This document describes methods for measuring the dynamic properties of composite materials through vibration testing. There are several key dynamic properties, including damping, relaxation, creep, and strain rate. Vibration testing allows measuring the complex modulus, which describes damping and dynamic stiffness. Specimens like beams and plates are vibrated and their natural frequencies measured to determine storage modulus and loss factor. Various techniques are discussed, including free vibration decay measurement and forced oscillation hysteresis loops. Impulse response testing provides an efficient method by exciting specimens with impacts. Dynamic testing provides an alternative to static testing and also measures important properties like damping.

1. Vibration test of composite materials on the basis of measurement of dynamic
properties
Tushar D. Dange
University of Massachusetts, Lowell

2. INTRODUCTION
On the basis of measurement of viscoelastic and dynamic properties, there are four important
parameters such as damping, relaxation, creep, and strain rate, which describe evidence of
viscoelastic behavior and can be calculated with the help of an experiment, but this paper
describes the method of test for the measurement of damping. In addition, the notation of
complex modulus describes conventionally for damping and dynamic stiffness of linear
viscoelastic materials, where the methods of vibration test are considered for measurement of
complex moduli of composites. With the help of this test of plates and beams to find dynamic
elastic moduli also get evaluated.
In vibration test, notation for complex modulus is suitable for portrayal of dynamic behavior of
linear viscoelastic composites. The damping and stiffness which are the constituent part of the
complex modulus are belongs to the dynamic mechanical properties, which may be measured
with the help of experiments with vibration and wave propagation experiments ,and the
measurement of the same is considered for dynamic mechanical analysis.
However, there are many traps with respect to the different kind of techniques which must get
avoided. In example, there was a development of commercial dynamic mechanical analyzers for
the testing of small specimen of unreinforced low modulus polymers, and stiffness is generally
not sufficient for usage with high modulus composites. As per requirement, the stiffness if we
reduce for valid data then it is required to use specimen thickness; otherwise testing of multi-ply
laminates might become impossible. Valid measurements of dynamic mechanical properties are
very hard to get, mostly with the composite materials [1].

3. The complex modulus with reference to a typical vibration test specimen is gained by finding out
the loss factor and storage modulus of the specimen with respect to its vibration. The specimens
are nothing but the beams, rods, and or plates which are supported in a manner that to decrease
the damping which get produced due to the atmosphere or apparatus. The error in the data of
damping can come from friction damping, aerodynamic drag, transducer attachment, and phase
log. To get the potential problems, the cross checks of number of methods used to find the
damping measurements is always good.
The storage modulus is one of the important factors which can be calculated with the help of
natural frequency and by solving equation of frequency for the specimen. A care is important and
has to be taken for making sure the effective modulus criteria which should have been met and
effects like transverse shear and coupling should calculated as per the requirement. The
transverse shear effects are more important for high modulus composites compare to
conventional materials, and here the Timoshenko beam theory may be useful for the valid
conclusions.

4. Figure 1: Correction factor needed to make a correction for the values of modulus from the
measurement of resonant frequency with the help of Bernoulli-Euler theory to values by
Timoshenko Beam theory. The factors get plotted as a function of a mode number [2].
The figure 1 above shows that the correction factors yields corrected modulus values are
consistent with the Timoshenko Beam theory [2].
The damping is characterized with the help of loss factor which comes from the notation of
complex modulus. For light damped systems, the loss factor is connected to the parameters used
to characterize the damping in single degree of freedom (SDOF) spring mass systems and are
calculated by curve fitting to the measured specimen response whether they belongs to the
forced or free vibration if single mode utilized for analysis.

5. Figure 2: Free vibration decay curve for log decrement measurement
The figure 2 above shows that in the experiment of free vibration, a specimen such as a beam or
rod is released from assumed initial displacement, or a steady state excitation has got removed,
and making sure that a decay of a free vibration of a specimen has observed. Here, a care must
be taken to make sure that only one mode of vibration has present in the response of decay curve,
since the value of damping should get calculated for a particular mode.

6. Figure 3: Hysteresis loop from the test of forced oscillation.
As per above figure 3, one of the method of type of forced vibration test get involves in a fixed
frequency oscillation of specimen in a testing machine with getting the graph concludes the
stress strain hysteresis loop. With the help of dimensions of a, b, and c with the known frequency
f, we can find the components of complex modulus with the help of following equations as [3]:

7. Figure 4: Frequency response curve, or graph of transfer function versus frequency.
Another technique is based on excitation frequency variation, plotting of phase or magnitude of
frequency response, simultaneous measurement of response domain. The resulting curve shows
that natural frequency of the specimen, and single degree of freedom techniques for curve fitting
for finding the complex modulus. The loss factor which depend on the storage modulus can be
calculated as,
where = bandwidth at half power point on peak,
and = peak frequency for nth mode of vibration.

8. For this kind of purpose, the Fast Fourier Transform (FFT) analyzers are used. The methods of
impulse frequency response are nothing but the easier and the fastest ones in this kind of
measurement methods [4] [5] [6].
Figure 5: Test set up of a cantilever beam for the impulse-frequency response method
Above figure shows a cantilever beam test apparatus on the basis of method of impulse
frequency response. Here, beam specimen excites with the help of a hammer and the response
get measured and monitored by a sensor, and then they get transferred to the FFT analyzer,

9. which produces the response with respect to the real time. Curve fitting and complex modulus
results will be shown the computer screen. On the basis of different lengths and number of
modes of vibrations, the frequency dependence can be calculated.
FUTURE USE
Impulse techniques get used in conjunction with laminate plate in vibration model to find the
elastic constants of plates which is made of composite materials [7] [8]. With the help of impulse
frequency response method, we can find the damping in the composites where face the damage
or degradation [9] [10]. An impulse test apparatus has also got developed for measurement of
complex modulus of reinforced fibers at different conditions of temperature [11] [12].
CONCLUSION
In coda, to find the composite stiffness, the methods for the dynamic testing provide alternatives
to the static test methods get used. Also, it provides the information on the internal damping,
which is one of the essential material properties, of the composite materials, which also useful in
nondestructive testing parameters. These test methods can be introduced in the process of
manufacturing to get on line control of monitoring as well as on property of the composite
materials.
REFERENCE(S)

10. [1] Gibson, R. F., "Vibration Test Methods for Dynamic Mechanical Property Characterization,"
in R. L. Pendolton and M. E. Tuttle (eds.), Manual on Experimental Methods for Mechanical
Testing of Composites, 151-164, Society of Experimental Mechanics, Bethel, CT (1989).
[2] Dudek, T. J., “Young’s and Shear Moduli of Unidirectional composites by a Resonant Beam
Method,” Journal of Composite Materials, 4, 232-241.
[3] Gibson R. F.," Vibration Test Methods for Dynamic Mechanical Property Characterization,"
in R. L. Pendleton and M. E. Tuttle (eds.), Manual on Experimental Methods for Mechanical
Testing of Composites, 151-164, Society of Experimental Mechanics, Bethel, CT (1989).
[4] Suarez, S. A. and Gibson, R. F., "Improved Impulse-Frequency Response Techniques for
Measurement of Dynamic Mechanical Properties of Composite Materials," Journal of Testing
and Evaluation, 15(2), 114-121 (1987).
[5] Suarez, S. A., Gibson, R. F. and Deobald, L. R., "Random and Impulse Techniques for
Measurement of Damping in Composite Materials," Experimental Techniques, 8(10), 19-24
(1984).
[6] Crane, R. M. and Gillispie, J. W., Jr., "A Robust Testing Method for Determination of the
Damping Loss Factor of Composites," Journal of Composites Technology and Research, 14(2),
70-79 (1992).
[7] Deobald, L. R. and Gibson, R. F., “Determination of Elastic Constants of Orthotropic Plates
by a Modal Analysis/ Rayleigh Ritz Technique,” Journal of Sound and Vibration, 124(2), 269-
283.

11. [8] Crane, R. M. and Gillespie, J. W., Jr., “A Robust Testing Method for determination of the
Damping Loss Factor of Composites,” Journal of Composite Technology and research, 14(2),
70-79.
[9] Mantena, R., Place, T. A., Gibson, R. F., “Characterization of Matrix Cracking in Composite
Laminates by the Use of Damping Capacity Measurements,” Role of Interfaces on Material
Damping, 79-93.
[10] Mantena, R., Gibson, R. F., and Place, T. A., “Damping Capacity Measurements of
Degradation in Advanced Materials,” SAMPE Quarterly, 17(3), 20-31.
[11] Gibson, R. F., Thirumalai, R., and Pant, R., "Development of an Apparatus to Measure
Dynamic Modulus and Damping of Reinforcing Fibers at Elevates Temperature," in Processing
1991 Spring Conference on Experimental Mechanics, 860-869, Society for Experimental
mechanics, Bethel, CT (1991).
[12] Pant, R. H. and Gibson, Rz. F., "Analysis and Testing of Dynamic Mechanical Behavior of
Composite Materials at Elevated Temperatures," in Vibroacoustic Characterization of Materials
and Structures, P. K. Rajn, (ed.), NCA vol. 14, 131-146, American Society of Mechanical
Engineers, New York (1992).