98, pp. 272–281, 2013.
[9] 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.
[10] 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.
[11] 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.
[12] 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.
[13] 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.
[14] 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.
[15] 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.
[16] 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.
[17] 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.
[18] 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.
[19] 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.
[20] S. K. Park and X. Gao, “Bernoulli – Euler beam model based on a,” vol. 2355, pp. 0–5, 2006.
[21] Lai, W. M., Rubin, D. H., Krempl, E., & Rubin, D. (2009). Introduction to continuum mechanics. Butterworth-Heinemann.
[22] 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.
Published
2019-09-01
How to Cite
Jafari Shahbazzadeh, Z., Vatankhah, R., & Eghtesad, M. (2019). Vibration Suppression of a Micropipe Conveying Fluid via Sliding Mode Technique. Majlesi Journal of Electrical Engineering, 13(3), 69-74. Retrieved from http://mjee.iaumajlesi.ac.ir/index/index.php/ee/article/view/2971
Section
Articles