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Research Papers

An Impedance-Based Approach for Rods With Shear-Type Damping Layer Treatment

[+] Author and Article Information
P. W. Wang

Assistant Professor
e-mail: meewpw@cc.hfu.edu.tw

D. Q. Zhuang

Graduate Research Assistant
Department of Mechatronic Engineering,
Huafan University,
New Taipei City, 223,
Taiwan, ROC

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received September 14, 2011; final manuscript received June 26, 2012; published online February 4, 2013. Assoc. Editor: Wei-Hsin Liao.

J. Vib. Acoust 135(1), 011009 (Feb 04, 2013) (9 pages) Paper No: VIB-11-1207; doi: 10.1115/1.4007263 History: Received September 14, 2011; Revised June 26, 2012

An impedance-based approach for analyzing an axial rod with shear-type damping layer treatment is proposed. The rod and shear-type damping layer are regarded as two subsystems and both impedances are calculated analytically. The system impedance can be obtained through the impedance coupling between the host rod and the damping layer. The shear-type damping layer is regarded as a shear spring with complex shear modulus. Under the traditional model, the damping coefficient diminishes with the increasing frequency. The paper develops two shear-type damping layer models, including the single degree-of-freedom (SDOF) model and continuous model to predict the behavior of the damping layer. Both damping layer models are compared with the traditional model and the system responses from these models are validated by finite element method (FEM) code COMSOL Multiphysics. Results show that the damping coefficients of both the traditional shear-spring model and SDOF model diminish as the increasing frequency so that the system responses are discrepant with that from COMSOL in the high frequency range. On the other hand, the system response from the continuous model is consistent with that from COMSOL in the full frequency range. Hence, the continuous damping layer model can predict a correct damping coefficient in the high frequency range and this property can be also employed to improve the analysis of the constrained-layer damping treated structures. Finally, the modal loss factor and fundamental frequency of the system with respect to different damping layer thicknesses are presented using the developed approach.

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References

Gatti, G., Brennan, M. J., and Gardonio, P., 2007, “Active Damping of a Beam Using a Physically Collocated Accelerometer and Piezoelectric Patch Actuator,” J. Sound Vib., 303(3–5), pp. 798–813. [CrossRef]
Shen, I. Y., 1994, “Hybrid Damping Through Intelligent Constrained Layer Treatments,” ASME J. Vib. Acoust., 116(3), pp. 341–349. [CrossRef]
Baz, A., and Ro, J., 1995, “Optimum Design and Control of Active Constrained Layers Damping,” ASME J. Vib. Acoust., 117(3), pp. 135–144. [CrossRef]
Chantalakhana, C., and Stanway, R., 2001, “Active Constrained Layer Damping of Clamped-Clamped Plate Vibrations,” J. Sound Vib., 241(5), pp. 755–777. [CrossRef]
Liu, T. X., Hua, H. X., and Zhang, Z. Y., 2004, “Robust Control of Plate Vibration via Active Constrained Layer Damping,” Thin Wall. Struct., 42(3), pp. 427–448. [CrossRef]
Yildiz, A., and Stevens, K.,1985, “Optimum Thickness Distribution of Unconstrained Viscoelastic Damping Layer Treatments for Plates,” J. Sound Vib., 103(2), pp. 183–199. [CrossRef]
Lumsdaine, A., and Scott, R. A., 1998, “Shape Optimization of Unconstrained Viscoelastic Layers Using Continuum Finite Elements,” J. Sound Vib., 216(1), pp. 29–52. [CrossRef]
McNamara, R. J., 1977, “Tuned Mass Dampers for Buildings,” J. Struct. Div., 103(ST9), pp. 1985–1988.
Kerwin, E. M., 1959, “Damping of Flexural Waves by a Constrained Viscoelastic Layer,” J. Acoust. Soc. Am., 31, pp. 952–962. [CrossRef]
DiTaranto, R. A., 1965, “Theory of Vibratory Bending for Elastic and Viscoelastic Layered Finite-Length Beams,” ASME J. Appl. Mech., 32, pp. 881–886. [CrossRef]
Mead, D. J., and Markus, S., 1969, “The Forced Vibration of a Three-Layer, Damped Sandwich Beam With Arbitrary Boundary Conditions,” J. Sound Vib., 10, pp. 163–175. [CrossRef]
Yan, M. J., and Dowell, E. H., 1972, “Governing Equations of Vibrating Constrained-Layer Damping Sandwich Plates and Beams,” ASME J. Appl. Mech., 39, pp. 1041–1046. [CrossRef]
Mead, D. J., and Yaman, Y., 1991, “The Harmonic Response of Rectangular Sandwich Plates With Multiple Stiffening: A Flexural Wave Analysis,” J. Sound Vib., 145, pp. 409–428. [CrossRef]
Chen, Y. C., and Huang, S. C., 1998, “A Simplified Theory for the Vibration of Plates With CLD Treatment,” J. Wave Mater. Interact., 13, pp. 34–57.
Lu, Y. P., Roscoe, A. J., and Douglas, B. E., 1991, “Analysis of the Response of Damped Cylindrical Shells Carrying Discontinuously Constrained Beam Elements,” J. Sound Vib., 150, pp. 395–403. [CrossRef]
Ramesh, T. C., and Ganesan, N., 1994, “Orthotropic Cylindrical Shells With a Viscoelastic Core: A Vibration and Damping Analysis,” J. Sound Vib., 175, pp. 535–555. [CrossRef]
Hu, Y. C., and Huang, S. C.,1999, “Forced Response of Sandwich Ring With Viscoelastic Core Subjected to Traveling Loads,” J. Acoust. Soc. Am., 106, pp. 202–210. [CrossRef]
Zhang, X. M., and Erdman, A. G., 2001, “Dynamic Response of Flexible Linkage Mechanisms With Viscoelastic Constrained Layer Damping Treatment,” Comput. Struct., 13, pp. 1265–1274. [CrossRef]
Nokes, D. S., and Nelson, F. C., 1968, “Constrained Layer Damping With Partial Coverage,” Shock Vib. Bull., 38, pp. 5–10.
Lall, A. K., Asnani, N. T., and Nakra, B. C., 1987, “Vibration and Damping Analysis of Rectangular Plate With Partially Covered Constrained Viscoelastic Layer,” J. Vib. Acoust., 109, pp. 241–247. [CrossRef]
Lall, A. K., Asnani, N. T., and Nakra, B. C., 1988, “Damping Analysis of Partially Covered Sandwich Beams,” J. Sound Vib., 123, pp. 247–259. [CrossRef]
Zheng, H., Tan, X. M., and Cai, C., 2006, “Damping Analysis of Beams Covered With Multiple PCLD Patches,” Int. J. Mech. Sci., 48, pp. 1371–1383. [CrossRef]
Cai, C., Zheng, H., and Liu, G. R., 2004,“Vibration Analysis of a Beam With PCLD Patch,” Appl. Acoust., 65(11), pp. 1057–1076. [CrossRef]
Kumar, N., and Singh, S. P., 2010, “Experimental Study on Vibration and Damping of Curved Panel Treated With Constrained Viscoelastic Layer,” Compos. Struct., 92, pp. 233–243. [CrossRef]
Chantalakhana, C., and Stanway, R., 2000, “Active Constrained Layer Damping of Plate Vibrations: A Numerical and Experimental Study of Modal Controllers,” Smart Mater. Struct., 9, pp. 940–952. [CrossRef]
Liang, C., Sun, F. P., and Rogers, C. A., 1994, “An Impedance Method for Dynamic Analysis of Active Material System,” ASME J. Vib. Acoust., 116, pp. 121–128. [CrossRef]
Zhou, S. W., Liang, C., and Rogers, C. A.,1996, “An Impedance-Based System Modeling Approach for Induced Strain Actuator-Driven Structures,” ASME J. Vib. Acoust., 118, pp. 323–331. [CrossRef]
Cheng, C. C., and Wang, P. W., 2001, “Applications of the Impedance Method on Multiple Piezoelectric Actuators Driven Structures,” ASME J. Vib. Acoust., 123(2), pp. 262–268. [CrossRef]
Bishop, R. E. D., and Johnson, D. C., 1979, The Mechanics of Vibration, University Press, Cambridge, UK, p. 277.

Figures

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Fig. 1

(a) Illustration of the system; (b) an equivalent model of Fig. 1(a)

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Fig. 2

Shear deformation of the nth segment of the damping layer

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Fig. 3

Inertial model of the shear-type damping layer

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Fig. 4

Continuous model of the shear-type damping layer

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Fig. 5

Shear impedance of the damping layer

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Fig. 6

Resultant impedance of the damping layer using SDOF model

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Fig. 7

Resultant impedance of the damping layer using continuous model

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Fig. 8

Comparison of the continuous model and the SDOF model

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Fig. 9

Real part of the resultant impedance of the damping layer

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Fig. 10

Driving point mobility of the system

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Fig. 11

Fundamental frequency of the system with respect to different damping layer thickness

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Fig. 12

System loss factor with respect to different damping layer thickness

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