0
TECHNICAL PAPERS

# Inferring Viscoelastic Dynamic Material Properties From Finite Element and Experimental Studies of Beams With Constrained Layer Damping

[+] Author and Article Information
Stephen A. Hambric

Applied Research Laboratory, The Pennsylvania State University, P.O. Box 30, State College, PA 16804sah19@only.arl.psu.edu

Andrew W. Jarrett

Carderock Division, Naval Surface Warfare Center, 9500 MacArthur Boulevard, West Bethesda, MD 20817-5700andrew.jarrett@navy.mil

Gilbert F. Lee

Carderock Division, Naval Surface Warfare Center, 9500 MacArthur Boulevard, West Bethesda, MD 20817-5700gilbert.f.lee@navy.mil

Jeffry J. Fedderly

Carderock Division, Naval Surface Warfare Center, 9500 MacArthur Boulevard, West Bethesda, MD 20817-5700jeffry.fedderly@navy.mil

In spite of the significant literature in the field of viscoelastic dynamic material property measurements, direct comparisons of the master curves produced by different measurement techniques made on a given material are not readily available.

Moduli are measured using the RA method at several resonance frequencies of the test specimen, which are typically much higher than the frequencies of measurement in the DMTA method. Appendix includes RA plots which are complementary to those in Figs.  45.

See Appendix for similar plots based on RA measurements.

The ANSI standards specify the natural logarithm, but many engineers use the base 10 logarithm instead. In this paper, the base 10 logarithm is used.

$c1$ and $c2$ vary with reference temperature. To compute new $c$ factors at a different reference temperature $Tnew$, $c2new=c2+Tnew−T0$, and $c1new=c1c2∕c2new$.

In traditional inference techniques, both system loss factor and resonance frequency are used to infer modulus and loss factor of the viscoelastomer. When system loss factors are high, however, it is more difficult to estimate resonance frequency accurately, and we consider only the loss factor in our trial and error procedure.

J. Vib. Acoust 129(2), 158-168 (Aug 04, 2006) (11 pages) doi:10.1115/1.2424984 History: Received April 21, 2006; Revised August 04, 2006

## Abstract

Viscoelastic materials are often used to add damping to metal structures, usually via the constrained layer damping method. The added damping depends strongly on material temperature and frequency, as do the underlying material properties of the viscoelastomer. Several standardized test methods are available to characterize the dynamic material properties of viscoelastomers. However, they rely on limited test data which is extrapolated using the time—temperature superposition technique. The authors have found that the different testing methods typically produce significantly different dynamic material properties, or “master curves.” An approach for inferring viscoelastomer dynamic moduli with better accuracy is suggested here. Several metal bars are treated using constrained layer damping. Experimental modal analyses are conducted on the bars at different temperatures to produce sets of system resonance frequencies and loss factors. Corresponding finite element (FE) models of the treated bars are analyzed using assumed viscoelastomer material properties based on master curves generated using a standardized test technique. The parameters which define the master curves are adjusted by trial and error until the FE-simulated system loss factors match those of the measurements. The procedure is demonstrated on two viscoelastomers with soft and stiff moduli.

<>

## Figures

Figure 1

Resonance apparatus (RA) testing; all testing performed in temperature controlled chamber

Figure 2

Dynamic measurement test apparatus (DMTA); all testing performed in temperature controlled chamber

Figure 3

Oberst beam testing; all testing performed in temperature controlled chamber

Figure 4

Young’s modulus (top) and loss factor (bottom) of Viscoelastomer 2, raw data from DMTA testing

Figure 5

Young’s modulus (top) and loss factor (bottom) of Viscoelastomer 2, shifted data (using WLF curvefit) from DMTA testing; T0=10°C, c1=12.0, and c2=96.2

Figure 6

Master shear modulus and loss factor HN curves fit to manually shifted data from DMTA testing of Viscoelastomer 2 at 10°C. Boxes indicate regions where manually and WLF shifted data disagree.

Figure 7

Manual and WLF shift factors for viscoelastomer 2 at 10°C, DMTA testing

Figure 8

Manually shifted shear moduli and loss factors, along with shift factors from DMTA and RA testing of viscoelastomer 2 at 10°C

Figure 9

Steel test bar with CLD treatment with free boundary conditions

Figure 10

FE model of bar with CLD

Figure 11

Typical bending mode at right end of FE model of CLD-treated bar. Constraining layer and viscoelastic material are at the top of the bar.

Figure 12

Measured and FE CLD-treated bar loss factors for Viscoelastomer 1, FE simulations used HN equation generated properties based on curve fits of RA (top), and DMTA (bottom) test data

Figure 13

Shear modulus (top), loss factor (middle), and shift factors (bottom) of Viscoelastomer 1 at 10°C—including new master curves inferred from FE analyses and measurements

Figure 14

Measured and FE CLD-treated bar loss factors for Viscoelastomer 1; FE simulations used WLF and HN equation generated properties based on trial and error

Figure 15

Measured and FE CLD-treated bar loss factors for Viscoelastomer 2, FE simulations used HN equation generated properties based on curve fits of DMTA test data

Figure 16

Shear modulus (top), loss factor (middle), and shift factors (bottom) of viscoelastomer 2 at 10°C—including new master curves inferred from FE analyses and measurements

Figure 17

Measured and FE CLD-treated bar loss factors for Viscoelastomer 2, FE simulations used WLF and HN equation generated properties based on trial and error

Figure 18

Young’s modulus (top) and loss factor (bottom) of Viscoelastomer 2, raw data from RA testing

Figure 19

Young’s modulus (top) and loss factor (bottom) of Viscoelastomer 2, shifted data from RA testing

Figure 20

Measured, FE, and RKU CLD-treated bar loss factors for Viscoelastomer 2, FE, and RKU simulations used HN equation generated properties based on trial and error

Figure 21

Finite element mesh discretization at right end of bar with CLD; top—mesh used for all studies presented in this paper, bottom—mesh refined along width and length to establish convergence

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections