In recent years, the crucial applications like aerospace and automotive industries
prefer the light weight polymer composite materials over the weighty metallic
structures where the considerable strength and stiffness is required at the
normal temperature (Adams and Maheri, 2003), as the
farmer possess the key properties like light weight, high specific strength,
impact resistance, thermal stability etc., required for those applications (Zhang
and Chen, 2006). It also offers the other benefits like high energy dissipation,
flexible bonding of fiber with the matrix, less stress concentration, corrosion
resistance, etc. (Rao et al., 1997). As the damping
is considered to be a major concern in many engineering fields, this work is
confined to the method of energy dissipation (damping) only. The recent researches
carried out to improve the damping by the several ways of various damping mechanisms
such as the viscoelastic behavior of polymer matrix, the different fiber orientations,
the hair line cracks, inter faces, flexible bonding of fiber with the matrix
and temperatures which help the composite structure to dissipate the absorbed
energy (Zhang and Chen, 2006; Rao
et al., 1997). Though, the Fiber Reinforced Polymer (FRP) composite
material provides higher damping it can be achieved only at the expense of strength
and stiffness. So, the research is still incomplete in improving the damping
without compromising the stiffness of FRP composites.
Adams and Bacon (1973) theoretically predicted the
effect of fiber orientation and laminate geometry on the flexural, torsional
damping and modulus of fiber reinforced composites. Later, to study the effect
of the same fiber orientation and moduli, Adams and Maheri
(1994) used the basic plane stress relations together with Adams-Bacon damping
criterion (Adams and Bacon, 1973). Gibson
and Plunkett (1976) represented analytical and experimental methods to find
the internal damping and elastic stiffness of E-glass fiber reinforced elastic
beams under flexural vibrations.
The effect of temperature on the modal parameters (resonance frequencies and
modal loss factors) of multi-damping layer anisotropic laminated composite beam
was predicted by the modal strain energy method using FEM as a tool by Rao
et al. (1997). Then Berthelot and Sefrani (2007),
Sefrania and Berthelot (2006) and Berthelot
(2006) also studied the damping behavior under the influence of temperatures,
apart from studying the effect of beam width. Rao et
al. (1997) and Zhang and Chen (2006) studied
the damping behavior of composites with integral viscoelastic layers under the
effect of ply angle of complaint layers and the location of viscoelastic layers.
The objective of this study is to improve the damping without compromising
much on the stiffness/frequency values by suitable layups. To achieve this,
the damping factors and frequency were experimentally determined from the different
range of fiber lay-ups. Similarly the values obtained from the experimental
work have also been compared with the same obtained from the FEA modal analysis.
MATERIALS AND METHODS
Materials: The low temperature curing epoxy resin, Rotex EP- 207S with a specific gravity of 1.14 at 25°C, the solvent based high temperature curing hardener, Rotex EH- 210S and the accelerator, Tertiary amine which were supplied by ROTO Polymers, Chennai, India, were used as the matrix and the unidirectional glass fiber supplied by SUNTECH Fibers, Chennai, India was taken as reinforcement in the composite.
Fabrication of FRP composites: The conventional hand layup technique,
described elsewhere Yuhazri et al. (2010) was
used to prepare the three identical test specimens with the dimension of 300x25
mm of the composite laminates, which were fabricated by stacking eight layers
and also by applying the mold pressure. The test specimen has different stacking
sequence such as unidirectional and angle plies with 50% volume fraction of
fiber in the composite. The different orientations of 21 layups have been given
Damping test of FRP composites: The impulse technique was used to find
the vibration characteristics of the specimen in terms of natural frequencies
and damping factors. The procedure of this technique is described elsewhere
(Kishi et al., 2004). The one end of laminated
specimen was rigidly clamped in a rigid support by screws and another end was
free on which the accelerometer was properly positioned, to vibrate like a cantilever
beam. The loss or damping factor of the composites was measured by mechanical
impedance in which the specimen was forced to vibrate at its end, as shown in
Fig. 1. The input load was used given by the instrumented
impacts hammer and the output (response) was taken by the accelerometer and
read by the national instrument data acquisition card used for vibration analysis.
The damping factor (η) is obtained by using the half power bandwidth method
as shown in Fig. 2 and the expression for damping factor (η)
is given by the following Eq. 1:
where, f1 and f2 is Band width at the half-power points of resonant peak for nth mode and fn is Natural frequency.
Damping factor and natural frequency of composite specimens with different fiber orientations and layup corresponding to the first mode were computed.
Mechanical test of FRP composites: The material properties of the composite specimen with respect to fiber direction were measured from the mechanical and dynamic tests and. To measure the Poisson ratio, the specimen on which two unidirectional strain gages with 120 Ω resistance both in vertical and horizontal directions were pasted at its centre was held and stretched in UTM (Manufacture: Blue hill, Model: UTE 40T), then the Damping factor and natural frequency of composite specimens with different fiber orientations and layup corresponding to the first mode were computed. required data were captured by a data acquisition (FIE through an extensometer) system using a software, named system 5000.
|| Schematic representation of experimental setup
|| Showing the Half power bandwidth method
|| Modeling of FRP composite
|| Mode shape of FRP composite
Finite element analysis: The SHELL 99 (Fig. 3) 3-D
shell element is used to model the structures. It allows a total of 250 uniform-thickness
layers with a side-to-thickness ratio of roughly 10 or greater. The natural
frequencies are determined for each individual element using the experimentally
obtained modulus values (Ex, Ey, Gxy), poison
ratio (vxy), density (ρ) and experimentally predicted damping
values after discretizing the model into fine elements. So, the higher natural
frequencies were accurately. Sefrania and Borthelot (2006)
predicted by refining the mesh with more and more no of fine elements and admitting
more number of degree of freedom. The dimension of composite material shown
in Fig. 3 is 0.3x0.025x0.0066 m. The numerical values were
obtained for the natural frequencies and Fig. 4 show the model
shape of the composite laminate which were arranged in different sacking sequence
such as unidirectional and angel plies.
RESULTS AND DISCUSSION
As the main aim of this study is to improve the damping at the negligible expense of stiffness, the damping factors and the frequencies are calculated from the lay-ups of fibers. More than 20 layups were tested and such huge numbers of the same have been tried first time. The layups have been categorized into the three groups (group A, group B and group C) consisting of different lay-ups based on the ascending order of frequency values and the descending order of the damping values arranged. Based on their magnitude, the best group and the lay-up number are selected.
It is desired to select higher damping value without compromising much on frequency values which directly relate to stiffness from the groups described above. Though the values calculated are for the three mode shapes, the first mode shape values are given the preference for the selection of best lay-up as the failure mostly initiate in the first mode only. From the twenty one layups it is observed that the laminates with orientations [90°/0°/±60°]s, [90°/0°]2s, [90°/0°/±45°] and [90°/0°/±30°]s of group C (shown in Table 3) exhibit the better results. When the properties of the layup [90°/0°/±60°]s is compared with the other layups [90°/0°]2s,[90°/0°/±45°/]s and [90°/0°/±30°]s, the former is considered to be better as their damping value in the mode shape 1 is comparatively high (0084) with negligible expense of frequency (87.387 Hz).
Thus, after considering the frequency and damping values, the best one has been chosen from these entire layups. But this paper does not end with only the selection of one layup. Based on the end applications which depend upon the required parameter of either the frequency (stiffness) alone or the damping alone or combination of the both, the each group could be chosen separately. When here is a light duty application with the need of more damping, the group A (Table 1) strength/stiffness/frequency with less of damping, the group C (Table 3) can be desired. On the other hand, an application where medium duty application is in need of both parameters (frequency and damping), the group B (Table 2) may be opted.
||Group A: Materials showing low stiffness (frequency) and high
||Group B: Materials showing moderate stiffness and high damping
||Group C: Materials showing high stiffness and high-low damping
In order to study the vibration characteristics of glass fiber reinforced polymer
composites, aiming to improve the damping without compromising much on the stiffness/frequency
values, the large number of different lay-ups of fiber were fabricated. After
carrying out a thorough investigation on damping characteristics of different
lay-ups experimentally and analytically, the lay-up [90°/0°/±60°]s
was selected to be good as the amount of the damping values are reasonably high
with their corresponding frequency (stiffness) values. And also, on concerning
the suitable lay-up for the required type of applications (light, medium and
heavy duty), these different layups were categorized into three groups by the
level of the stiffness(frequency) values after arranging them in ascending order.