Torsional Vibration Method of Cantilever Square Plate for Testing Shear Modulus of Wood

Abstract

The present invention provides a method of torsional vibration of a cantilever square plate for testing the shear modulus of wood. According to the energy principle and regression analysis, the formula for testing the principal shear modulus of wood and the corresponding formula for the vibration mode coefficient are given; this method uses a cantilever square plate as the specimen, which has the advantages of simple operation, convenience and high testing accuracy, and effectively reveals the numerical difference in the shear modulus in two mutually perpendicular directions on the principal plane of wood. In this regard, it is superior to other dynamic methods for testing the shear modulus of wood; this method is applicable to cantilever square plate specimens with a width-to-thickness ratio of 6-30 (or 9-25) for testing the LT, LR, and RT shear moduli of wood and the TL shear modulus (reflected in the vibration mode coefficient C1 and C2 formulas and formula (10) from formula (2) to formula (9)). When the width-to-thickness ratio is 15, the test value of the shear modulus has sufficient accuracy.

Description

Technical Field

[0001] The present invention relates to a method for testing the shear modulus of wood, specifically, a method for testing the shear modulus of wood based on the torsional vibration of a cantilever square plate. Background Art

[0002] References 【1】 A method for testing the shear modulus of wood using a cantilever plate is disclosed. However, the applicable ranges of the vibration shape coefficients C1 and C2 are such that for tangential and radial or cross (cut) - direction cantilever plates of wood, the aspect ratio is 2 - 5 or 2 - 4, and the thickness - width ratio is 5 - 13.7. Moreover, this method cannot show the numerical difference in the shear modulus in two mutually perpendicular directions on the main plane of the wood. Summary of the Invention

[0003] The purpose of the present invention is to provide a torsional vibration method of a cantilever square plate for testing the shear modulus of wood. It uses a cantilever square plate (l / b = 1) as a specimen, with simple method, convenient operation, accurate results, and can show the numerical difference in the shear modulus in two mutually perpendicular directions on the main plane of the wood.

[0004] In the torsional vibration method of a cantilever square plate for testing the shear modulus of wood according to the present invention, one end of the cantilever square plate is fixed; the percussion point is at 0.2l from the fixed end along the long side of the plate, the sound level meter is placed below the free corner point, the percussion point is hammered to make the cantilever square plate vibrate freely, the sound signal is received by the sound level meter, the frequency spectrum of the cantilever square plate specimen is obtained, and the first - order bending frequency f b and the first - order torsional frequency f t of the cantilever square plate are identified from the frequency spectrum diagram; and then the shear modulus G is calculated as follows:

[0005]

[0006] Where: G - shear modulus, Pa; ρ - air - dry density of the material, kg / m 3 ; l - length of the cantilever square plate, m; b - width of the cantilever square plate, m; l = b; h - thickness of the cantilever square plate, m; C1, C2 - vibration shape coefficients of the cantilever square plate; f t - first - order torsional frequency of the cantilever square plate, Hz; β - rectangular cross - section shape factor,

[0007] E 修正 =(1 - 0.1242h / b + 6.2499h 2 / b 2 )E(10)

[0008] That is, the formula for testing the elastic modulus of an Euler beam, E, E 修正 - elastic modulus, Pa; f b-First bending frequency of the cantilever square plate, Hz;

[0009] The cantilever square plate is used as a specimen for testing the shear modulus of wood. When the cantilever square plate undergoes first-order torsional vibration, in addition to considering the kinetic energy and torsional strain energy, the tensile (compressive) strain energy of the cantilever square plate is also taken into account.

[0010] For the above-mentioned torsional vibration method of the cantilever square plate for testing the shear modulus of wood, the mode shape coefficients C1 and C2 of the cantilever square plate of wood (in the LT, LR, and RT directions), and the applicable aspect ratio of the square plate: b / h = 6 - 30; for the cantilever square plate of wood in the TL direction, the mode shape coefficients C1 and C 2， The applicable aspect ratio of the square plate: b / h = 9 - 25.

[0011] Wood tangential plane (LT direction, that is, one end in the L direction is the fixed end of the cantilever square plate):

[0012] C1 = 12.2248 - 2.6533h / b - 39.1946h 2 / b 2 (2)

[0013] (R 2 = 0.9991, n = 7), (b / h = 6 - 30)

[0014] C2 = 0.0707 - 0.1457h / b (3)

[0015] (R = -0.9946, n = 7), (b / h = 6 - 30)

[0016] Wood tangential plane (TL direction, that is, one end in the T direction is the fixed end of the cantilever square plate):

[0017] C1 = 8.5151 - 5.1351h / b (4)

[0018] (R = 0.9999, n = 4), (b / h = 9 - 25)

[0019] C2 = 0.2225 - 1.1436h / b (5)

[0020] (R = -0.9990, n = 4), (b / h = 9 - 25)

[0021] Wood radial plane (LR direction):

[0022] C1 = 11.9466 - 6.9104h / b - 31.2802h 2 / b 2 (6)

[0023] (R 2 = 0.9970, n = 7), (b / h = 6 - 30)

[0024] C2 = 0.0760 - 0.2234h / b (7)

[0025] (R = -0.9919, n = 7), (b / h = 6 - 30)

[0026] Cross-section of wood (RT direction):

[0027] C1 = 12.2815 + 0.0826h / b - 8.1128h 2 / b 2 (8)

[0028] (R 2 = 0.9943, n = 7), (b / h = 6 - 30)

[0029] C2 = 0.0755 - 0.0459h / b, (b / h = 6 - 30) (9)

[0030] (R = -0.9794, n = 7), (b / h = 6 - 30)

[0031] To ensure the test accuracy, a cantilever square plate with a width-to-thickness ratio of 15 is used as the specimen for testing the shear modulus of wood by the torsional vibration method of the cantilever square plate; for a cantilever square plate with a width-to-thickness ratio of 15, the ratio of the test values of the shear modulus in the LT direction to the TL direction of larch is 1.09; the ratio of the test values of the longitudinal and transverse shear moduli of LVL is 1.01; for a cantilever square plate with a width-to-thickness ratio of 10, the ratio of the test values of the shear modulus in the LT direction to the TL direction of larch is 1.16; the ratio of the test values of the longitudinal and transverse shear moduli of LVL is 1.14.

[0032] The correction formula applicable to the test of the elastic modulus of wood with a cantilever square plate:

[0033] E 修正 = (1 - 0.1242h / b + 6.2499h 2 / b 2 )E (10)

[0034] That is, the formula for testing the elastic modulus of an Euler beam, l - the overhanging length of the beam, substitute the width b of the square plate (l = b) when using.

[0035] Where: E, E 修正 - Elastic modulus, Pa; l - the length of the cantilever square plate, m; h - the thickness of the cantilever square plate, m; f b - The first-order bending frequency of the cantilever square plate, Hz.

[0036] Advantages of the present invention: The torsional vibration method of a cantilever square plate for testing the shear modulus of wood can quantitatively show the numerical difference in the shear modulus in two mutually perpendicular directions on the main plane of the wood. In this regard, it is superior to other dynamic methods for testing the shear modulus of wood. Description of the Drawings

[0037] Figure 1 It is a schematic diagram of the coordinate system of a cantilever square plate (l = b);

[0038] Figure 2 It is a schematic diagram of the correspondence between the main directions L, T, R and x, y, z of the square plate (l = b) on the main planes of LT, LR, and RT;

[0039] Figure 3 It is a block diagram of the spectrum test of a cantilever square plate (l = b);

[0040] Figure 4 It is a spectrum diagram of a larch cantilever square plate (b = 100 mm) in the LT direction;

[0041] Figure 5 It is a spectrum diagram of a larch cantilever square plate (b = 100 mm) in the TL direction;

[0042] Figure 6 It is a spectrum diagram of an LVL longitudinal cantilever square plate (b = 145);

[0043] Figure 7 It is a spectrum diagram of an LVL transverse cantilever square plate (b = 145). Detailed Embodiment

[0044] 1. Principle of Testing the Shear Modulus of Wood by the Torsional Vibration Method of a Cantilever Square Plate

[0045] The coordinate system of the cantilever square plate is as Figure 1 shown.

[0046] The method of testing the shear modulus of wood by the torsional vibration of a cantilever square plate is different from the torsional mode method of a cantilever plate 【1】 , specifically manifested in that the modal coefficient in the shear modulus relationship formula is tested according to the first-order torsional frequency of the cantilever square plate.

[0047] The relationship between the shear modulus of wood, the first-order torsional frequency of the cantilever square plate, and the elastic modulus:

[0048]

[0049] The modal coefficients C1 and C2 in Equation (1) are as follows:

[0050] For the tangential plane (LT direction) of wood:

[0051] C1 = 12.2248 - 2.6533h / b - 39.1946h 2 / b 2 (2)

[0052] (R 2 = 0.9991, n = 7), (b / h = 6 - 30)

[0053] C2 = 0.0707 - 0.1457h / b (3)

[0054] (R = -0.9946, n = 7), (b / h = 6 - 30)

[0055] Tangential plane of wood (TL direction):

[0056] C1 = 8.5151 - 5.1351h / b (4)

[0057] (R = 0.9999, n = 4), (b / h = 9 - 25)

[0058] C2 = 0.2225 - 1.1436h / b (5)

[0059] (R = -0.9990, n = 4), (b / h = 9 - 25)

[0060] Radial plane of wood (LR direction):

[0061] C1 = 11.9466 - 6.9104h / b - 31.2802h 2 / b 2 (6)

[0062] (R 2 = 0.9970, n = 7), (b / h = 6 - 30)

[0063] C2 = 0.0760 - 0.2234h / b (7)

[0064] (R = -0.9919, n = 7), (b / h = 6 - 30)

[0065] Transverse (cross) section of wood (RT direction):

[0066] C1 = 12.2815 + 0.0826h / b - 8.1128h 2 / b 2 (8)

[0067] (R 2 = 0.9943, n = 7), (b / h = 6 - 30)

[0068] C2 = 0.0755 - 0.0459h / b, (b / h = 6 - 30) (9)

[0069] (R = -0.9794, n = 7), (b / h = 6 - 30)

[0070] Elastic modulus E correction

[0071] Based on the simulation calculation and regression analysis of the elastic modulus of spruce, Scots pine, and beech cantilever square plates with width-to-thickness ratios of 6, 8, 10, 15, 20, 25, and 30, the correction formula for calculating the elastic modulus from the first-order bending frequency of the cantilever square plate is

[0072] E 修正 = (1 - 0.1242h / b + 6.2499h 2 / b 2 )E(10)

[0073] Where

[0074]

[0075] Through the simulation calculation of the elastic modulus of spruce, Scots pine, and beech cantilever square plates at different width-to-thickness ratios, it is known that when the width-to-thickness ratio of the cantilever square plate is greater than 15, the maximum relative error between the elastic modulus calculated by equations (10) and (11) and the reference value of the elastic modulus is less than 2%. Therefore, when the width-to-thickness ratio of the cantilever square plate is less than 15, equation (10) is required for correction.

[0076] The term C2E in equation (1) 修正 comes from the tensile and compressive strain energy included when the cantilever square plate undergoes first-order torsional vibration. That is, when the cantilever square plate undergoes first-order torsional vibration, the strain energy it has is the sum of the torsional strain energy and the tensile and compressive strain energy. Thus, when applying the energy method to derive equation (1), the term C2E 修正 appears.

[0077] Although equation (1) of this application has similarities with the reference document 【1】 , the applicable ranges and values of the mode shape coefficients C1 and C2 in the equation are different. In the reference document 【1】 , for the C1 and C2 applicable ranges, for wood in the tangential and radial directions or cross (cut) direction cantilever plates, the aspect ratio is 2 - 5 or 2 - 4, but the width-to-thickness ratio is 5 - 13.7. However, for the C1 and C2 applicable ranges in equation (1) of this application, for wood in the tangential, radial, and cross (cut) direction cantilever square plates, the aspect ratio is 1, and the applicable width-to-thickness ratio is 6 - 30. In particular, the TL direction mode shape coefficients C1 and C2 of the tangential plane of the wood in this patent application have not been mentioned in the reference document 【1】 .

[0078] The cantilever square plate is superior to the free square plate in testing the shear modulus of wood, which is manifested in that: when the cantilever square plate is used as a specimen, its longitudinal dimension is equal to its transverse dimension. Through clamping, the differences in the test values of the shear modulus in two mutually perpendicular directions (such as the LT direction and the TL direction) on the main plane of the wood can be effectively distinguished, which cannot be achieved when the free square plate is used as a specimen.

[0079] 2. Simulated values of the shear modulus of wood calculated for the cantilever square plate

[0080] For the cantilever square plates of six tree species, namely spruce, beech, Scots pine, ash, mahogany, and Douglas fir, the ANSYS V19.0 modal program block was used for the simulation calculation of the main-direction shear modulus of wood. The solid 185 element was adopted, and the mesh division was 40×40×6. The aspect ratios of the cantilever square plates involved were 10, 15, 20, and 25 (the plate length and width were both 140 mm). The input material constants calculated by ANSYS are shown in Table 1.

[0081] Table 1 Input parameters for the simulation calculation of the shear modulus of tree species such as spruce, beech, Scots pine, ash, mahogany, and Douglas fir [2]

[0082]

[0083] The corresponding relationship between the subscripts x, y, z of the material constants in Table 1 and the main directions L, T, R of the wood:

[0084] Tangential plane LT, x→L, y→T, z→R; tangential plane TL, x→T, y→L, z→R; radial plane LR, x→L, y→R, z→T; transverse plane RT, x→R, y→T, z→L( Figure 2 )

[0085] The aspect ratios of the calculated cantilever square plates were 10, 15, 20, and 25 (the plate width was 140 mm). The calculated first-order bending frequency and first-order torsional frequency were substituted into Equations (1) to (7) to calculate the simulated values of the main-direction shear modulus. The calculation results show that: (1) For the five tree species of spruce, Scots pine, beech, Douglas fir, and ash, the relative errors of the simulated values of the tangential, radial, and transverse shear moduli with respect to their main-direction shear modulus reference values are within 7% when the aspect ratio of the cantilever square plate is not less than 15; (2) For mahogany, when the aspect ratio is 15, the relative error of the simulated value of the transverse shear modulus with respect to its reference value is less than 7%; if the relative errors of the simulated values of the tangential and radial shear moduli of mahogany with respect to their reference values are both within 7%, then the aspect ratio of its cantilever square plate must be greater than 25.

[0086] 3. Experiment

[0087] 3.1 Experimental design

[0088] 3.1.1 Test Objectives and Methods

[0089] Select larch tangential large boards and LVL whole boards to fabricate larch specimens in the LT direction (along the grain direction of the tangential large board) and the TL direction (across the grain direction of the tangential large board), as well as specimens in the longitudinal direction (along the length of the whole board) and the transverse direction (along the width of the whole board) of the LVL. Apply the torsional vibration method of a cantilever square plate to measure their shear moduli, so as to explore the numerical differences in the shear moduli of wood in two mutually perpendicular directions.

[0090] To verify the effectiveness of the torsional vibration method of a cantilever square plate for measuring the shear modulus of wood, select the free square plate torsional mode method (dynamic) [3] and the asymmetric four-point bending beam method (static) [4] as verification tests.

[0091] 3.1.2 Specimens

[0092] The size of the larch tangential large board is 657 mm × 186 mm × 40 mm, the length along the grain (the length of the large board) is 657 mm, the length across the grain (the width of the large board) is 186 mm, and the thickness of the large board is 40 mm.

[0093] Cut specimens from the larch tangential large board: along the grain (LT direction): 3 pieces of 198 mm × 100 mm × 6.8 mm; 3 pieces of 320 mm × 20 mm × 20 mm; across the grain (TL direction): 3 pieces of 186 mm × 100 mm × 6.2 mm; 3 pieces of 100 mm × 100 mm × 6.8 mm.

[0094] For the 198 mm × 100 mm × 6.8 mm specimens, freely measure E and G; then clamp the 198 mm × 100 mm × 6.8 mm specimens with a clamping depth of 98 mm to realize the measurement of G for the 100 mm × 100 mm × 6.8 mm cantilever square plate; measure G for the 100 mm × 100 mm × 6.8 mm free square plate.

[0095] For the larch TL-direction 186 mm × 100 mm × 6.2 mm specimens, freely measure E and G; clamp them with a clamping depth of 86 mm to realize the measurement of G for the 100 mm × 100 mm × 6.2 mm larch TL-direction cantilever square plate.

[0096] Cut specimens from the LVL whole board along its longitudinal and transverse directions:

[0097] For the LVL longitudinal 295 mm × 145 mm × 10.8 mm specimens, freely measure E and G; then clamp the LVL longitudinal 295 mm × 145 mm × 10.8 mm specimens with a clamping depth of 150 mm to realize the measurement of the LVL longitudinal G for the 145 mm × 145 mm × 10.8 mm longitudinal cantilever square plate;

[0098] For the LVL specimen with dimensions of 295mm×145mm×10.8mm in the transverse direction, E and G are freely tested, and then it is clamped with a depth of 150mm to achieve the test of the transverse cantilever square plate with dimensions of 145mm×145mm×10.8mm for the longitudinal G of the LVL.

[0099] 3.2 Test block diagram (see Figure 3 )

[0100] 3.3 Frequency spectrum

[0101] When testing the frequency spectrum of the cantilever square plate, the tapping point is at 0.2l from the fixed end along the plate edge, and the sound level meter is placed below the free corner point. The first-order bending frequency and the first-order torsional frequency of the cantilever square plate on the frequency spectrum diagram are determined through frequency identification. Figure 4 and Figure 5 respectively show the frequency spectra of the cantilever square plates of larch in the tangential longitudinal (longitudinal) and radial (transverse) directions.

[0102] Figure 4 and Figure 5 respectively show the frequency spectra of the cantilever square plates of larch in the LT direction (100mm×100mm×6.8mm) and the TL direction (100mm×100mm×6.2mm). It can be seen from Figure 4 that the first-order bending frequency f b is 500Hz, and the first-order torsional frequency f t is 684.38Hz. Figure 5 In b the first-order bending frequency f t is 112.5Hz, and the first-order torsional frequency f b is 398.13Hz. Figure 6 and Figure 7 respectively show the frequency spectra of the longitudinal and transverse cantilever square plates (145mm×145mm×10.8mm) of LVL. It can be seen from Figure 6 that the first-order bending frequency f t is 355.63Hz, and the first-order torsional frequency f b is 498.75Hz. Figure 7 In t the first-order bending frequency f

[0103] 4 Results and analysis

[0104] The elastic modulus of larch in the LT direction tested freely is 19.3GPa (1.8%), the elastic modulus of larch in the TL direction is 0.83GPa (3.9%). The ratio of the elastic modulus E L of larch in the LT direction to the elastic modulus E T in the TL direction, E L / E T = 23.3;

[0105] The longitudinal elastic modulus of the free-tested LVL is 13.7 GPa (6.5%), and the transverse elastic modulus of the LVL is 0.66 GPa (3.6%). The longitudinal elastic modulus E of the LVL 纵向 and the transverse elastic modulus E 横向 ratio E 纵向 / E 横向 = 20.8.

[0106] Considering that the LVL is made by gluing and pressing 2-mm-thick veneers cut from poplar wood, and the E 纵向 / E 横向 = 20.8 of the LVL, which is similar to wood, the shape vibration coefficients used in testing and calculating the longitudinal and transverse shear moduli of the LVL are processed according to the LT direction and TL direction of the tangential plane of the wood.

[0107] The shear moduli of larch in the LT direction and TL direction and the longitudinal and transverse shear moduli of LVL tested by the torsional vibration method of a cantilever square plate are shown in Table 2. The shear moduli tested by the torsional mode method of a free square plate are also listed in Table 2.

[0108] Table 2 Shear moduli of larch in the LT direction and TL direction and the longitudinal and transverse shear moduli of LVL tested by the torsional vibration method of a cantilever square plate

[0109]

[0110]

[0111] The data in Table 2 show that: (1) For the torsional vibration method of a cantilever square plate, when the aspect ratio of the cantilever square plate is approximately equal to 15, the mean value of the shear modulus of larch in the LT direction tested is 1020 MPa, and the coefficient of variation is 8.7%. The tested value of the shear modulus of larch in the TL direction has a mean value of 937 MPa, and the coefficient of variation is 4.3%. Thus, the ratio G LT / G TL = 1.09. In addition, the mean value of the shear modulus of larch in the LT direction tested by the asymmetric four-point bending method is 1083 MPa, and the coefficient of variation is 3.0%. The relative error compared with the shear modulus of larch in the LT direction tested by the torsional vibration method of a cantilever square plate is only 5.8%. Therefore, the effectiveness of the torsional vibration method of a cantilever square plate for testing the shear modulus of wood is verified by the asymmetric four-point bending method 【4】 ; (2) When the aspect ratio of the cantilever square plate is approximately equal to 10, the mean value of the shear modulus of larch in the LT direction tested by the torsional vibration method of a cantilever square plate is 912 MPa, and the coefficient of variation is 5.6%. The tested value of the shear modulus of larch in the TL direction has a mean value of 785 MPa, and the coefficient of variation is 8.3%. At this time, G LT / G TL= 1.16; (3) For the free larch square plate in the tangential direction (width-thickness ratio = 15), the length (along the grain) dimension of the square plate is equal to the width (across the grain) dimension, and the four sides of the square plate are free. Unlike the cantilever square plate where the orientation of the clamping edge can be selected, it can measure both the larch LT shear modulus and the larch TL shear modulus. The average value of the larch tangential shear modulus measured by the free square plate torsion mode method is 1067 MPa, and the coefficient of variation is 0.7% (at this time, the numerical difference between the LT shear modulus and the TL shear modulus cannot be distinguished). From the average value, the larch tangential shear modulus measured by the free square plate torsion mode method is 4.2% greater than the larch LT shear modulus measured by the cantilever square plate torsional vibration method. This may be related to the stiffness of the clamped specimen; (4) For the 145 mm×145 mm×10.8 mm LVL cantilever square plate specimen, the ratio of the LVL longitudinal shear modulus to the transverse shear modulus measured by the cantilever square plate torsional vibration method is 1.01, and the LVL shear modulus measured by the free square plate is 5.9% greater than the LVL longitudinal shear modulus measured by the cantilever square plate; (5) For the 100 mm×100 mm×10.8 mm LVL cantilever square plate specimen, the ratio of the LVL longitudinal shear modulus to the transverse shear modulus measured by the cantilever square plate torsional vibration method is 1.14.

[0112] 4 Conclusions

[0113] 4.1 The cantilever square plate torsional vibration method can quantitatively distinguish the numerical differences in the measured values of the longitudinal and transverse shear moduli of wood along the grain, and the difference is related to the width-thickness ratio of the cantilever square plate;

[0114] 4.2 When the width-thickness ratio of the cantilever square plate is 15, the ratio of the larch LT (longitudinal in the tangential plane) shear modulus to the TL (transverse in the tangential plane) shear modulus is 1.09, while for the LVL, the ratio of the longitudinal shear modulus to the transverse shear modulus is 1.01; when the width-thickness ratio of the cantilever square plate is 10, the ratio of the larch LT shear modulus to the TL shear modulus is 1.16, while for the LVL, the ratio of the longitudinal shear modulus to the transverse shear modulus is 1.14;

[0115] 4.3 The effectiveness of the cantilever square plate torsional vibration method for measuring the wood shear modulus is verified by the free square plate torsion mode method (dynamic) and the asymmetric four-point bending beam method (static).

[0116] In summary, to explore the differences in the measured values of the shear modulus in two perpendicular directions on the main plane of wood and its size effect, this patent application proposes a new method for testing the shear modulus of wood, namely the torsional vibration method of a cantilever square plate. First, based on the energy principle and regression analysis, the formula for testing the main shear modulus of wood by the torsional vibration method of a cantilever square plate and the corresponding vibration mode coefficient formula are given; then, the shear modulus simulations of the main LT, LR, and RT directions of wood are carried out on 6 tree species and cantilever square plates with aspect ratios of 10, 15, 20, and 25, and it is found that the cantilever square plate with an aspect ratio of 15 has sufficient accuracy for testing the main shear modulus of wood; at the same time, the first-order torsional vibration modes of the cantilever square plates in the TL main direction of 5 tree species and with aspect ratios of 9, 15, 20, and 25 are calculated to obtain the vibration mode coefficients of the TL cantilever square plates of wood; finally, the shear modulus in the LT direction and the TL direction of larch and the shear modulus in the longitudinal and transverse directions of poplar LVL are tested by the torsional vibration method of a cantilever square plate. The test results show that for the cantilever square plates with aspect ratios of 15 and 10, the ratios of the measured values of the shear modulus in the LT direction and the TL direction of larch are 1.09 and 1.16 respectively; while the ratios of the measured values of the shear modulus in the longitudinal and transverse directions of LVL are 1.01 and 1.14 respectively. The effectiveness of the torsional vibration method of a cantilever square plate for testing the shear modulus in the LT direction of larch is verified by the asymmetric four-point bending beam method (static) and the free square plate torsional mode method (dynamic). The torsional vibration method of a cantilever square plate effectively shows that there are differences in the numerical values of the shear modulus in the mutually perpendicular directions on the main plane of wood, reflecting the anisotropy of wood, and in this regard, it is superior to other dynamic methods for testing the shear modulus of wood.

[0117] References:

[0118] [1] Zhiheng Wang, Yunlu Wang, Yu Cao, Zheng Wang. Measurement of shear modulus of materials based on the torsional mode of cantilever plate [J]. Construction and Building Materials, 2016, 124: 1059 - 1071.

[0119] [2] Yin Sici. Wood Science [M]. China Forestry Publishing House, 1996.

[0120] [3] Wang Zheng, Ding Yewei, Zhang Yifan, etc. Free square plate torsional vibration mode method for testing the shear modulus of wood-based structural panels and wood: China, ZL201910245298.5 [P]. 2019 - 3 - 29.

[0121] [4] Yoshihara H. Edgewise shear modulus of plywood measured by square - plate twist and beam flexure methods. Construction and Building Materials, 2009, 23: 3537–3545. https: / / doi.org / 10.1016 / j.conbuildmat.2009.06.041.

Claims

1. The cantilever square plate torsional vibration method for testing the shear modulus of wood, characterized in that: Relationship between the shear modulus of wood, the first-order torsional frequency of a cantilever square plate, and the elastic modulus of wood: （1） Where: G - shear modulus, Pa; - air-dried density of the material, kg / m 3 ; - length of the cantilever square plate, m; - width of the cantilever square plate, m; = b ; - thickness of the cantilever square plate, m; - mode shape coefficient of the cantilever square plate; - first-order torsional frequency of the cantilever square plate, Hz; - shape factor of the rectangular cross-section, ; The cantilever square plate is used as a specimen for testing the shear modulus of wood; when the cantilever square plate undergoes first-order torsional vibration, in addition to considering kinetic energy and torsional strain energy, the tensile strain energy or compressive strain energy of the cantilever square plate needs to be taken into account. Modified formula applicable to the cantilever square plate for testing the elastic modulus of wood: （10） That is, the Euler beam test elastic modulus formula, - The overhanging length of the beam, which is substituted with the width of the cantilever square plate when in use b Substitute; Wherein: E， - Elastic modulus, Pa; f b - First-order bending frequency of the cantilever square plate, Hz.

2. The cantilever square plate torsional vibration method for testing the shear modulus of wood according to claim 1, characterized in that: The mode shape coefficients C1 and C2 of the cantilever square plates of wood in the LT, LR, and RT directions, applicable aspect ratios of the square plates: ; The mode shape coefficients C1 and C2 of the cantilever square plates of wood in the TL direction, applicable aspect ratios of the square plates: ; Chordal plane of wood in the LT direction: （2） （3） Chordal plane of wood in the TL direction: （4） （5） Radial plane of wood in the LR direction: （6） （7） Cross-sectional plane of wood in the RT direction: （8） （9）。 3. The torsional vibration method of a cantilever square plate for testing the shear modulus of wood according to claim 1, characterized in that: When testing the shear modulus of wood by the torsional vibration method of a cantilever square plate, a cantilever square plate with a width-to-thickness ratio of 15 is used as the specimen.

4. The torsional vibration method of a cantilever square plate for testing the shear modulus of wood according to claim 1, wherein: For a cantilever square plate with a width-to-thickness ratio of 15, the ratio of the measured shear modulus values in the LT and TL directions of larch is 1.09; the ratio of the measured shear modulus values in the longitudinal and transverse directions of LVL is 1.01; for a cantilever square plate with a width-to-thickness ratio of 10, the ratio of the measured shear modulus values in the LT and TL directions of larch is 1.16; the ratio of the measured shear modulus values in the longitudinal and transverse directions of LVL is 1.14.

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