Smoothing, Interpolating, and Modeling Complex Modulus Data for Viscoelastic Damping Materials, Including a New Approach to Temperature Shift Functions
The present theory and implementation methodology for the smoothing, interpolation, and modeling of complex modulus data for viscoelastic damping materials has achieved a substantial level of maturity, accuracy, and efficiency; moreover, interconversion among any of the dynamic mechanical properties, the display of relaxation and retardation spectra, and estimated relative molecular weight distribution are greatly facilitated. One key aspect of the approach is to use a ratio (where the order of the numerator and denominator are equal) of polynomials of first order factors to model the complex modulus; this guarantees intrinsically that the required properties of linear systems are satisfied, while also providing an ease of numerical convergence and of interconversion. A second key aspect is the use of the Wicket Plot to 1) edit and perform a quality check on the data, 2) smooth and interpolate the data, 3) map its arc length onto reduced radian frequency, thereby intrinsically defining the complex valued modulus as a function of the reduced radian frequency, and 4) determine the value of the temperature shift function for each experimental data point, an entirely new procedure.