Modeling, Analysis and Control of a Smart Composite Structure

Authors: Nader H. Ghareeb, Mohamed S. Gaith, Sayed M. Soleimani

Abstract:

In modern engineering, weight optimization has a priority during the design of structures. However, optimizing the weight can result in lower stiffness and less internal damping, causing the structure to become excessively prone to vibration. To overcome this problem, active or smart materials are implemented. The coupled electromechanical properties of smart materials, used in the form of piezoelectric ceramics in this work, make these materials well-suited for being implemented as distributed sensors and actuators to control the structural response. The smart structure proposed in this paper is composed of a cantilevered steel beam, an adhesive or bonding layer, and a piezoelectric actuator. The static deflection of the structure is derived as function of the piezoelectric voltage, and the outcome is compared to theoretical and experimental results from literature. The relation between the voltage and the piezoelectric moment at both ends of the actuator is also investigated and a reduced finite element model of the smart structure is created and verified. Finally, a linear controller is implemented and its ability to attenuate the vibration due to the first natural frequency is demonstrated.

Keywords: Active linear control, Lyapunov stability theorem, piezoelectricity, smart structure, static deflection.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125793

References:

[1] S. Narayanan and V. Balamurugan, “Finite Element Modelling of Piezolaminated Smart Structures for Active Vibration Control with Distributed Sensors and Actuators,” Journal of Sound and Vibration, no. 262, pp. 529-562, 2003.
[2] R. Vepa, “Dynamics of Smart Structures”, John Wiley & Sons, 2010.
[3] N. Ghareeb, M. Gaith, T. Alloush and M. Al-Sarraf, ”Energy Harvesting from Vibrating Piezo-Electric Structures”, Journal of Robotics and Mechanical Engineering Research, vol. 1, issue 3, pp. 14-21, 2016
[4] W. Nash, “Strength of Materials”, McGraw-Hill New, York, 1972.
[5] T. Ikeda, “Fundamentals of Piezoelectricity”, Oxford University Press, Oxford, 1990.
[6] N. Ghareeb, “Design and Implementation of Linear Controllers for the Active Control of Reduced Models of Thin-Walled Structures”, PhD Thesis, RWTH Aachen University of Technology, Germany, 2013.
[7] A. Townley, “Vibrational energy harvesting using MEMS piezoelectric generators”, Electrical engineering release, University of Pennsylvania, 2009.
[8] J. Fanson, and J. Chen, “Structural Control by the Use of Piezoelectric Active Members”, Proc. of NASA/DOD Control-Structures Interaction Conference, NASA CP-2447, vol. 2, pp. 809-830, 1986.
[9] R. Craig and M. Bampton, “Coupling of Substructures for Dynamic Analyses”, AIAA J., vol. 6, no. 7, pp. 1313-1319, 1968.
[10] J. Block and T. Straganac, “Applied Active Control for a Nonlinear Aeroelastic Structure”, J. of Guidance, Control, and Dynamics, vol. 21, no. 6, pp. 838-845, 1998.
[11] M. Petyt, “Introduction to Finite element Vibration Analysis”, Cambridge University Press, 2003.