关键词: 悬臂板, 扭转振形系数, 动态测试, 剪切模量

Abstract: [Objective]The principle and method of testing shear modulus of orthotropic materials(wood)and isotropic materials based on the torsional mode of cantilever plate are discussed.[Method]Firstly, based on the first-order torsional vibration shapes of the cantilever plate according to the ANSYS calculation, the first-order torsional vibration shape function of the displacement w and u, which are perpendicular and parallel to the middle of the plane respectively,are obtained by applying optimization principle. Then, the energy method is used to derive the relational expressions between the first-order torsional frequency and elastic/shear modulus of the cantilever plate, the two vibration shape coefficients are calculated through the integral related with kinetic energy, torsion/tension/compression strain energy, and the binary linear regression of the calculated value of the vibration shape coefficient depends on related expressions of the width-to-length ratio and thickness-to-width ratio.[Result]The relational expressions derived between the first-order torsion frequency and elastic/shear modulus of the cantilever plate, it can be used to calculate shear modulus by the first-order torsional frequency only after obtaining elastic modulus through measuring the first-order bending frequency of the cantilever plate.[Conclusion]The relationship between the first-order torsional frequency and the elastic/shear modulus of the cantilever plate is derived, and the vibration shape coefficient is dependent on the width-to-length ratio and the thickness-to-width ratio. The correctness of relational expressions are verified not only by the dynamic shear modulus determined from low carbon steel, rolling aluminum, Swietenia mahagoni, Fraxinus americana and Ochroma pyramidale, but also by the dynamic and static shear modulus tested from low carbon steel, Picea sitchensis(radial section and transverse section), Quercus mongolica(parallel to grain),Pinus tabulaeformis(tangential section and radial section)and so on. Based on the first-order torsional mode of the cantilever plate and the torsional vibration shape method of the free plate, shear modulus of wood or isotropic materials are in good agreement. The first-order torsional mode based on the cantilever plate provides a simple and rapid method to determine the dynamic shear modulus using cantilever plate. This method can be used not only to test wood shear modulus G_LT, G_LR and G_RT in the three main directions, but also be applied in testing shear modulus of isotropic materials.

Key words: cantilever plate, torsional vibration shape coefficient, dynamic test, shear modulus