关键词: 悬臂板, 一阶弯曲模态, 应力, 应变, 泊松比

Abstract: [Objective] To explore the principle and methods for dynamic measurement of lumbers Poisson's ratio,the theoretical basis for the dynamic test of Poisson's ratio was given, and a simple and practical method to test the Poisson's ratio of wood was provided.[Method] In this paper, the principle and method of the dynamic measuring Poisson's ratio of wood were described by two aspects:the stress-strain physical relationship (Hooke's law) and the stress and strain analysis of the first-order cantilever bending mode. Five kinds of sawn timber including balsa (Ochroma lagopus), spruce (Picea asperata), scots pine (Pinus sylvestris), ash (Fraxinus chinensis) and beech (Fagus sylvatica). were selected. Cantilever boards were cut with aspect ratio of 6, 5, 4, 3 in tangential section, radial section and cross section. Then the ANSYS shell63 unit was applied to calculate the strain and stress under the first-order bending mode. Strain rosette paste position for dynamic measuring the Poisson's ratio of wood was determined by analysis of the stress-strain relationships. Finally, static tests were conducted to verify the correction of dynamic Poisson's ratio tests.[Result] When the cantilever board suffered first-order bending vibration, the ratio of the transverse strain ε_y and longitudinal strain ε_x was increased with the increasing distance between the loading point and the cantilever end. The ratio of the transverse stress σ_y and longitudinal stress σ_w was small in the whole board, and decreased from a positive value to negative value with the increase of the distance to the cantilever end. In the position of σ_y equal to zero, the absolute value of the ratio of transverse strain and longitudinal strain was not only equal to Poisson's ratio μ_LT, μ_LR and μ_RT was also equal to the ANSYS input Poisson's ratio. Therefore, the strain rosette paste position for dynamic testing the Poisson's ratio of wood could be determined.[Conclusion] The strain rosette paste position for dynamic testing the Poisson's ratio, and of wood was depended on the position where the transverse stress was equal to the zero. As for the cantilever board with tangential section, the strain rosette paste position was related to the density and the width-and-length ratio of board. With regard to the cantilever board with radial section and cross section, the strain rosette paste position was only depended on the length-and-width ratio of board. The lateral and longitudinal strain spectrum was measured by transient excitation, and the dynamic Poisson's ratio was determined by the ratio of transverse and longitudinal strain's linear spectral amplitude of the first-order bending frequency. The ratio of the transverse stress and longitudinal stress in the cantilever board were very small, the maximum ratio for beech was 0.043, and the maximum ratio for balsa wood, spruce, Scots pine and ash wood were all about 0.02. Therefore, the stress distribution in cantilever boards was different from the isotropic material such as low carbon steel and aluminum. However, due to the greatly different in wood orthotropic elastic modulus, the ratio of transverse stress σ_y and longitudinal stress σ_x should not be ignored when dynamic testing the Poisson's ratio of wood. The correction of the dynamic method was verified by the static axial tension test and four point bending test. Furthermore, the dispersion of the wood Poisson's ratio was improved by dynamic measurement compared with the static test.

Key words: the cantilever board, the first-order bending mode, stress, strain, Poisson's ratio