Analysis of damping characteristics for viscoelastic laminated beams

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T.-L. Teng, N.-K. Hu / Comput. Methods Appl. Mech. Engrg. 190 (2001) 3881±3892
Fig. 1. The con®guration of viscoelastic damping structures.
A constraining layer is added on the top of the viscoelastic material. The ¯exural modulus of the constraining layer is comparable to that of the base structure. Figs. 1(a) and (b) illustrate the con®guration of viscoelastic damping structures. The theory of the damped structures has been thoroughly investigated in recent years. Kerwin [1] developed a theory for the damping of ¯exural waves by a viscoelastic damping layer that is constrained between the surface to be damped and third, sti layer. Ungar [2] derived for the loss factors of axially uniform linear composite structures in terms of properties of the constituents. Ross et al. [3] closely examined the de®nition of loss factor in terms of energy, particularly for highly damped composite structures. Mead and Markus [4] derived the sixth-order dierential equation of motion in terms of the transverse displacement for a three-layer sandwich beam with a viscoelastic core. Groothuhuis [5] described the control of vibrations with three applications of high damping materials. Mead and Markus [6] presented the dierential equation for damped normal modes of a three-layer encastre sandwich beam, in conjunction with appropriate boundary conditions, to determine the characteristic equation for the resonant frequency, loss factor and modal roots. Yan and Dowell [7] deduced a simply linear equation governing the vibrations of sandwich ®nite plates or beams. The damping characteristics of a constrained layer sandwich can also be studied by using complex elastic constants in the frequency domain. By using viscoelastic cores, Rao and Nakra [8] analyzed the ¯exural vibration of unsymmetrical sandwich beams and plates. In addition to transverse inertia eects, the investigation included longitudinal translatory and rotary inertia eects. Lu et al. [9±11] discussed theoretical and experimental results for the transverse driving point mechanical impedances, as well as for the transfer impedances, of damped composite rings, beams and plates made up of a thin viscoelastic layer sandwiched between two elastic layers. Chen et al. [12] presented the fundamental damping mechanism of polymer-laminated steel sheets as well as variables aecting the damping eciency. Rao and He [13] developed a comprehensive yet simple model to elucidate the dynamic behavior of a multi-damping layer composite beam with anisotropic laminated constraining layer. Johnson [14] brie¯y reviewed the techniques employed for designed-in passive damping for vibration control. The investigation also discussed how viscoelastic materials and design methods for passive damping were tested and characterized. In a related work, Ramesh and Ganesan [15] studied three theories used to analyze vibration and damping characteristics of cylindrical shells with constrained damping treatment using the ®nite element method. Marcelin et al. [16] discussed the optimal damping of beams constrained by viscoelastic layers when only one or several portions of the beam are covered. Lin and Ling [17] demonstrated the feasibility of identifying damping characteristics by correlating ®nite element modeling with vibration test results. For achieving such an objective, an eective method was also proposed. Optimally designing, accurately predicting and eectively controlling the vibration of a structure with viscoelastic damping treatment depend on thoroughly understanding the damping characteristics of viscoelastically damped structures. This study analyzes the design parameters for constrained layer damping structures by employing the Ross±Kerwin±Ungar (RKU) model [1±3]. The extent to which temperature,
Βιβλιοθήκη Baidu
Abstract Vibration is normally viewed as undesirable, not only owing to the resulting unpleasant motions, noise, and dynamic stresses possibly leading to fatigue and failure of the structure or machine, but also owing to the energy losses and degraded performance. Technological advances have further enhanced the means of controlling vibration in mechanical engineering, aerospace engineering, civil engineering and related applications. The feasibility of developing a viscoelastic damping material of structures for vibration damping has received extensive interest. Surface treatment uses high damping viscoelastic materials ®rmly attached to the surface of structural elements. Optimal design depends on the ability to accurately predict and eectively control the vibration of a structure with viscoelastic damping treatment. Understanding the damping characteristics of viscoelastically damped structures becomes necessary. This study analyzes the design parameters for constrained layer damping structures by employing the Ross±Kerwin±Ungar (RKU) model. The eects of temperature, frequency and the dimensions of damped structures on vibration damping characteristics are also discussed. Ó 2001 Elsevier Science B.V. All rights reserved.
Comput. Methods Appl. Mech. Engrg. 190 (2001) 3881±3892
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Analysis of damping characteristics for viscoelastic laminated beams
*
Corresponding author.
0045-7825/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 5 - 7 8 2 5 ( 0 0 ) 0 0 3 0 5 - 4
1. Introduction Vibration, the repetitive motion of objects relative to a stationary frame of reference or nominal position, occurs in most machines, structures and dynamic systems. Vibration is normally viewed as undesirable, not only owing to the resulting unpleasant motions, noise, and dynamic stresses possibly leading to fatigue and failure of the structure or machine, but also owing to the energy losses and degraded performance. Increasing the capability and life of equipment involves reducing the mechanical vibration of a system. Technological advances have further enhanced the means of controlling vibration in mechanical engineering, aerospace engineering, civil engineering and related applications. These vibration control techniques can be categorized as active and passive. An active control system is equipped with an external energy supply. The energy can be supplied manually or automatically. While operating without using any external energy supply, passive control mechanisms use the potential energy generated by the structural response to supply the control force. Passive techniques include an isolator, dynamic absorber and surface damping treatments. The feasibility of developing a viscoelastic damping material of structures for vibration damping has received extensive interest in recent years. Surface treatment uses high damping viscoelastic materials ®rmly attached to the surface of the structural elements. Two conventional methods of viscoelastic damping treatment are the free layer and constrained layer damping structures. The former consists of a simple layer for an appropriate damping material bounded to those surfaces of the structure that are vibrating primarily in a bending type of mode. The latter uses the notion of a constraining layer.
Tso-Liang Teng a,*, Ning-Kang Hu b
a
Department of Industrial Engineering & Management, Hsiuping Institute of Technology, Taichung, Taiwan, ROC b System Engineering Department, Chung Cheng Institute of Technology, Tahsi, Taoyuan 33509, Taiwan, ROC Received 2 December 1999