Measurement of shear modulus of materials based on the torsional mode of cantilever plate

Abstract

In this work, the first-order torsional mode shape functions in both directions vertical and parallel to the middle plane of cantilever plate were obtained according to ANSYS software and the optimization principle. The coupling equation of elastic modulus, shear modulus and first-order torsional frequency of cantilever plate was derived with the aid of energy method. The integral of the two mode shape coefficients in the equation, kinetic energy, torsional strain energy and tensile-compressive strain energy were computed. The calculated value was then conducted with binary linear regression to derive the relationship of mode shape coefficient with width-to-length and height-to-width ratios. The correctness of coupling equation was verified by dynamic and static tests of isotropic materials and lumbers of various tree species. The method of measuring shear modulus by frequency spectrum of cantilever plate was proposed and it has advantages of convenience, celerity and good repeatability. This method applies to testing shear modulus of isotropic materials and three main-direction shear modulus (GLT, GLR and GRT) of timbers.