Technical Report: Vibration Damping Materials and Their Performance Measurement 11

When loss coefficient measurement data is plotted with Young's modulus on the x-axis and loss coefficient on the y-axis, the data points are arranged in an inverted "U" shape. This plotting position is the same regardless of the reference temperature T0, and the better the measurement accuracy of the loss coefficient, the more the plot points are arranged on an inverted U shape. Here, the inverted U-shaped curve is drawn based on the curve fitting result of Young's modulus, so if the curve fitting is not done well, the correlation with the measurement data (plot) will be poor. Therefore, data should be read using a converted frequency nomogram rather than from the inverted U-shaped plot. The inverted U-shaped plot is useful for verifying the accuracy of the Young's modulus curve foot and for verifying the measurement accuracy of the loss coefficient and resonant frequency of a test specimen.

As an approximate characteristic of the loss factor-converted frequency, the curve shown in Figure 10 below is curve-fitted. The following equation is used as the approximation formula.

Type 13

Here, k is

Type 14

○ Loss coefficient parameters (8 parameters)

: Slope to the left of the loss coefficient peak
: The right-hand slope of the loss coefficient peak
: Common logarithm of the maximum value of the loss coefficient
: Common logarithm of the converted frequency at which the loss factor is maximized
c: curvature
Qh: Bending strength on the right side of the loss factor
ηh: Loss coefficient at maximum converted frequency
: The bend-equivalent frequency on the right side of the loss factor

As an approximate characteristic of the Young's modulus-converted frequency equation, the curve shown in Figure 11 below is curve-fitted.

The following formula is used as an approximation.

15 type

○ Young's modulus parameters (4 parameters)

Q: Slope of the elastic modulus in the middle
Em: Median of the elastic modulus
fm: Converted frequency of the central part of the elastic modulus
El: Elastic modulus at the minimum equivalent frequency

By determining the curve-fit parameters for the loss coefficients (8) and Young's modulus (4) in this way, the loss coefficients and Young's modulus can be expressed using equations that only involve frequency and do not include temperature, which is expected to allow their application to simulation software such as the finite element method.