Skip to main content

Advertisement

SpringerLink
Log in

Genetic algorithm based optimal design for vibration control of composite shell structures using piezoelectric sensors and actuators

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

The present article deals with the design of optimal vibration control of smart fiber reinforced polymer (FRP) composite shell structures using genetic algorithm (GA) based linear quadratic regulator (LQR) and layered shell coupled electro-mechanical finite element analysis. Open loop procedure has been used for optimal placement of actuators considering the control spillover of the higher modes to prevent closed loop instability. An improved real coded GA based LQR control scheme has been developed for designing an optimal controller in order to maximize the closed loop damping ratio while keeping actuators voltages within limit. Results show that increased closed loop-damping has been achieved with a large reduction of control effort considering control spillover.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Abdullah, M.M., Richardson, A., Hanif, J.: Placement of sensors/actuators on civil structures using genetic algorithms. Earthquake Eng. Struct. Dynam. 30(8), 1167–1184 (2001). doi:10.1002/eqe.57

    Article  Google Scholar 

  • Ahamad, S., Irons, B.M., Zienkiewicz, O.C.: Analysis of thick and thin shell structure by curved elements. Int. J. Numer. Meth. Eng. 2, 419–451 (1970). doi:10.1002/nme.1620020310

    Article  Google Scholar 

  • Ang, K.K., Wang, S.Y., Quek, S.T.: Weighted energy linear quadratic regulator vibration control of piezoelectric composite plates. J. Smart Mater. Struct. 11, 98–106 (2002). doi:10.1088/0964-1726/11/1/311

    Article  Google Scholar 

  • Bailey, T., Hubbard, J.E.: Distributed piezoelectric polymer active vibration control of a cantilever beam. J. Guid. Control Dyn. 85, 605–611 (1985). doi:10.2514/3.20029

    Article  Google Scholar 

  • Balagurugan, V., Narayanan, S.: Active vibration control of smart shells using distributed piezoelectric sensors and actuators. Smart Mater. Struct. 10, 173–180 (2001). doi:10.1088/0964-1726/10/2/301

    Article  Google Scholar 

  • Balagurugan, V., Narayanan, S.: A piezoelectric higher-order plate finite for the analysis of multi-layer smart composite laminates. Smart Mater. Struct. 16, 2026–2039 (2007). doi:10.1088/0964-1726/16/6/005

    Article  Google Scholar 

  • Balagurugan, V., Narayanan, S.: A piezolaminated composite degenerated shell finite element for active control of structures with distributed piezosensors and actuators. Smart Mater. Struct. 17, 015031 (18 pp) (2008)

    Google Scholar 

  • Bhattacharya, P., Suhail, H., Sinha, P.K.: Finite element analysis and distributed control of laminated composite shells using LQR/IMSC approach. Aerosp. Sci. Technol. 6, 273–281 (2002). doi:10.1016/S1270-9638(02)01159-8

    Article  MATH  Google Scholar 

  • Bruch, J.C., Sloss, J.M., Sadek, I.S.: Optimal piezo-actuator locations/lengths and applied voltage for shape control of beams. J. Smart Mater. Struct. 9, 205–211 (2002)

    Article  Google Scholar 

  • Chee, C.Y.K., Tong, L., Steven, G.P.: A mixed model for composite beams with piezoelectric actuators and sensors. J. Smart Mater. Struct. 8, 417–432 (1999). doi:10.1088/0964-1726/8/3/313

    Article  Google Scholar 

  • Chen, S.H., Yao, G.F., Huang, C.: A new intelligent thin shell element. J. Smart Mater. Struct. 9, 10–18 (2000). doi:10.1088/0964-1726/9/1/302

    Article  Google Scholar 

  • Christensen, R.H., Santos, I.F.: Design of active controlled rotor-blade systems based on time-variant modal analysis. J. Sound Vibrat. 280, 863–882 (2005). doi:10.1016/j.jsv.2003.12.046

    Article  MathSciNet  Google Scholar 

  • Crawley, E.F., Luis, J.: Use of piezoelectric actuators as elements of intelligent structures. AIAA J. 25(10), 1373–1385 (1987). doi:10.2514/3.9792

    Article  Google Scholar 

  • Deb, K., Gulati, S.: Design of truss-structures for minimum weight using genetic algorithms. Finite Elem. Anal. Des. 37, 447–465 (2001). doi:10.1016/S0168-874X(00)00057-3

    Article  MATH  Google Scholar 

  • Guo, H.Y., Zhang, L., Zhang, L.L., Zhou, J.X.: Optimal placement of sensors for structural health monitoring using improved genetic algorithm. J. Smart Mater. Struct. 13, 528–534 (2004). doi:10.1088/0964-1726/13/3/011

    Article  Google Scholar 

  • Han, J.H., Lee, L.: Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms. J. Smart Mater. Struct. 8, 257–267 (1999). doi:10.1088/0964-1726/8/2/012

    Article  MathSciNet  Google Scholar 

  • Hiramoto, K., Doki, H., Obinata, G.: Optimal sensor/actuator placement for active vibration control using explicit solution of algebraic Riccati equation. J. Sound Vibrat. 229(5), 1057–1075 (2000). doi:10.1006/jsvi.1999.2530

    Article  MathSciNet  Google Scholar 

  • Hwang, W.S., Park, H.C.: Finite element modeling of piezoelectric sensors and actuators. AIAA J. 31(5), 930–937 (1993). doi:10.2514/3.11707

    Article  Google Scholar 

  • Kang, Y.K., Park, H.C., Kim, J., Choi, S.B.: Interaction of active and passive vibration control of laminated composite beams with piezoceramics sensors/actuators. Mater. Des. 23, 277–286 (2002)

    Google Scholar 

  • Kulkarni, S.A., Bajoria, K.M.: Finite element modeling of smart plates/shells using higher order shear deformation theory. Compos. Struct. 62, 41–50 (2003). doi:10.1016/S0263-8223(03)00082-5

    Article  Google Scholar 

  • Kusculuoglu, Z.K., Royston, T.J.: Finite element formulation for composite plates with piezoelectric layers for optimal vibration control applications. J. Smart Mater. Struct. 14, 1139–1153 (2005). doi:10.1088/0964-1726/14/6/007

    Article  Google Scholar 

  • Lee, C.K.: Theory of laminated piezoelectric plates for the design of distributed sensors/actuators Part 1: governing equations and reciprocal relationships. J. Acoust. Soc. Am. 87(3), 1144–1158 (1990). doi:10.1121/1.398788

    Article  Google Scholar 

  • Lee, S., Goo, N.S., Park, H.C., Yoon, K.J., Cho, C.: A nine- node assumed strain shell element for analysis of a coupled electro-mechanical system. Smart Mater. Struct. 12, 355–362 (2003). doi:10.1088/0964-1726/12/3/306

    Article  Google Scholar 

  • Lewis, F.L.: Optimal control. Wiley, New York (1986)

    MATH  Google Scholar 

  • Li, Q.S., Liu, D.K., Tang, J., Zhang, N., Tam, C.M.: Combinatorial optimal design of number and positions of actuators in actively controlled structures using genetic algorithm. J. Sound Vibrat. 270, 611–624 (2004). doi:10.1016/S0022-460X(03)00130-5

    Article  MathSciNet  Google Scholar 

  • Liu, W., Hou, Z.K., Demetriou, M.A.: A computational scheme for the optimal sensor/actuator placement of flexible structures using spatial H-2 measures. Mech. Syst. Signal Process. 20(4), 881–895 (2006). doi:10.1016/j.ymssp.2005.08.030

    Article  Google Scholar 

  • Marinković, D., Köppe, H., Gabbert, U.: Degenerate shell element for geometrically nonlinear analysis of thin-walled piezoelectric active structures. Smart Mater. Struct. 17, 015030 (10 pp) (2008)

    Google Scholar 

  • Narayanan, S., Balamurugan, V.: Finite element modeling of piezolaminated smart structures for active vibration control with distributed sensors and actuators. J. Sound Vibrat. 262, 529–562 (2003). doi:10.1016/S0022-460X(03)00110-X

    Article  Google Scholar 

  • Nguyen, Q., Tong, L.: Voltage and evolutionary piezoelectric actuator design optimisation for static shape control of smart plate structures. Mater. Des. 28, 387–399 (2007)

    Google Scholar 

  • Ram, K.S.S., Kiran, S.K.: Static behavior of laminated composite spherical shell cap with piezoelectric actuators. Smart Mater. Struct. 17, 015010 (9 pp) (2008)

    Google Scholar 

  • Ray, M.C., Bhattacharyya, R., Samanta, B.: Static analysis of intelligent structure by the finite element method. Comput. Struc. 52(4), 617–631 (1994). doi:10.1016/0045-7949(94)90344-1

    Article  MATH  Google Scholar 

  • Reddy, J.N.: Exact solution of moderately thick laminated shells. J. Eng. Mech. 110(5), 794–809 (1984)

    Google Scholar 

  • Robandi, I., Nishimori, K., Nishimura, R., Ishihara, N.: Optimal feedback control design using genetic algorithm in multimachine power system. Electr. Power Energy Syst. 23, 263–271 (2001). doi:10.1016/S0142-0615(00)00062-4

    Article  Google Scholar 

  • Roy, T., Chakraborty, D.: GA-LQR based optimal vibration control of smart FRP composite structures with bonded PZT patches. J. Reinforced Plastics Composites (2008). doi:10.1177/0731684408089506

  • Sadri, A.M., Wright, J.R., Wynne, R.: Modeling and optimal placement of piezoelectric actuators in isotropic plates using genetic algorithm. J. Smart Mater. Struct. 8, 490–498 (1999). doi:10.1088/0964-1726/8/4/306

    Article  Google Scholar 

  • Saravanos, D.A., Christoforou, A.P.: Impact response of adaptive piezoelectric laminated plates. AIAA J. 40(10), 2087–2095 (2002)

    Article  Google Scholar 

  • Swann, C., Chattopadhyay, A.: Optimization of piezoelectric sensor location for delamination detection in composite laminates. Eng. Optim. 38(5), 511–528 (2006). doi:10.1080/03052150600557841

    Article  Google Scholar 

  • Tzou, H.S., Tsang, C.I.: Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a finite element approach. J. Sound Vibrat. 138(1), 17–24 (1990). doi:10.1016/0022-460X(90)90701-Z

    Article  Google Scholar 

  • Tzou, H.S., Ye, R.: Analysis of piezoelectric structures with laminated piezoelectric triangle shell elements. AIAA J. 34, 110–115 (1996). doi:10.2514/3.12907

    Article  MATH  Google Scholar 

  • Wan, J.G., Tao, B.Q.: Design and study on a 1-3 anisotropy piezocomposite sensor. Mater. Des. 21, 533–536 (2000)

    Google Scholar 

  • Wang, Q., Wang, C.: A controllability index for optimal design of piezoelectric actuators in vibration control of beam structures. J. Sound Vibrat. 242(3), 507–518 (2001). doi:10.1006/jsvi.2000.3357

    Article  Google Scholar 

  • Wang, S.Y., Tai, K., Quek, S.T.: Topology optimization of piezoelectric sensors/actuators for torsional vibration control of composite plates. J. Smart Mater. Struct. 15(2), 253–269 (2006)

    Article  Google Scholar 

  • Yang, Y., Jin, Z., Soh, C.K.: Integrated optimal design of vibration control system for smart beams using genetic algorithm. J. Sound Vibrat. 282, 1293–1307 (2005). doi:10.1016/j.jsv.2004.03.048

    Article  Google Scholar 

  • Zhang, N., Kirpitchenko, I.: Modelling dynamics of a continuous structure with a piezoelectric sensor/actuator for passive structural control. J. Sound Vibrat. 249(2), 251–261 (2002). doi:10.1006/jsvi.2001.3792

    Article  Google Scholar 

  • Zheng, S., Wang, X., Chen, W.: The formulation of refined hybrid enhanced assumed strain solid shell element and its application to model smart structures containing distributed piezoelectric sensors/actuators. Smart Mater. Struct. 13(43-N), 50 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    Tarapada Roy & Debabrata Chakraborty

Authors
  1. Tarapada Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Debabrata Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Debabrata Chakraborty.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roy, T., Chakraborty, D. Genetic algorithm based optimal design for vibration control of composite shell structures using piezoelectric sensors and actuators. Int J Mech Mater Des 5, 45–60 (2009). https://doi.org/10.1007/s10999-008-9085-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10999-008-9085-z

Keywords

Search

Navigation