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Relationship of logarithmic decrement and density with loss modulus In one variant linear regression analysis above, although there was a highly significant linear relationship between E ’ and ρ as well as between E ” and Δ for the three types of panels tested, the correlation coefficient between E ” and Δ was not particularly high. Thus, a modified regression model was generated where Δ and ρ of the panels were selected as the independent variables x 1 and x 2 , and E ” was selected as the dependent variable y . Their linear regression equations and related parameters are listed in Table 6. Table 6. Linear Regression Equations and Parameters Relating Loss Modulus with Logarithmic Decrement and Density between Three Types of Panels
y = a x 1 + b x 2 + c
Number of Panels
Correlation Coefficient ( r)
Standard Regression Coefficient*
F- statistic
Panel
Variable
a
b
c
1.1455 0.7132 0.7425 0.6153 0.9385 0.4519
x 1 x 2 x 1 x 2 x 1 x 2
PB
69
949.2 0.57
-389
0.922
182.5
MDF
67
1091 0.243 -177
0.946
282.6
PW
58
983.8 0.385 -184
0.911
133.8
*Level of significance = 0.001
The correlation coefficients between E ” , Δ , and ρ among the types of panels tested were significantly higher than those between E ” and ρ in the one variant linear regression analysis discussed previously, which illustrated that a multiple regression model is meaningful for an automatic testing device. Moreover, the linear relationship between ρ and E ” as well as between Δ and E ” were both highly significant at the 0.001 level; as observed from the standard regression coefficients, Δ had a greater effect than ρ on E ” . Results Analysis of Dynamic Viscoelasticity in the Two Kinds of Methods Comparisons with the cantilever beam vibration test were from only one small specimen cut from each panel. Due to possible poor uniformity of the panels tested, there were differences between the density of the panel and density of the small cantilever specimen. In terms of the analysis above, a good linear relationship was still found between E ’ and ρ . However, to minimize the impact of a density difference between the small specimen and full-size WCP on the E ’ s values of small specimens, the impact of density on E ’ s was accounted for by Eq. 8 (Moslemi 1967),
U
'
'
b U E E
(8)
s
s
where E ’ b is the adjusted storage modulus of small specimen, and ρ and ρ s are the average densities of full-size WCP and small specimen, respectively. The density ratio between full-size WCPs and corresponding small specimens ranged from 0.91 to 1.09. s is the unadjusted storage modulus for the small specimen, E ’
4601
Guan et al . (2016). “Dynamic viscoelasticity,” B io R esources 11(2), 4593-4604.
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