Direct Method for Measuring the Dynamic Shear ... - ACS Publications

Chapter 5

Direct Method for Measuring the Dynamic Shear Properties of Damping Polymers S. S. Sattinger

Downloaded by MONASH UNIV on May 4, 2015 | http://pubs.acs.org Publication Date: May 1, 1990 | doi: 10.1021/bk-1990-0424.ch005

Mechanics Department, Westinghouse Science and Technology Center, 1310 Beulah Road, Pittsburgh, PA 15235

A non-resonance, direct-force method for dynamic shear properties measurements is described, and the results of tests on two commercially available damping polymers are presented. Novel aspects of this method include the means for supporting the sample and for measuring the imposed force and the resultant shear deformation. Addressed in this article are the test configuration, the principle of operation, the data reduction procedure, some typical measured properties, consistency checks on the data, and a brief description of an i n i t i a l application of the data. To generate accurate damping performance predictions, designers of constrained-layer damping treatments must have a good knowledge of the dynamic shear properties of the viscoelastic damping polymers they will use. The conventional characterization of these damping materials is the complex shear modulus, G* = G' + jG" = G' (1 + irj)

(1)

where G' is the real part of this modulus (often designed as the storage modulus), G" is the quadrature part (often designated as the loss modulus), and rj is the material damping loss factor. The quantity rj is frequently expressed as tan 6, where 6 is the phase angle between the stress and strain phasors. Dynamic properties tests on viscoelastic materials f a l l into the general categories of resonance tests and non-resonance tests (1). They can be further subdivided into tests using base motion excitation (2), (3) and direct force excitation (4), (5). S t i l l another classification may be made according to whether the specimen is stressed in extension, shear, or dilatation. An important issue in the selection of test methods is whether i t will 0097-6156/90/0424-0079$06.00/0 © 1990 American Chemical Society

In Sound and Vibration Damping with Polymers; Corsaro, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.


80

SOUND AND VIBRATION DAMPING WITH POLYMERS

be necessary to obtain data well into the rubbery and glassy regions of temperature and frequency for a given material. The measurement method described in this article is an embodiment of the non-resonance, direct-force-excitation approach that subjects a double-lap shear sample of damping polymer to force from a vibration shaker. In concept this approach can be applied irrespective of whether the material is in a rubbery, glassy, or intermediate state. Each material specimen is small in size and behaves as a damped spring over the entire frequency range. The small specimen size is in contrast with some alternate approaches in which the specimens have sufficiently large dimensions to be wave-bearing. This method combines the advantages of simplicity, direct control of frequency, and minimum reliance on mathematical modeling assumptions. It differs from other embodiments of the direct-force approach (4), (5) in the means for reacting the forces applied to the sample and in the techniques for measuring the imposed force and the resultant shear deformation. Described in this article are the test configuration, the principle of operation, the method of data reduction, typical measurements, consistency checks, and an application of measured data. Test Configuration Figure 1 shows the entire test system in schematic form. The test sample is comprised of two specimens of a viscoelastic damping polymer loaded in shear by force from an electromagnetic shaker. Each specimen is cemented between a centrally located, driven steel sample block and one of two clamped reaction blocks. The dimensions of each block in this apparatus are 25.4mm height, 38.1mm width, and 12.7mm thickness (1.00 in x 1.50 in x 0.50 in), but the specimens do not necessarily cover the f u l l areas of the 25.4mm x 38.1mm faces of the blocks. Excitation force is transferred from the armature of the shaker to the driven sample block through a piezoelectric force gage. The reaction blocks of the sample are bolted to a steel fixture that transfers the sample reaction force back to the shaker field assembly through a set of thermally-insulating fiberglass/ epoxy standoffs. The entire force path upward to the sample and then downward into the field assembly is designed to be as stiff as possible. Not shown in the figure is a pair of spacers that preclude beam-mode lateral vibrations of the fixture legs supporting the sample. At frequencies in the i n i t i a l range of interest (100 Hz to 1 kHz), accelerometers are the preferred means of motion measurements. Because the stiff design of fixturing does not ensure total immobility of the reaction blocks, signals from a pair of accelerometers, one on the driven block and one on a reaction block, are differenced electronically by an operational amplifier. The resultant difference signal provides an accurate measure of shear deflection in the specimens. The signal from a third accelerometer, which is mounted on the specimen-side flange of the force gage, is used to electronically compensate the force signal for the effects of specimen-side force gage mass. Sinusoidal dwells are used to maximize signal/noise ratios.


5. SATTINGER

Direct Method for Measuring Dynamic Shear Properties

Corrected Acceleration (y) Signal


Accelerometers

Frequency Meter

Vibration Shaker Rated Force = 50 lb pk f

Power Supply

Isomode Pad

Figure 1. Test system for dynamic shear property measurements on viscoelastic damping polymers.


81

82


Data Reduction The complex shear modulus of the viscoelastic damping polymer is obtained directly from measurements on the sample using the relationship


where k* = the complex dynamic stiffness of the sample h = the thickness of each of two damping polymer specimens included in the sample A = the shear area of each specimen. The sample's dynamic stiffness is obtained from the measured force and motion amplitudes. The formula for this dynamic stiffness is derived below with reference to the Figure 2 measurement system model. The support impedance element in this model represents the combined effects of the flexibility of the downward force train into the shaker field assembly, the mass of the field assembly, and the oscillating magnetic reaction force exerted on the field assembly from the armature. The sample block's differential equation of motion is mx* + k*(x-x ) = F

(3)

Q

where the double dot superscript denotes the second derivative with respect to time, and a l l quantities are defined in Figure 2. Equation 3 can be rewritten as: my + k*y = F - mx'

(4)

o

where y = x-x is the vertical (shear) displacement across the thickness of each specimen. Under steady-state sinusoidal excitation, the time varying quantities can be expressed as: 0

y = Y eJ ; w t

F =F j

u t

;

X

q

=X

Q

e

J

w t

(5)

where u = 2w£ is the excitation frequency in radians/sec and the barred quantities are complex amplitudes. Substituting (5) into (4) gives: k =

+u m 1+

(6)

Observation of the accelerometer signals shows that the support motion, x , is considerably smaller in amplitude than the shear displacement, y. In addition, the driven block mass correction term, arm, is small in comparison with the ratio F/Y for tests at frequencies well below resonance of the sample. Therefore, the approximately-corrected complex stiffness value can be expressed as: G



SATTINGER

Direct Methodfor Measuring Dynamic Shear Properties

///////////

Mechanical Impedance of Sample Support Complex Stiffness of Sample

S777777

Absolute Displacement Coordinates

Mass of Driven Sample Block /T7t777 c

Measured Force Figure 2.

Dynamic model of measurement system.


84


(7) Combining (1), (2), and (7) yields the results


"-k\«

Direct Method for Measuring the Dynamic Shear ... - ACS Publications

Recommend Documents