Partial and Segmented Modal Sensors for Beam Structures

Abstract

The idea of using shaped sensors, and to a lesser extent actuators, for beam- and plate-type structures has been a subject of intense interest for many years. Typically for beam-type problems, the sensor width is varied along the length of the beam. The shape of the sensor is obtained by considering the modes of the beam and usually requires that the sensor covers the whole beam. This paper extends the previous results for distributed sensors for beams in two ways: the optimum sensor shapes that cover only a portion of the beam-type structures are derived and the optimum shapes for segmented sensors, that enable multiple modes to be sensed, are derived. The effect of geometric tolerances and the sensor output response to higher modes has been established. Although it is possible to derive the required sensor shapes, geometric tolerances will often make these sensors difficult to manufacture. The approach is demonstrated with a pinned-pinned beam example.

Keywords

Sensor modal vibration control

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References

Burke, S.E. and Hubbard, J.E. , 1991, "Distributed transducer vibration control of thin plates ," Journal of the Acoustical Society of America 90(2), 937-944.

Callahan, J. and Baruh, H. , 1995, "Active control of flexible structures using segmented Piezoelectric actuators," in Proceedings of the SPIE Smart Structures and Materials Conference: Smart Structures and Integrated Systems, San Diego, CA, vol. 2443, pp. 630-642.

Clark, R.L. and Burke, S.E. , 1996, "Practical limitations in achieving shaped modal sensors with induced strain materials," ASME, Journal of Vibration and Acoustics 118, 668-675.

Fletcher, R. , 1981, Practical Methods of Optimization: Volume 2 Constrained Optimization, John Wley, New York . Lee, C.-K. and Moon, F.C. , 1990, "Modal sensors/actuators ," ASME, Journal of Applied Mechanics 57, 434-441.

Maddox, I.J. , 1970, Elements of Functional Analysis, Cambridge University Press, Cambridge, UK.

Meirovitch, L. , 1986, Elements of Vibration Analysis, McGraw-Hill , New York.

Tanaka, N. , Synder, S.D. , and Hansen, C.H. , 1996, "Distributed parameter modal filtering using smart sensors ,"ASME, Journal of Vibration and Acoustics 118, 630-640.

Tzou H. S., Bao, Y. , and Venkayya, V.B. , 1996, "Parametric study of segmented transducers laminated on cylindrical shells, Part 1: Sensor patches," Journal of Sound and Vibration 197(2), 207-224.

Zhuang, Y. and Baras, J.S. , 1994, "Shape optimisation of distributed sensors and actuators for smart structure control," in Proceedings of the SPIE Smart Structures and Materials Conference: Smart Structures and Intelligent Systems, Orlando, FL, vol. 2190, pp. 381-388.