测试木材剪切模量的自由方板扭转模态法

doi:10.11707/j.1001-7488.LYKX20220293

Abstract

Abstract:

Objective: In order to expand the applicable range of the free square plate when testing the principal shear modulus of wood, this paper proposes a new method for dynamically testing the shear modulus of wood, namely the free square plate torsional modal method. Method: According to the unique first-order torsional mode characteristics and energy method of the wood free square plate, the relationship between the principal shear modulus of wood and the first-order torsional frequency of the free square plate is derived. First-order torsional modal frequencies of free-square plates were calculated using ANSYS for different tree species and different width-to-thickness ratios. Simulation and regression analysis were performed to obtain the modified equation between the principal directional shear modulus of wood and its first-order torsion frequency of the free-square plate (free-square plate torsion modal law equation). Result: The torsional mode characteristics of wood free slabs are divided into three categories according to the aspect ratio(l/b) of the free slab: l/b ≥3, l/b= 2 and l/b=1. The torsional mode shape of a free plate with l/b ≥3 varies along its long side curve, while it varies linearly along its broad side. The torsional mode shape of a free square plate (l/b=1) varies linearly along its long side and curves along its broad side. The torsional mode shape of a free plate with aspect ratio of 2(l/b= 2) varies curvilinearly along both its long and wide edges. Conclusion: The free square plate torsional modal method for testing the principal shear modulus of wood has a reliable theoretical basis. The square plate width-to-thickness ratio used to test the principal shear modulus of wood is in the range of 7-30 for the chordwise, radial and transverse square plates of wood, to reduce the limit of the width-to-thickness ratio of the opposite plate. The free square plate torsional modal method is suitable for testing both the principal shear modulus of wood and the shear modulus of wood composite panels and isotropic materials. Its effectiveness is verified by the free-bar torsional vibration method and the asymmetric four-point bending method. The method has the advantages of simple test operation and high-test accuracy. Theoretical analysis and experimental results both show that the shear modulus of wood composites and wood by the traditional free square plate torsional vibration method is low, and the low degree is related to the material type and the square plate width-to-thickness ratio.

Key words: free square plate, wood, wood composite panels, shear modulus, torsion vibration mode, torsional frequency, testing

CLC Number:

S781.2

Zheng Wang,Xiaoyu Gu,Yuhao Zhou,Yifan Zhang,Zhaoyu Shen,Yujie Huang. Free Square Plate Torsional Mode Method for Measurement of Shear Modulus of Timber[J]. Scientia Silvae Sinicae, 2023, 59(5): 145-156.

Figures/Tables 18

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References 0

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树种 Species	ρ/(kg·m^?3)	主向面 Main-direction plane	E_x/GPa	E_y/GPa	E_z/GPa	μ_xy	μ_yz	μ_xz	G_xy/GPa	G_yz/GPa	G_xz/GPa
西加云杉 Picea sitchensis	390	LT	11.60	0.50	0.90	0.47	0.250	0.370	0.720	0.039	0.75
		LR	11.60	0.90	0.50	0.37	0.430	0.470	0.750	0.039	0.72
		RT	0.90	0.50	11.60	0.43	0.020	0.029	0.039	0.720	0.75
山毛榉 Fagus longipetiolata	750	LT	13.70	1.14	2.24	0.51	0.360	0.450	1.060	0.460	1.61
		LR	13.70	2.24	1.14	0.45	0.750	0.510	1.610	0.460	1.06
		RT	2.24	1.14	13.70	0.75	0.044	0.073	0.460	1.060	1.61
欧洲赤松 Pinus sylvestris	550	LT	16.30	0.57	1.10	0.57	0.310	0.420	0.680	0.066	1.16
		LR	16.30	1.10	0.57	0.42	0.680	0.570	1.160	0.066	0.68
		RT	1.10	0.57	16.30	0.68	0.150	0.038	0.066	0.680	1.16
北美黄杉 Pseudotsuga menziesii	590	LT	16.40	0.90	1.30	0.37	0.400	0.430	0.910	0.079	1.18
		LR	16.40	1.30	0.90	0.43	0.630	0.370	1.180	0.079	0.91
		RT	1.30	0.90	16.40	0.63	0.024	0.028	0.079	0.910	1.18

方板宽厚比 Width-thickness ratio	木材方板主向振型系数 Main-direction mode shape coefficient
方板宽厚比 Width-thickness ratio	LT	LR	RT
7	7.566 3	7.569 4	8.479 0
10	7.640 7	7.646 8	8.491 3
15	7.698 5	7.724 9	8.512 3
20	7.717 7	7.752 8	8.538 2
25	7.730 4	7.771 2	8.566 8
30	7.706 4	7.766 6	8.587 2
均值Mean	7.671 5	7.698 0	8.524 1
变异系数 Coefficient of variation (%)	0.77	1.01	0.51

材质或树种 Material	l/mm	b/mm	h/mm	数量 Quantity/piece	b/h	ρ/(kg·m^?3)	含水率 Moisture content（%）
胶合板(7层) Plywood (7 layers)	240	240	9.00	5	26.7	581	9.0
定向刨花板 OSB	120	120	10.94	6	11.0	623	9.0
铁杉弦向 Tangential Tsuga chinensis	135	135	12.95	5	10.4	422	9.5
红雪松弦向 Tangential Thuja plicata	147	147	13.96	5	10.5	385	9.0
西加云杉径向 Radial Picea sitchensis	115	115	12.44	6	9.2	408	9.5
西加云杉横向 Transverse Picea sitchensis	116	116	11.89	6	9.8	368	9.0
落叶松弦向 Tangential Larix gmelinii	155	155	9.61	8	16.1	590	9.0
落叶松径向 Radial Larix gmelinii	118	118	11.41	6	10.3	748	9.0
落叶松弦向 Tangential Larix gmelinii	240	20	20.12	6	非对称四点弯曲 Asymmetric four-point bending	628	9.5
落叶松径向 Radial Larix gmelinii	240	20	24.03	6	非对称四点弯曲 Asymmetric four-point bending	748	8.0

材质或树种 Material	l/mm	b/mm	h/mm	数量 Quantity/piece	ρ/(kg·m^?3)	含水率 Moisture content（%）
胶合板(7层) Plywood (7 layers)	340	60	8.98	8	550	9.5
定向刨花板 OSB	699	113	11.27	3	639	9.0
铁杉弦向 Tangential Tsuga chinensis	405	133	12.80	3	475	9.0
红雪松弦向 Tangential Thuja plicata	768	148	19.92	3	389	9.0
西加云杉径向 Radial Picea sitchensis	400	71	12.39	8	379	9.5
西加云杉横向 Transverse Picea sitchensis	400	71	12.36	8	367	9.0

l/ mm	b/ mm	h/ mm	数量 Quantity/piece	b/h	ρ/ (kg·m^?3)	$ {G}_{\mathrm{L}\mathrm{T},\mathrm{ }\mathrm{E}2} $ / MPa	$ {G}_{\mathrm{L}\mathrm{T},\mathrm{ }\mathrm{E}5} $ / MPa
155	155	9.60	8	16.1	590	880(10.8%)	917(10.7%)
115	115	9.65	8	11.9	579	839(12.4%)	913(12.4%)
90	90	9.68	8	9.3	567	800(15.5%)	917(15.5%)
70	70	9.68	8	7.2	569	765(19.0%)	944(19.0%)

Free Square Plate Torsional Mode Method for Measurement of Shear Modulus of Timber

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树种 Species	主向 Main-direction plane	自由方板扭转模态法剪切模量 G obtained by free square plate torsional mode method /MPa	自由杆件扭转振动法剪切模量 G obtained by free rod torsional vibration method/MPa
铁杉 Tsuga chinensis	LT	686(3.3%)	637 (7.7%)
红雪松 Thuja plicata	LT	704 (6.2%)	698 (7.5%)
西加云杉 Picea sitchenrsis	LR	699 (1.4%)	737 (9.5%)
西加云杉 Picea sitchenrsis	RT	44.6 (12.9%)	47.0(8.3%)

材质 Material	自由方板扭转模态法剪切模量 G obtained by free square plate torsional mode method /MPa	自由杆件扭转振动法剪切模量 G obtained by free rod torsional vibration method/MPa
OSB	1 328(6.8%)	1 329(4.9%)
胶合板 Plywood	763 (4.3%)	699 (5.2%)

材质和树种 Material	宽宽厚比 b/h	自由方板扭转模态法剪切模量G obtained by free square plate torsional mode method/MPa	自由方板扭转振动法剪切模量 G obtained by free rod torsional vibration method/MPa
铁杉弦向 Tangential Tsuga chinensis	11.3	686 (3.3%) )	559 (3.3%)
红雪松弦向 Tangential Thuja plicata	10.5	704（6.2%)	576 (10.1%)
西加云杉径向 Radial Picea sitchenrsis	9.2	699 (1.4%)	510 (1.1%)
西加云杉横向 Transverse Picea sitchenrsis	9.8	44.6 (12.9%)	36.2 (14.6)
OSB	11.0	1 328(6.8%)	1 137 (7.2%)
胶合板 Plywood (7 layers)	26.7	763 (4.3%)	736 (4.3%)

长 Length/mm	宽 Width/mm	厚 Thickness/mm	长宽比 Aspect ratio	自由板扭转振型法 Free plate torsional mode method G/MPa	自由杆件扭转振动法 Free-rod torsional vibration method G/MPa
320	100	10.8	3.2	915（2.5%）	985（3.2%）
220	100	10.8	2.2	884（5.9%）	978（5.9%）
100	100	10.8	1.0	757（1.4%）	794（1.4%）

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