Free vibration testing

Dynamic Young s modulus (EJ of wood was also calculated using free-free vibration testing. A significant increment was obtained for the PF-Nanoclay impregnated WPNC samples. 

Unfortunately, in reality, very little is known about structural damping. Free vibration testing of real buildings indicates that the damping in the first mode, though not purely viscous, is very close to viscous and we could say that (/i = 50.o)... 

Fig. 5.24 Torsional pendulum for free vibration test (A = amplitude, P = period, logarithmic decrement = In A1/A2 = A2/A3 = A3/A4, etc.)...

Before considering particular test methods, it is useful to survey the principles and terms used in dynamic testing. There are basically two classes of dynamic motion, free vibration in which the test piece is set into oscillation and the amplitude allowed to decay due to damping in the system, and forced vibration in which the oscillation is maintained by external means. These are illustrated in Figure 9.1 together with a subdivision of forced vibration in which the test piece is subjected to a series of half-cycles. The two classes could be sub-divided in a number of ways, for example forced vibration machines may operate at resonance or away from resonance. Wave propagation (e.g. ultrasonics) is a form of forced vibration method and rebound resilience is a simple unforced method consisting of one half-cycle. The most common type of free vibration apparatus is the torsion pendulum. 

In free vibration methods, the rubber test piece, with or without an added mass, is allowed to oscillate at the natural frequency determined by the dimensions and viscoelastic properties of the rubber and by the total inertia. Due to damping in the rubber, the amplitude of oscillations will decay with time and, from the rate of decay and the frequency of oscillation, the dynamic properties of the test piece can be deduced. 

ISO 4663 gives no advice as to the relative merits of the three methods it specifies. Method C, which is not strictly a free vibration method, removes the difficulties associated with changing amplitude through the course of the test but at the expense of a rather more complex apparatus. When the inertia member is supported by a torsion wire, as in method B, the tensile strain in the test piece can be controlled to a low level by means of counterweights. 

Test methods where there is free vibration applied and then allowed to decay. 

Free vibration in which the test piece is set into oscillation and the amplitude allowed to decay due to damping in the system... 

To reduce undesirable vibration effects, the source may be isolated by means of vibration absorbers. The answer to the isolation problan is the correct mounting of the source (machine) on springs and dampers, that is, on rubber blocks [14], Because dynamic properties are of great concern in engineering applications, including springs and dampers, dynamic tests are much more useful than the simple static tests. As said above, there are two classes of dynamic motions free vibration and forced vibration. 

Torsion pendulum n. A device for performing dynamic mechanical analysis in which a sample is deformed torsionally and allowed to oscillate in free vibration. Shah V (1998) Handbook of plastics testing technology. John Wiley and Sons, New York. 

I. Rotaru, C. Bujoreanu, A. Bele, M. Cazacu, D. Olaru, Experimental testing on free vibration behaviour for silicone rubbers proposed within lumbar disc prosthesis. Materials Science and Engineering C, ISSN 0928-4931 42 (September 1, 2014) 192-198. http //dx.doi.Org/10.1016/j.msec.2014.05.021. 

Dynamic Modulus. The ratio of stress to strain under vibratory conditions (calculated frdata obtained from either free or forced vibration tests, in shear, compression, or elongation). 

Because of the frequency dependence of Tg, the convention adopted for assignment of the glass transition temperature is an important consideration. Traditionally, a frequency of 1 Hz has been used as a standard value. This is based on the historic precedence, since the torsion pendulum was the most widely used DMA technique in the early days of viscoelastic property measurements. The torsion pendulum is a free vibration technique with a natural frequency of approximately 1 Hz. The 1 Hz value also is reasonably close (within 10 °C) to the Tg values determined by other widely used methods such as DSC, dilatometry, and TMA. The relation between DMA and DSC Tg values is considered further at the end of this chapter (Sircar and Drake 1990). Because of the ambiguity inherent in the kinetic nature of Tg, it is most important that the test frequency be reported along with any Tg value determined by a DMA technique. 

Suppose that a microfabricated cantilever beam is to be used as a sensor for detecting the presence of a certain bacterium in a hquid solution see Figure 1.31. Following its fabrication, the beam is first coated with an antibody that is specific to the particular bacterium of interest and its free vibration characteristics are determined. The beam is then dipped into the solution to be tested. If the bacteria of interest are present, they will attach themselves to the surface of the beam, attracted by the antibody. The beam is then removed from the solution and its free vibration characteristics are re-examined. Estimate the influence of an added mass due to the attached bacterium cells, say rib cells each of mass mb, on the fundamental natural frequency of the beam. (The effectiveness of this approach for detection of bacteria has been demonstrated by Ilic et al. (2000).)... 

Free vibration and forced vibration methods have been employed to determine the respective data. Free vibration was common earlier in polymer blend studies, but forced vibration data is much more common today due to the availability of more sophisticated testing equipment. Free vibration methods include the torsion pendulum, the vibrating reed and the torsional braid analyzer. The torsion pendulum is comprised of an inertial source (disk or rod), which can freely vibrate and is attached to a specimen, which is rigidly fixed at one end. Upon angular deformation of the inertial source and releasing, a damped sinusoidal curve depicts the resultant deformation of the sample [18,19]. Tan S can be calculated from... 

Operational modal analysis, or ambient modal identification, aims at identifying the modal properties (natural fi equency, damping ratio, mode shape, etc.) of an instrumented structure using only the (output) vibration response (acceleration, velocity, etc.). The input excitation to the structure is not measured but is assumed to be broadband random, often referred to as ambient. This allows vibration data to be collected when the structure is in its working or operating condition without much intervention, therefore implying significant economy over free-vibration (initially excited but no input afterwards) or forced-vibration tests (known input). The broadband random assumption essentially requires that the spectral characteristics (shape) of the measured response reflect the properties of the modes rather than those of the excitation, which is assumed to be constant in the vicinity of the natural frequencies. 

Damping can be determined using the half-power bandwidth method or from the logarithmic decrement by placing the sample in free vibration (ASTM 2007). This technique has been modified to allow cyclic torsional shear testing to strain levels above those typically achieved during a... 

Vibration (high-cycle fatigue life) testing was conducted to determine (1) if there were measurable differences in the performance of the down-selected solder alloys, or (2) if the mode of failure of the Pb-free solders was distinguishably different from eutectic Sn-Pb solder in a vibration environment. Of all components vibration tested on both RTV-SM and STV assemblies, only the LCCC-44 and PLCC-84 parts experienced failures related to solder performance that were analyzed further. The PQFP-208 and PQFP-132 parts exhibited lead fractures for all solders, not just the stronger lead-free solders. The PLCC-44 components did not exhibit enough failures to be meaningfully analyzed. The 1206 discrete devices did not exhibit any failures. 

In pulse version of MIA method the probes excite in tested object (TO) free attenuating pulses. Their carrier frequencies coincide with natural frequencies of transmitting probe vibrator loaded to the mechanical impedance Zg = / (Z -tZ,), where Z is elastic... 

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