Periodic Isolator Design Enhancement via Vibration Confinement through Eigenvector Assignment and Piezoelectric Circuitry

Abstract

The objective of this research is to investigate the feasibility of utilizing eigenvector assignment and piezoelectric circuitry for enhancing vibration isolation performance of periodic isolators. For a classical periodic structure, stop bands are created due to material discontinuity so that wave propagation of external excitation can be suppressed within the stop band frequency range. While effective, such a method cannot always create wide enough stop bands such that all disturbance frequencies are covered. In this study, the eigenvector assignment technique and piezoelectric circuitry are utilized to reduce the transmissibility of the isolator modes near the boundary of the stop bands, and therefore widen the effective frequency range of vibration suppression of the periodic isolator. The principle of eigenvector assignment is to alter the mode shapes of the system so that the modal components corresponding to the concerned coordinates are as small as possible. By applying the eigenvector assignment method on the spatially tailored periodic isolator structure, the response amplitude of the attenuated end (the end of the isolator designed to have small vibration) at resonant frequencies near the stop band can be reduced, which enhances the vibration isolation performance in the frequency range of interest. On the other hand, piezoelectric circuits connecting to the isolator structure increase the degrees of freedom of the integrated system, and enlarge the design space for achievable eigenvectors. The eigenvectors of this integrated system are selected such that the modal energy in the concerned coordinates is minimized by using the Rayleigh Principle. The integrated system with assigned eigenvectors will re-distribute vibratory energy of the complete electromechanical system. Small vibration at the attenuated end of the isolator is achieved since the energy is confined in the circuitry and other parts of the isolator. Numerical simulations are performed to evaluate the effectiveness of the proposed method on vibration confinement for isolator designs. An integrated closed-loop system with state estimator is developed to realistically implement the proposed algorithm. It is shown that with the piezoelectric circuitry and eigenvector assignment, the system energy is redistributed and confined in the unconcerned regions, which can greatly enhance the performance of the vibration isolation system.

Keywords

Periodic isolator eigenvector assignment piezoelectric circuit vibration confinement.

Get full access to this article

View all access options for this article.

References

Andry, A. N. Jr. , Shapiro, E.Y. , and Chung, J.C. , 1983, “Eigenstructure assignment for linear systems ”, IEEE Transactions on Aerospace and Electronic Systems AES19(5), 711—729.

Chen, C.T. , 1984, Linear System Theory and Design, Holt, Rinehart, and Winston, Austin, Texas.

Corr, L.R. and Clark, W.W. , 1995, “Active and passive vibration confinement using piezoelectric transducers and dynamic vibration absorbers”, Proceedings of SPIE 3668, 747—758.

Cunningham, T.B. , 1980, “Eigenspace selection procedures for closed-loop response shaping with modal control”, Proceedings of the American Control Conference, December, pp.178—186.

Klema, V.C. and Laub, A.J. , 1980, “The singular value decomposition: its computation and some applications”, IEEE Transactions on Automatic Control AC25(2), 164—176.

Kwon, B.H. and Youn, M.J. , 1987, “Eigenvalue-generalized eigenvector assignment by output feedback”, IEEE Transactions on Automatic Control AC32(5), 417—421.

Mead, D.J. , 1996, “Wave propagation in continuous periodic structures: research contributions from Southampton 1964-1995,” Journal of Sound and Vibration 190(3), 495—524.

Meirovitch, L. , 1980, Computational Methods in Structural Dynamics, Sijthoff & Noorhoff.

Miller, L.R. , Ahmadian, M. , Nobles, C.M. , and Swanson, D.A. , 1995, “Modeling and performance of an experimental active vibration isolator”, ASME Journal of Vibration and Acoustics 117, 272—278.

10.

Morgan, R. and Wang, K.W. , 2002, “Active-passive piezoelectric absorbers for suppression of multiple non-stationary harmonic excitations”, Journal of Sound and Vibration 255(4), 685—700.

11.

Panza, M.J. , McGuire, D.P. , and Jones, P.J. , 1997, “Modeling, actuation, and control of an active fluid vibration isolator”, ASME Journal of Vibration and Acoustics 119, 52—59.

12.

Sciulli, Dino and Inman, Daniel J. , 1996, “Comparison of single- and two-degree-of-freedom models for passive and active vibration isolation design”, Proceedings of SPIE 2720, 293—304.

13.

Shelley, F.J. and Clark, W.W. , 2000a, “Active mode localization in distributed parameter systems with consideration of limited actuator placement, part 1: Theory”, ASME Journal of Vibration and Acoustics 122(2), 160—164.

14.

Shelley, F.J. and Clark, W.W. , 2000b, “Active mode localization in distributed parameter systems with consideration of limited actuator placement, part 2: Simulations and experiments”, ASME Journal of Vibration and Acoustics 122(2), 165—168.

15.

Szefi, J.T. , Smith, E.C. , and Lesieutre, G.A. , 2003, “Design and analysis of high-frequency periodically layered isolators for helicopter gearbox isolation”, in AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Vol. 5, pp. 3489—3502.

16.

Tang, J. and Wang, K.W. , 2004, “Vibration confinement via optimal eigenvector assignment and piezoelectric networks”, ASME Journal of Vibration and Acoustics 126(1), 27—36.

17.

Thorp, O. , Ruzzene, M. , and Baz, A. , 2001, “Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches”, Smart Materials and Structures 10(5), 979—989.

18.

Tsai, M.S. and Wang, K.W. , 1996, “Control of a ring structure with multiple active-passive hybrid piezoelectric networks”, Smart Materials and Structures 5(5), 695—703.