An analytical model is developed for active control of nonlinear flexural vibrations of cylindrical shells under random excitation. A velocity feedback control scheme is integrated into the governing equations of motion using discrete surface-bonded piezoelectric materials as collocated sensors/actuators. Donnell's thin shell theory is used to develop the governing equations of motion. A Monte Carlo simulation of stationary random processes, multi-mode Galerkin like approach, and numerical integration procedures are used to develop nonlinear response solutions of simply-supported cylindrical shells. Numerical results include time domain response histories, root mean square values and histograms of probability density. Parametric studies are performed to investigate the effect of nonlinearity, actuator placement, actuator number and size, and control gains.
Get full access to this article
View all access options for this article.
References
1.
Anderson, E. H. and N. W. Hagood. 1994. "Simultaneous piezoelectric sensing/actuation: analysis and application to controlled structures,"Journal of Sound and Vibration, 174(5):617-639.
2.
ANSI/IEEE Standard 176 . 1987. Piezoelectricity, Institute of Electric and Electronics Engineers, New York.
3.
Baz, A. , K. Imam and J. McCoy. 1990. "Active vibration control of flexible beams using shape memory actuators,"Journal of Sound and Vibration, 140(3):437-456.
4.
Chu, H. N.1961. "Influence of large amplitude on flexural vibrations of a thin circular cylindrical shell,"Journal of The Aerospace Sciences, 28:602-609.
5.
Crawley, E. F. and J. De Luis. 1987. "Use of piezoelectric actuators as element of intelligent structures,"AIAA Journal, 25(10):1373-1385.
6.
Crawley, E. F. and K. B Lazarus. 1991. "Induced strain actuation of isotropic and anisotropic plates,"AIAA Journal, 29(6):944-951.
7.
Crawley, E. F.1994. "Intelligent structures for aerospace: A technology overview and assessment,"AIAA Journal, 32(8):1689-1699.
8.
Dogan, V. and R. Vaicaitis. 1999. "Nonlinear response of cylindrical shells to random excitation," to appear in Nonlinear Dynamics, An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems.
9.
Dosch, J. J. , D. J. Inman and E. Garcia. 1992. "A self-sensing piezoelectric actuator for collocated control,"Journal of Intelligent Material Systems and Structures, 3:166-185.
10.
Dowell, E. H. and C. S. Ventres. 1968. "Modal equations for the nonlinear flexural vibrations of a cylindrical shell,"International Journal of Solids and Structures, 4:975-991.
11.
Fuller, C. R , C. A. Rogers and H. H. Robertshaw. 1992. "Control of sound radiation with active/adaptive structures,"Journal of Sound and Vibrations, 157(1):19-39.
12.
Fuller, C. R. , S. D. Snyder, C. H. Hansen and R. J. Sicox. 1992. "Active control of interior noise in model aircraft fuselages using piezoceramic actuators,"AIAA Journal, 30(11):2613-2617.
13.
Kim, S. J. and J. D. Jones. 1991. "Optimal design of piezoactuators for active noise and vibration control,"AIAA Journal, 29(12):2047-2053.
14.
Koshigoe, S. and J. W. Murdock. 1993. "A unified analysis of both active and passive damping for a plate with piezoelectric transducers,"The Journal of Acoustical Society of America, 93(1):346-355.
15.
Koshigoe, S. , J. T. Gillis and E. T. Falangas. 1993. "A new approach for active control of sound transmission through an elastic plate backed by a rectangular cavity,"The Journal of Acoustical Society of America, 94(2):900-907.
16.
Lee, J. K.1990. "Theory of laminated piezoelectric plates for design of distributed sensors/actuators. Part I: Governing equations and reciprocal relationships,"The Journal of Acoustical Society of America, 87(3):1144-1158.
17.
Pan, J. , H. H. Colin and D. Snyder. 1992. "A study of the response of a simply supported beam to excitation by a piezoelectric actuator,"Journal of Intelligent Material Systems and Structures, 3:3-16.
Shinozuka, M. and C. M. Jan. 1972. "Digital simulation of random processes and its applications,"Journal of Sound and Vibration, 25(1):111-128.
20.
Simpson, M. A. , T. M. Luong, C. R. Fuller and J. D. Jones. 1991. "Full scale demonstration tests of cabin noise reduction using active vibration control,"Journal of Aircraft, 28(3):208-215.
21.
Soedel, W.1993. Vibrations of Shells and Plates, Marcel Dekker Inc., New York.
22.
Tzou, H. S. and H. Q. Fu. 1994. "A study of segmentation of distributed piezoelectric sensors and actuators, part 1: Theoretical analysis,"Journal of Sound and Vibration, 172(2):247-259.
23.
Tzou, H. S. , Y Bao and V. B. Venkayya. 1996a. "Parametric study of segmented transducers laminated on cylindrical shells, part l: sensor patches,"Journal of Sound and Vibration, 197(2):207-224.
24.
Tzou, H. S. , Y Bao and V. B. Venkayya. 1996b. "Parametric study of segmented transducers laminated on cylindrical shells, part 2: actuator patches,"Journal of Sound and Vibration, 197(2):225-249.
25.
Tzou, H. S. , 1993. Piezoelectric Shells Distributed Sensing and Control of Continua, Kluwer Academic Publishers, Dordrecht.
26.
Uchino, K.1986. "Electrostrictive actuators: Materials and applications", Ceramic Bulletin65(4):647-652.
27.
Wada, B. K. , J. L. Fanson and E. F. Crawley. 1990. "Adaptive structures,"Journal of Intelligent Material Systems and Structures, 1: 157-174.
28.
Wang, C. Y and R. Vaicaitis. 1998. "Active control of vibrations and noise of double wall cylindrical shells,"Journal of Sound and Vibration, 216(5):865-888.
29.
Wei, Y. and R. Vaicaitis. 1997. "Nonlinear models for double-wall systems for vibrations and noise control,"Journal of Aircraft, 34(6):802-810.
