Resonant acoustic determination of complex elastic moduli
Abstract
A simple, inexpensive, yet accurate method for measuring the dynamic complex modulus of elasticity is described. Using a 'freefree' bar selectively excited in three independent vibrational modes, the shear modulus is obtained by measuring the frequency of the torsional resonant mode and the Young's modulus is determined from measurement of either the longitudinal or flexural mode. The damping properties are obtained by measuring the quality factor (Q) for each mode. The Q is inversely proportional to the loss tangent. The viscoelastic behavior of the sample can be obtained by tracking a particular resonant mode (and thus a particular modulus) using a phase locked loop (PLL) and by changing the temperature of the sample. The change in the damping properties is obtained by measuring the inphase amplitude of the PLL which is proportional to the Q of the material. The real and imaginary parts or the complex modulus can be obtained continuously as a function of parameters such as temperature, pressure, or humidity. For homogeneous and isotropic samples only two independent moduli are needed in order to characterize the complete set of elastic constants, thus, values can be obtained for the dynamic Poisson's ratio, bulk modulus, Lame constants, etc.
 Publication:

Technology 2001: The Second National Technology Transfer Conference and Exposition, Volume 2
 Pub Date:
 December 1991
 Bibcode:
 1991tetr....2...32B
 Keywords:

 Dynamic Modulus Of Elasticity;
 Q Factors;
 Torsion;
 Vibration;
 Viscoelasticity;
 Bulk Modulus;
 Damping;
 Humidity;
 Isotropy;
 Low Cost;
 Phase Locked Systems;
 Poisson Ratio;
 Acoustics