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Abstract
This paper presents both theoretically and experimentally a new kind of a broadband vibration isolator. It is a table-like system formed by four parallel hybrid periodic rods connected between two plates. The rods consist of an assembly of periodic cells, each cell being composed of a short rod and piezoelectric inserts. By actively controlling the piezoelectric elements, it is shown that the periodic rods can efficiently attenuate the propagation of vibration from the upper plate to the lower one within critical frequency bands and consequently minimize the effects of transmission of undesirable vibration and sound radiation. In such a system, longitudinal waves can propagate from the vibration source in the upper plate to the lower one along the rods only within specific frequency bands called the "Pass Bands" and wave propagation is efficiently attenuated within other frequency bands called the "Stop Bands". The spectral width of these bands can be tuned according to the nature of the external excitation. The theory governing the operation of this class of vibration isolator is presented and their tunable filtering characteristics are demonstrated experimentally as functions of their design parameters. This concept can be employed in many applications to control the wave propagation and the force transmission of longitudinal vibrations both in the spectral and spatial domains in an attempt to stop/attenuate the propagation of undesirable disturbances.
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References
- Asiri, S., 2005, "Vibration Isolation of Automotive Vehicle Engine Using Periodic Mounting Systems,"SPIE 2005, San Diego, California, USA.
- Asiri, S., Baz, A. and Pines, D., 2004, "Active Periodic Struts for Gearbox support System," Proc. of SPIE, Smart Structures and Materials 2004: Damping and Isolation, Vol. 5386, pp. 347-358.
- Asiri, S., Baz, A. and Pines, D., 2002, "Periodic Struts for
- Gearbox Support System," Proc. Of the 2002 International Congress and Exposition on Noise Control Engineering, Inter Noise 2002, Paper number IN02-644, Dearborn, MI, USA.
- Baz, A., 2001, "Active Control of Periodic Structures," ASME Journal of Vibration and Acoustics, Vol. 123, pp. 472-479.
- Baz, A., 2002, "Vibration Damping," Class Notes, University of Maryland at College Park.
- Baz, A., 2000, "Spectral Finite Element Modeling of Longitudinal Wave Propagation in Rods with Active Constrained Layer Damping," Smart Materials and Structures, Vol. 9(3), pp. 372-377.
- Brillouin, L., 1953, "Wave Propagation in Periodic Structures," 2nd ed. Dover.
- Cremer, L., Heckel, M. and Ungar, E., 1973, "Structure- Borne Sound," Springer-Verlag, New York.
- Doyle, J., 1997, "Wave Propagation in Structures," 2nd ed., Springer-Verlag, New York.
- Faulkner, M. and Hong, D., 1985, "Free Vibration of a Mono-Coupled Periodic System," J. of Sound and Vibrations, Vol. 99, pp. 29-42.
- Gupta, S., 1970, "Natural Flexural Waves and the Normal
- Modes of Periodically-Supported Beams and Plates," J. of Sound and Vibration, Vol. 13, pp. 89-111.
- Mead, D. J. , 1986, "A New Method of Analyzing Wave Propagation in Periodic Structures; Applications to Periodic Timoshenko Beams and Stiffened Plates," J. of Sound and Vibration, Vol. 114, pp. 9-27.
- Mead, D.J., 1970, "Free Wave Propagation in Periodically Supported, Infinite Beams," J. of Sound and Vibration, Vol. 11, pp. 181-197.
- Mead, D. J., 1971, "Vibration Response and Wave Propagation in Periodic Structures," J. of Engineering for Industry, Vol. 21, pp. 783-792.
- Mead, D. J., 1975, "Wave Propagation and Natural Modes in Periodic Systems: I. Mono-Coupled Systems," J. of Sound and Vibration, Vol. 40, pp. 1-18.
- Mead, D. J., 1996, "Wave Propagation in Continuous Periodic Structures: Research Contributions from Southampton," J. of Sound and Vibration, Vol. 190, pp. 495-524.
- Mead, D. J. and Bardell, N. S., 1987, "Free Vibration of a Thin Cylindrical Shell with Periodic Circumferential Stiffeners," J. of Sound and Vibration, Vol. 115, pp. 499-521.
- Mead, D. J. and Markus, S., 1983, "Coupled Flexural- Longitudinal Wave Motion in a Periodic Beam," J. of Sound and Vibration, Vol. 90, pp. 1-24.
- Mead, D. J. and Yaman, Y., 1991, "The Harmonic Response of Rectangular Sandwich Plates with Multiple Stiffening: AFlexural Wave Analysis," J. of Sound and Vibration, Vol. 145, pp. 409-428.
- Orris, R. and Petyt, M., 1974, "A Finite Element Study of Harmonic Wave Propagation in Periodic Structures," J. of Sound and Vibration, Vol. 33(2), pp. 223-237.
- Patera, A., 1984, "A Spectral Element Method for Fluid Dynamics: Laminar Flow in Channel Expansion," J. of Comput. Physics, Vol. 54, pp. 468-488.
- Pierre, C., 1988, "Mode Localization and Eigenvalue Loci Veering Phenomena in Disordered Structures," J. of Sound and Vibration, Vol. 126, pp. 485-502.
- Ravindra, B. and Mallik, K., 1992, "Harmonic Vibration Isolation Characteristics of Periodic Systems," J. of Sound and Vibration, Vol. 154(2), pp. 249-259.
- Richards, D. and Pines, D.J., 2003, "Passive Reduction of Gear Mesh Vibration Using a Periodic Drive Shaft," J. of Sound and Vibration, Vol. 264(2), pp. 317-342.
- Roy, A. and Plunkett, R., 1986, "Wave Attenuation in Periodic Structures," J. of Sound and Vibration, Vol. 114, pp. 395-411.
- Ruzzene, G. and Baz, A., 2000, "Control of Wave Propagation in Periodic Composite Rods using Shape Memory Inserts," J. of Vibration and Acoustics, Vol. 122, pp. 151-159.
- Sackman, S., Kelly, J. and Javid, A. A., 1999, "Layered Notch Filter for High-Frequency Dynamic Isolation," J. of Pressure Vessel Technology, Vol. 111, pp. 17-24.
- Singh, A., Pines, D. and Baz, A., 2004, "Active/Passive Reduction of Vibration of Periodic One-Dimensional Structures using Piezoelectric Actuators," Smart Materials and Structures, Vol. 13, pp. 698-711.
- Snowden, J.C., 1979, "Vibration Isolation: Use and Characterization," NBS Handbook, Vol. 128, US National Bureau of Standards.
- Szefi, J., Smith, E. and Lesieutre, G., 2004, "Design and Testing of a Compact Layered Isolator for High- Frequency Helicopter Gearbox Isolation," Prec. Of 45th AIAA Structures, Structural Dynamics and Materials Conference, Palm Spring, CA, USA.
References
Asiri, S., 2005, "Vibration Isolation of Automotive Vehicle Engine Using Periodic Mounting Systems,"SPIE 2005, San Diego, California, USA.
Asiri, S., Baz, A. and Pines, D., 2004, "Active Periodic Struts for Gearbox support System," Proc. of SPIE, Smart Structures and Materials 2004: Damping and Isolation, Vol. 5386, pp. 347-358.
Asiri, S., Baz, A. and Pines, D., 2002, "Periodic Struts for
Gearbox Support System," Proc. Of the 2002 International Congress and Exposition on Noise Control Engineering, Inter Noise 2002, Paper number IN02-644, Dearborn, MI, USA.
Baz, A., 2001, "Active Control of Periodic Structures," ASME Journal of Vibration and Acoustics, Vol. 123, pp. 472-479.
Baz, A., 2002, "Vibration Damping," Class Notes, University of Maryland at College Park.
Baz, A., 2000, "Spectral Finite Element Modeling of Longitudinal Wave Propagation in Rods with Active Constrained Layer Damping," Smart Materials and Structures, Vol. 9(3), pp. 372-377.
Brillouin, L., 1953, "Wave Propagation in Periodic Structures," 2nd ed. Dover.
Cremer, L., Heckel, M. and Ungar, E., 1973, "Structure- Borne Sound," Springer-Verlag, New York.
Doyle, J., 1997, "Wave Propagation in Structures," 2nd ed., Springer-Verlag, New York.
Faulkner, M. and Hong, D., 1985, "Free Vibration of a Mono-Coupled Periodic System," J. of Sound and Vibrations, Vol. 99, pp. 29-42.
Gupta, S., 1970, "Natural Flexural Waves and the Normal
Modes of Periodically-Supported Beams and Plates," J. of Sound and Vibration, Vol. 13, pp. 89-111.
Mead, D. J. , 1986, "A New Method of Analyzing Wave Propagation in Periodic Structures; Applications to Periodic Timoshenko Beams and Stiffened Plates," J. of Sound and Vibration, Vol. 114, pp. 9-27.
Mead, D.J., 1970, "Free Wave Propagation in Periodically Supported, Infinite Beams," J. of Sound and Vibration, Vol. 11, pp. 181-197.
Mead, D. J., 1971, "Vibration Response and Wave Propagation in Periodic Structures," J. of Engineering for Industry, Vol. 21, pp. 783-792.
Mead, D. J., 1975, "Wave Propagation and Natural Modes in Periodic Systems: I. Mono-Coupled Systems," J. of Sound and Vibration, Vol. 40, pp. 1-18.
Mead, D. J., 1996, "Wave Propagation in Continuous Periodic Structures: Research Contributions from Southampton," J. of Sound and Vibration, Vol. 190, pp. 495-524.
Mead, D. J. and Bardell, N. S., 1987, "Free Vibration of a Thin Cylindrical Shell with Periodic Circumferential Stiffeners," J. of Sound and Vibration, Vol. 115, pp. 499-521.
Mead, D. J. and Markus, S., 1983, "Coupled Flexural- Longitudinal Wave Motion in a Periodic Beam," J. of Sound and Vibration, Vol. 90, pp. 1-24.
Mead, D. J. and Yaman, Y., 1991, "The Harmonic Response of Rectangular Sandwich Plates with Multiple Stiffening: AFlexural Wave Analysis," J. of Sound and Vibration, Vol. 145, pp. 409-428.
Orris, R. and Petyt, M., 1974, "A Finite Element Study of Harmonic Wave Propagation in Periodic Structures," J. of Sound and Vibration, Vol. 33(2), pp. 223-237.
Patera, A., 1984, "A Spectral Element Method for Fluid Dynamics: Laminar Flow in Channel Expansion," J. of Comput. Physics, Vol. 54, pp. 468-488.
Pierre, C., 1988, "Mode Localization and Eigenvalue Loci Veering Phenomena in Disordered Structures," J. of Sound and Vibration, Vol. 126, pp. 485-502.
Ravindra, B. and Mallik, K., 1992, "Harmonic Vibration Isolation Characteristics of Periodic Systems," J. of Sound and Vibration, Vol. 154(2), pp. 249-259.
Richards, D. and Pines, D.J., 2003, "Passive Reduction of Gear Mesh Vibration Using a Periodic Drive Shaft," J. of Sound and Vibration, Vol. 264(2), pp. 317-342.
Roy, A. and Plunkett, R., 1986, "Wave Attenuation in Periodic Structures," J. of Sound and Vibration, Vol. 114, pp. 395-411.
Ruzzene, G. and Baz, A., 2000, "Control of Wave Propagation in Periodic Composite Rods using Shape Memory Inserts," J. of Vibration and Acoustics, Vol. 122, pp. 151-159.
Sackman, S., Kelly, J. and Javid, A. A., 1999, "Layered Notch Filter for High-Frequency Dynamic Isolation," J. of Pressure Vessel Technology, Vol. 111, pp. 17-24.
Singh, A., Pines, D. and Baz, A., 2004, "Active/Passive Reduction of Vibration of Periodic One-Dimensional Structures using Piezoelectric Actuators," Smart Materials and Structures, Vol. 13, pp. 698-711.
Snowden, J.C., 1979, "Vibration Isolation: Use and Characterization," NBS Handbook, Vol. 128, US National Bureau of Standards.
Szefi, J., Smith, E. and Lesieutre, G., 2004, "Design and Testing of a Compact Layered Isolator for High- Frequency Helicopter Gearbox Isolation," Prec. Of 45th AIAA Structures, Structural Dynamics and Materials Conference, Palm Spring, CA, USA.