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Temperature Derivatives of Elastic Stiffnesses Derived from the Frequency-Temperature Behavior of Quartz Plates,
PRINCETON UNIV NJ DEPT OF CIVIL ENGINEERING
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Linear field equations for small vibrations superposed on thermally induced deformations by steady and uniform temperature changes are derived from the non-linear field equations of thermoelasticity in Lagrangian formulation. From the solutions of these equations for the thickness-vibrations, the temperature derivatives of elastic stiffnesses are related analytically to the known or measured properties such as the second and third order elastic stiffnesses, thermal expansion coefficients, and temperature coefficients of frequency of quartz plates.
APPROVED FOR PUBLIC RELEASE