Amplitude dependent damping behaviour of fundamental mode for CFRP composite tubes: Effect of cross-section
Introduction
Near resonance vibration is a major cause of fatigue and other kind of service failures in structures. This is because, at resonance, the structure is subjected to high amplitude of vibration. The amplification in vibration can be suppressed through the addition of structural damping or by designing the structure with sufficient inherent damping. Fibre reinforced polymer (FRP) composite structures are extensively used in many engineering applications, especially related to aeronautics and space owing to higher strength-to-weight ratio of these elements. These structures are often subjected to significant dynamic loads and thus, require proper design for ensuring the continued performance. However, it is very difficult to introduce a structural damper in aeronautic and space components without adding significant extra weight to these components. Thus, in these types of components, there is a need to enhance the inherent damping properties without increasing the weight of the system. One such way to enhance damping properties of these components without adding extra weight is to increase their inherent damping properties by proper selections of material, loading condition and optimizing the cross-section as pointed out by Lazan [1].
Several damping theories and models were suggested in past for evaluation of specific damping capacity (SDC) of FRP composites [[2], [3], [4], [5], [6], [7], [8]]. The effects of fibre orientation and laminate geometry on dynamic properties such as flexural modulus and SDC of FRP composite beams were investigated by Adams and Bacon [2], Ni and Adams [3], and Adams and Maheri [6]. Saravanos [4] presented a micromechanics model based on hysteric damping (due to matrix, fibers and interfacial friction) for prediction of SDC in unidirectional FRP composites. Billups and Cavalli [7] compared the damping predictions for an arbitrary composite laminate with specific lay-up/material combinations using the aforementioned two-dimensional composite laminate damping models.
The amplitude dependency on damping was discussed in several studies [[9], [10], [11], [12], [13], [14], [15], [16]]. Gibson and Plunkett [9] described the approaches to measure the internal damping and elastic stiffness of E-glass fibre-reinforced epoxy beams subjected to flexural vibration. Damping was found to be much sensitive towards damage particularly at high amplitude of vibration when the strain amplitude crossed its threshold limit. Gibson and Plunkett [10] and Gibson et al. [11] further extended this study to investigate the amplitude and frequency dependencies of material damping in aluminum and 0/90 Scotch ply beam specimens subjected to flexural vibration. Kenny and Marchetti [12] analysed the elasto-plastic behaviour of composite laminates (containing thermoplastic matrix) under static and cyclic sinusoidal loadings. A strong increase in damping was reported at high stress levels because of the higher energy dissipation as a result of plastic deformation (i.e., depending on the matrix properties). Tu and Wang [13] and Strano et al. [14] investigated damping in steel and titanium tubes filled with different type of metal foams. It was suggested that the damping capacity can significantly be increased under high amplitude of excitation by filling the tube with metal foams. Klaerner et al. [15,16] discussed the amplitude dependent damping of metal-plastic composites with constraint layer [16], stiff steel face sheets and thin compliant polymer cores [15]. Significant amount of damping due to shear deformation and its amplitude dependency was reported from both the approaches.
In addition, several approaches were reported in past in order to optimize the inherent damping of an isotropic structural member [1,[17], [18], [19]]. Lazan [1] introduced three vibration amplification factors for a beam subjected to the resonance condition, namely, (a) material factor, (b) stress distribution factor and (c) cross-section factor. Experiments were performed on beam specimens (made of aluminum) having square, circular and diamond cross-sections. Damping capacity was found to be affected by the member's cross-section and the loading conditions.
A few research studies have focused on the issue of inherent damping in polymer based composites [[20], [21], [22], [23], [24], [25], [26], [27]]. To improve the inherent material damping in composite specimens, a few aspects were described in these studies. It was suggested that the damping can significantly be increased with addition of a small amount of highly damped materials in the composite matrix during the material preparation process.
So far, studies have dealt with the damping enhancement in isotropic and polymer-based composites. A relatively fewer studies are available on the influence of member's cross-section on damping. As per authors' knowledge, no work has been done so far on this aspect while considering FRP composites. It can also be noted from the literature that damping constants (J1, J2 and n Rahmathulla and Mallik [19]) required for estimation of inherent damping are not available for FRP composite. Besides, studies were limited only for an isotropic member having a solid cross-section. Since, tubular members and pultruded FRP composites are widely used in many important applications, it is essential to understand how different cross-sectional shapes affect damping behaviour of such members.
This study provides a closed form solution for amplitude dependent damping behaviour of a cantilever orthotropic member when subjected to dynamic loads. Damping ratio is obtained as a function of the stress fields, material and geometrical constants. Effect of member's cross-section on damping behaviour is investigated by considering elliptical, circular, hexagonal and square cross-sections. Shake table experiments are performed on cantilever woven carbon fibre reinforced polymer (CFRP) composite tubes of different cross-sections subjected to harmonic base excitation of varying amplitudes. In order to obtain the dynamic response of the tube, accelerometers are mounted at varying positions along the tube length. Besides, to obtain base acceleration and the shake table displacement, accelerometer and linear variable differential transformer (LVDT) are attached at the table, respectively. One strain gauge is also attached near the bottom of the tube. The acceleration, strain and LVDT data are recorded using a data acquisition system. At first, material constants of woven CFRP composite are experimentally evaluated using the recorded acceleration and strain data. Later, for tubes of different cross-sections, the damping ratio of the fundamental mode is evaluated using experimental results and compared with the values obtained from the proposed expressions. Finally, conclusions are drawn on the efficiency of the proposed approach in terms of capturing the experimentally obtained damping behaviour.
Section snippets
Stress-damping relationship in an orthotropic composite
At resonance, the damping capacity of a structural member is represented as ratio of the total dissipated energy and the total strain energy under a given state of loading. Dissipation of the vibrational energy may vary form one material to another depending on the inherent damping present in such materials. In composites, the inherent damping significantly contributes to the overall damping due to involvement of several energy dissipation mechanism such as interfacial slip, micro-cracking,
Numerical illustration and experimental verification
It is clear from Eq. (11) that, for evaluation of modal damping ratio under a given loading, although, most of the parameters (such as material properties and stress fields) are either known or can be evaluated, the values of J1, J2 and n are material specific. Thus, these constants have to be evaluated experimentally or to be supplied by the manufacturer. In this work, at first, the values of J1, J2 and n are evaluated for a set of chosen bidirectional woven composite tubes experimentally. The
Conclusions
In this work, a systematic approach is presented to investigate the amplitude dependent damping behaviour of the fundamental mode for FRP composite tubes. In the proposed approach, an expression of damping ratio is derived, which accounts for the stress fields (σx, τxy and τxz), material properties/constants (Ex, Gxy, Gxz, J1, J2 and n) and geometrical constants/configurations. Experiments are conducted on woven CFRP composite tubes (square, hexagonal and circular), wherein harmonic base
CRediT authorship contribution statement
Komal Chawla: Conceptualization, Data curation, Formal analysis, Writing - original draft. Samit Ray-Chaudhuri: Conceptualization, Methodology, Formal analysis, Writing - review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to thank lab technicians and staff of structural engineering laboratory, Indian Institute of Technology, Kanpur for their help and guidance during the work. This work was partially supported by Indian Space Research Organization (ISRO) through ISRO-IITK Space Technology Cell and Ministry of Human Resource Development (MHRD).
References (34)
- et al.
The effects of three-dimensional states of stress on damping in laminated composites
Compos. Sci. Technol.
(1991) - et al.
Dynamic flexural properties of anisotropic fibrous composite beams
Compos. Sci. Technol.
(1994) - et al.
2d damping predictions of fiber composite plates: layup effects
Compos. Sci. Technol.
(2008) - et al.
Elasto-plastic behavior of thermoplastic composite laminates under cyclic loading
Compos. Sruct.
(1995) - et al.
Improvement of damping characteristics of structural members with high damping elastic inserts
J. Sound Vib.
(1973) - et al.
Some aspects of vibration damping improvement in composite materials
Composites Part B
(1998) - et al.
Recent research on enhancement of damping in polymer composites
Compos. Struct.
(1999) - et al.
Passive vibration damping enhancement using carbon nanotube-epoxy reinforced composites
Compos. Sci. Technol.
(2005) - et al.
Damping analysis of composite materials and structures
Compos. Struct.
(2008) - et al.
Experimental investigation of the damping enhancement in fiber-reinforced composites with carbon nanotubes
Carbon
(2013)
Enhanced composite damping through engineered interfaces
Int. J. Solid Struct.
Saint-Venant bending of an orthotropic beam
Compos. Struct.
Failure prediction of out-of-plane woven composite joints using cohesive element
Compos. Struct.
On estimating system damping from frequency response bandwidths
J. Sound Vib.
Effect of damping constants and stress distribution on the resonance response of members
J. Appl. Mech., Trans. ASME
Effect of fibre orientation and laminate geometry on the dynamic properties of cfrp
J. Compos. Mater.
The damping and dynamic moduli of symmetric laminated composite beams-theoretical and experimental results
J. Compos. Mater.
Cited by (2)
Analytical model for damping behaviour of an orthotropic cantilever hollow member with polygonal perforations
2022, Applied Mathematical ModellingINVERSE ANALYSIS OF THE AMPLITUDE-DEPENDENT DAMPING PROPERTIES OF EPOXY/GLASS FIBER LAMINATES
2024, Composites: Mechanics, Computations, Applications