Measurement of the Poisson’s Ratio of Materials Based on the Bending Mode of the Cantilever Plate

Zizhen Gao, Xian Zhang, Yunlu Wang, Renchen Yang, Ganggang Wang, Zheng Wang


Principles and methods to dynamically test the Poisson’s ratio of isotropic material and timber are proposed in this work. Five species of lumbers were processed into cantilever plates of tangential, radial, and cross sections with different length-width ratios of 6, 5, 4, and 3. The “Shell 63” element in ANSYS software was adopted to calculate strain and stress under the first-order bending mode. The paste position of the strain rosette for the Poisson’s ratio of timber was obtained through strain-stress relationship and regression analysis under states of stress, strain analysis, and plane stress. This method was also applied to steel, aluminum, and glass. For both isotropic and orthotropic materials such as timber, the paste positions of the strain rosette were determined by the position where transverse stress within the plate was zero during the first-order bending vibration. Meanwhile, the lateral and longitudinal strains of the spectrum were measured using the transient excitation method. In the spectrum, the ratio of linear amplitude between the lateral and longitudinal strain of the first-order bending frequency was taken as the measured value of the Poisson’s ratio of the material. The accuracy of the results was verified by axial tension and static four-point bending tests.


Cantilever plate; First-order bending mode; Stress; Strain; Poisson’s ratio

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