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TECHNICAL PAPERS

Damping Characteristics of Beams with Enhanced Self-Sensing Active Constrained Layer Treatments Under Various Boundary Conditions

[+] Author and Article Information
J. X. Gao

Associate ProfessorMember ASMESmart Materials and Structures Laboratory, Department of Automation and Computer-Aided Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

W. H. Liao1

Associate ProfessorMember ASMESmart Materials and Structures Laboratory, Department of Automation and Computer-Aided Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

1

Corresponding author: e-mail: whliao@cuhk.edu.hk

J. Vib. Acoust 127(2), 173-187 (Jun 04, 2004) (15 pages) doi:10.1115/1.1891816 History: Received June 17, 2003; Revised June 04, 2004

In this paper, an energy-based approach is developed to investigate damping characteristics of beams with enhanced self-sensing active constrained layer (ESACL) damping treatments. Analytical formulations for the active, passive, and total hybrid modal loss factors of the cantilever and simply-supported beams partially covered with the ESACL are derived. The analytical formulations are validated with the results in the literature and experimental data for the cantilever beam. Beams with other boundary conditions can also be solved and discussed using the presented approach. The results show that the edge elements in the ESACL can significantly improve the system damping performance as compared to the active constrained layer damping treatment. The effects of key parameters, such as control gain, edge element stiffness, location, and coverage of the ESACL patch on the system loss factors, have been investigated. It has also been shown that the boundary conditions play an important role on the damping characteristics of the beam structure with the ESACL treatment. With careful analysis on the location and coverage of the partially covered ESACL treatment, effective vibration control for beams under various boundary conditions for specific modes of interest would be achieved.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Structure with enhanced self-sensing ACL (ESACL)

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Figure 2

Beam with partially covered EACL

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Figure 3

Geometry and deformation of a sandwich beam

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Figure 4

Configuration of the cantilever beams: (a) top view of the beam, (b) side view of the ACL treatment, and (c) side view of the EACL treatment

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Figure 5

Experimental setup

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Figure 6

Passive, active, and total hybrid modal loss factors vs. control gain for SACL system (KL=KR=0): ———total hybrid loss factor; – – –passive loss factor; - - -active loss factor

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Figure 7

Passive, active, and hybrid modal loss factors vs. control gain for ESACL system with different edge element stiffness: ———total hybrid loss factor; – – –passive loss factor; - - -active loss factor. (a) first mode (KL=KR=4×106N∕m), (b) first mode (KL=KR=5×107N∕m), (c) second mode (KL=KR=4×106N∕m), (d) second mode (KL=KR=5×107N∕m), (e) third mode (KL=KR=4×106N∕m), and (f) third mode (KL=KR=5×107N∕m)

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Figure 8

Passive, active, and hybrid modal loss factors vs. edge element stiffness for ESACL system with different control gain: ———total hybrid loss factor, – – –passive loss factor, - - -active loss factors (a) first mode with kg=0.01, (b) first mode with kg=0.1, (c) second mode with kg=0.01, (d) second mode with kg=0.1, (e) third mode with kg=0.01, and (f) third mode with kg=0.1

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Figure 9

The first three total hybrid modal loss factors of the ESACL system vs. the control gain and edge element stiffness

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Figure 10

Passive, active, and hybrid modal loss factors vs. location of ESACL: ———total hybrid loss factor, – – –passive loss factor, - - -active loss factor. (a) first mode with KL=KR=6×106N∕m and kg=0.05, (b) first mode with KL=KR=5×107N∕m and kg=0.1, (c) second mode with KL=KR=6×106N∕m and kg=0.05, (d) second mode with KL=KR=5×107N∕m and kg=0.1, (e) third mode with KL=KR=6×106N∕m and kg=0.05, and (f) third mode with KL=KR=5×107N∕m and kg=0.1

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Figure 11

The first three total hybrid loss factors vs. coverage ratio of ESACL with KL=KR=6×106N∕m and kg=0.05: ———first modal loss factor, – – –second modal loss factor, - - -third modal loss factor

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Figure 12

The first three total hybrid modal loss factors of the simply-supported beam with ESACL vs. control gain and edge element stiffness

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Figure 13

Passive, active, and hybrid modal loss factors vs. location of ESACL for simply-supported beam with ESACL: ———total hybrid loss factor, – – –passive loss factor, - - -active loss factor: (a) first mode with KL=KR=4×106N∕m, (b) first mode with KL=KR=107N∕m, (c) second mode with KL=KR=4×106N∕m, (d) second mode with KL=KR=107N∕m, (e) third mode with KL=KR=4×106N∕m, and (f) third mode with KL=KR=107N∕m

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Figure 14

The first three total hybrid modal loss factors vs. coverage ratio of ESACL for simply-supported beam with KL=KR=107N∕m and kg=0.01: ———first modal loss factor, – – –second modal loss factor, - - -third modal loss factor

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