Polynomial expressions for estimating elastic constants from the resonance of circular plates

Two approaches were taken to make convenient spread sheet calculations of elastic constants from resonance data and the Tables in ASTM C1259 and E1876: (1) polynomials were fit to the tables; (2) an automated spread sheet interpolation routine was generated. To compare the approaches, the resonant frequencies of circular plates made of glass, hardened maraging steel, alpha silicon carbide, silicon nitride, tungsten carbide, tape cast NiO–YSZ, and zinc selenide were measured. The elastic constants, as calculated via the polynomials and linear interpolation of the tabular data in ASTM C1259 and E1876, were found comparable for engineering purposes, with the differences typically being less than 0.5%. Calculation of additional ν values at t/R between 0 and 0.2 would allow better curve fits. This is not necessary for common engineering purposes, however, it might benefit the testing of emerging thin structures such as fuel cell electrolytes, gas conversion membranes, and coatings when Poissonʹs ratio is less than 0.15 and high precision is needed.