Damping test equation

The test results of a material damping test are most useful when placed on a reduced temperature nomograph, which plots the limited number of test results to a graph from which one can obtain the damping properties (modulus and loss factor) at any given combination of temperature and frequency. The WLF equation (51 is used to obtain a nomograph for the results of each test. 

This equation is accurate at low damping (A < 1), but the error becomes large at high damping. More exact equations have been discussed by Struik (II) and Nielsen (4). The standard ASTM test is D2236-69. 

The resonant beam test technique forms the basis of the ASTM Standard E756-83 for measuring the viscoelastic properties of damping materials. Fundamentally, the beam test requires that the resonant frequencies of a metal-beam, mounted in cantilever fashion, be determined as a function of temperature and frequency the beam is then coated with a polymer and the resonant frequencies and corresponding modal damping of the composite beam are determined as a function of temperature and frequency. From these two data sets, the vibration damping properties of the polymer can be evaluated. The ASTM Standard provides the necessary equations to obtain the complex modulus data from the collected test data and also provides guidelines for the proper choice of the specimens (1.21. The principal difference between the beam test and the other methods used here is that the beam test calculates the material properties from the test results on the metal beam and the composite beam whereas the... 

According to this equation, the mechanical behavior observed depends very much on the ratio of the test time to the orientation time tr. With / > tr, the exponential term in Equation (11-59) makes almost no contribution to the total deformation. Conversely, the damping contribution as described by this term in the total deformation will become more noticeable the nearer the test and orientation times / and tr approach each other (see Figure 11-12). 

By applying free damped vibrations in torsion pendulum testing the mechanical vibration damping can be expressed in terms of the logarithmical decrement A which can be expressed as the ratio of two sequent amplitudes according to equation 3.13. 

Doolittle s torsional viscosimeter was essentially a damped, oscillating Couette viscometer, and Doolittle chose as the unit of viscosity the "number of degrees of retardation between the first and second complete arcs." There is no mention In this paper of the Hagen-Poiseuille law, the Navier-Stokes equations, the treatise of Lamb (1879) or the work of Basset (1888), and it would appear that Doolittle was unaware of the studies of fluid mechanics carried out in the previous century and half. Nearly two decades later, Gillet (1909) began his paper entitled "Analysis and Friction Tests of Lubricating Greases" with the comment ... 

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