PEER-REVIEWED RTICLE alysis of Wood Vibratio Eergy tteuatio Based o FFT Vibratio Sigal Yuayua Miao, Miliag Zhog, Zhebo Liu,* ad Fegliag Su The iteral frictio eergy loss of vibratio is a importat idicator showig the vibratioal performace of wood. This paper aalyzed vibratio sigals based o the fast Fourier trasform spectrum. The logarithmic average, logarithmic regressio slope, ad expoetial fuctio fittig methods were used to calculate the atteuatio coefficiet of frictio eergy of wood vibratio i the full time ad differet time periods. The correlatios of δ gaied from differet methods were compared ad aalyzed. The results showed that the liear correlatios betwee differet methods were sigificat i the etire period. The values obtaied usig the logarithmic average ad logarithmic regressio slope methods were similar. For differet time periods, the rate of amplitude decay decreased over time. The values obtaied usig the logarithmic average method had the smallest fluctuatio. I differet time periods, the logarithmic average ad logarithmic regressio slope methods showed a sigificat liear correlatio. However, the expoetial fuctio fittig method showed a low correlatio with the logarithmic average ad logarithmic regressio slope methods. Keywords: Vibratio performace; Wood; Iteral frictio eergy loss; tteuatio coefficiet Cotact iformatio: Northeast Forestry Uiversity, Key Laboratory of Bio-based Material Sciece ad Techology of Natioal Miistry of Educatio, 26 Hexig Rd, Harbi, Heilogjiag, P.R. Chia 50040 Chia; *Correspodig author: liu.zhebo@foxmail.com INTRODUCTION The vibratio atteuatio coefficiet of wood, δ, is a importat parameter of wood vibratioal eergy atteuatio. This coefficiet ot oly represets the degree of wood vibratio eergy atteuatio but also has a crucial ifluece o wood vibratio performace (Norimoto 982; Oo ad Norimoto 983; Norimoto et al. 986; Li 995; Ilic 200; Liu et al. 2005; Cui ad Zhag 2006; Cui ad Zhag 2009; Traore et al. 200). By studyig the atteuatio coefficiet, some vibratio parameters would be obtaied, such as vibratio dampig. Thereby, oe ca use odestructive testig (NDT) to test wood defects. Chiese scholars have made use of the atteuatio coefficiet to calculate the wood vibratio dampig ratio. The umber of kots i wood defects were determied by aalyzig the dampig ratio (She 200). By utilizig formula betwee the atteuatio coefficiet ad modulus of elasticity, oe ca calculate the modulus of elasticity. Thereby, it is possible to evaluate ad classify the mechaical properties of wood (Kubojima et al. 996, 997; She ad Liu 200). Based o previous research (Matsushita et al. 984; Voichita 2005), the vibratio atteuatio coefficiet of wood is a importat parameter that has some ifluece o the accuracy of determiatio of other parameters i wood, such as dampig ratio ad modulus of elasticity. t preset, some scholars have aalyzed the atteuatio coefficiet i the etire time period oly, which may be regarded as lackig i detail (Oo et al. Miao et al. (205). Wood vibratio atteuatio, BioResources 0(), 272-28. 272
PEER-REVIEWED RTICLE 983; Norimoto et al. 986; Bakary et al. 200; Kazuya et al. 200). Vibratio eergy atteuatio has two cases. Oe case represets liear processes of atteuatio, whereas the other case is for oliear atteuatio. s such, aalyzig the atteuatio coefficiet over the etire time period oly would elarge the error of the resultig atteuatio coefficiet, which directly affects the accuracy of the dampig ratio ad modulus of elasticity. Piecewise aalysis of vibratioal eergy could effectively reduce the error. It is of great sigificace for research of vibratio performace ad NDT to use the right method to aalyze vibratioal eergy. I this paper, a fast Fourier trasform (FFT) aalyzer was used to obtai the material vibratio image. Excel calculatios were used to aalyze the time domai sigal. Extractig the maximum ad miimum values also meas extractig the amplitude value. The logarithmic average, logarithmic regressio of slope, ad expoetial fuctio fittig methods were applied to compute the wood vibratioal atteuatio coefficiet δ. Simultaeously, the atteuatio coefficiet δ was aalyzed i differet time periods. Fially, the differece ad correlatio of the atteuatio coefficiet δ obtaied usig differet methods were compared ad aalyzed. By aalyzig data from the etire time period ad differet time periods, oe ca derive the optimal calculatio method of data of the atteuatio coefficiet δ i specific circumstaces. This the allows aalysis of the dampig ratio ad modulus of elasticity or other parameters based o most accurate atteuatio coefficiet δ. EXPERIMENTL Materials Good acoustic properties were observed for two tree species used i this experimet, amely, Picea jezoesis ad Paulowia elogata S.Y. Hu. The samples were cut from the heartwood of 45-year-old Picea jezoesis ad 20-year-old Paulowia elogata S.Y. Hu. They were dried to a moisture cotet of 2%, ad coditioed at 20 C ad 65% relative humidity for 6 moths before testig. total of 66 specimes were used i this study. The sizes of the tree species are show i Table. Table. Various Parameters of the Specimes Specimes* Legth (cm) Width (cm) Thickess (cm) Desity (g/cm 3 ) Picea jezoesis 300 29.923 2.984.034 0.458 Picea jezoesis 30 2.89 2.987.08 0.474 Paulowia elogata S.Y.Hu 300 3.965 3.290.022 0.253 Paulowia elogata S.Y.Hu 30 2.937 3.289.09 0.264 * Picea jezoesis 300, 300 mm Picea jezoesis; Picea jezoesis 30, 30 mm Picea jezoesis; Paulowia elogata S.Y.Hu 300, 300 mm Paulowia elogata S.Y.Hu; Paulowia elogata S.Y. Hu 30, 30 mm Paulowia elogata S.Y.Hu Methods The flexural vibratio method was used i this work. Figure shows that a elastic strig was used for hagig the specime horizotally o the wave-type ode of clear lumber. The, the ode locatio was determied based o the theory of vibratio. Miao et al. (205). Wood vibratio atteuatio, BioResources 0(), 272-28. 273
PEER-REVIEWED RTICLE The vibratioal mode of the fudametal wave (pseudo-primaries) was 0.224 times as log as the specime from the ode to the ed. Iitially, a small woode hammer was used to kock o oe ed of the specime or at its heart. microphoe was placed at the other ed of the specime to receive the sigal. fter this sigal passed through the preamplifier ad filter, the FFT aalyzer was employed to process the time domai sigal ad frequecy domai sigal durig vibratio of the specime. Wood could vibrate uder a outer impact force or a periodic force. fter the exteral force disappeared, the dampig vibratio state commeced. The amplitude icreased with time, as atteuatio follows the proximately egative expoetial law. Whe wood vibrates, vibratioal eergy would gradually decay because of iteral frictio. tteuatio speed is a importat idicator showig wood acoustic vibratio performace. I this research, the logarithmic average, logarithmic regressio of slope, ad expoetial fuctio fittig methods were applied to compute the wood vibratioal eergy atteuatio coefficiet. To compute the iteral frictio idex of wood vibratioal eergy, obtaiig the amplitude value is critical. For each cycle of the origial time domai data, the amplitude icreases with time, as atteuatio follows the proximately egative expoetial law icompletely. s such, the atteuatio coefficiet of the vibratio sigal iitially computed was iaccurate. Therefore, data preprocessig was required. The movig average method was used for data preprocessig of the amplitude value, with the followig calculatio formula, i i m 2 mi where is the umber of movig poits. () Fig.. Wood vibratio characteristic parameter test device Logarithmic average method of the atteuatio coefficiet () The logarithmic ratio of the specific value of the adjacet amplitude value after data preprocessig was computed as follows: Miao et al. (205). Wood vibratio atteuatio, BioResources 0(), 272-28. 274
PEER-REVIEWED RTICLE l, 2 2 l,, 3 l (2) (2) The amplitude value would be the average value of all logarithmic ratios that were obtaied: 2 (l l l ) l (3) 2 3 Logarithmic regressio of slope method of the atteuatio coefficiet () The logarithmic of each amplitude value ratio after data preprocessig was computed as follows: l, 2 l,, 3 l (4) (2) The quatities {, 2,, -} were set as the idepedet variable ad the quatities{ l, l,, l }were set as the depedet variable. s such, the 2 3 slope of the regressio equatios is the atteuatio coefficiet L of the logarithmic value. - xi yi x y i L (5) - 2 2 x x i i xi ={, 2,, -}; yi ={ l, 2... x ; 2 2 l y l,, 2 3 l 3 l } (6)... l l 2 3... Expoetial fuctio fittig method of the atteuatio coefficiet gai the quatities {, 2,, } served as the idepedet variable. The, the preprocessed amplitude value {, 2,, }were set as the depedet variables. These variables were computed o the basis of the expoetial fuctio, as follows: (7) y a e x S (8) xi yi x y i S (9) 2 2 x x i i xi ={, 2,, }; yi ={l, l 2,, l } 2... l l 2... l l 2... x ; y (0) 2 Miao et al. (205). Wood vibratio atteuatio, BioResources 0(), 272-28. 275
PEER-REVIEWED RTICLE Calculated i sectios method of the atteuatio coefficiet The vibratioal time domai sigal was divided ito two or three phases based o time. The, the correspodig atteuatio coefficiet was computed. period of s was devoted to data acquisitio i the test for the 30 mm specimes. Time was divided ito three phases, amely, s to 0.0 s, 0.0 s to s, ad s to 0.03 s. period of s was spet o data acquisitio i the test for the 300 mm specimes. Time was divided ito two phases, amely, s to s ad s to s. The logarithmic average, logarithmic regressio of slope, ad expoetial fuctio fittig methods were applied to compute the wood vibratioal atteuatio coefficiet i differet time periods. RESULTS ND DISCUSSION verage Value of the tteuatio Coefficiet by Differet Computatioal Methods Table 2 shows that the atteuatio coefficiet of Paulowia elogata S. Y. Hu was greater tha that of P. jezoesis, ad the atteuatio coefficiet of 30 mm specimes was greater tha that of 300 mm specimes. Tables 3 ad 4 show the average value of the atteuatio coefficiet i differet time periods. The tables show that the rate of amplitude decay of differet specimes decreased over time. The values obtaied usig the logarithmic average method had the smallest fluctuatio. Table 2. verage Value of the tteuatio Coefficiet by Differet Computatioal Methods Specimes Picea jezoesis 300 Picea jezoesis 30 Paulowia elogata S.Y.Hu 300 Paulowia elogata S.Y.Hu 30 Logarithmic average tteuatio Coefficiet(δ0) Stadard Deviatio Logarithmic regressio of slope tteuatio Stadard Coefficiet(δ L0) Deviatio Expoetial fuctio fittig tteuatio Coefficiet(δ S0) Stadard Deviatio 0.094 25 26 7 0.094 25 0.0397 3 0.0393 99 0.0396 2 32 62 82 67 3 62 70 89 69 4 64 93 Miao et al. (205). Wood vibratio atteuatio, BioResources 0(), 272-28. 276
PEER-REVIEWED RTICLE Table 3. verage Value of the tteuatio Coefficiet i Differet Time Periods (30 mm Specimes) Expoetial fuctio fittig Logarithmic average Logarithmic regressio of slope Specimes Paulowia elogata Picea jezoesis 30 S.Y.Hu 30 tteuatio Stadard tteuatio Stadard Coefficiet Deviatio Coefficiet Deviatio δ S s to 0.0 s 6 0.0 72 0.03 δ S2 0.0 s to s 8 2 22 0 δ S3 s to 0.03 s 06 2 02 2 δ s to 0.0 s 0.0395 9 82 20 δ 2 0.0 s to s 0.0393 06 69 07 δ 3 s to 0.03 s 0.0390 03 67 22 δ L s to 0.0 s 07 9 82 0 δ L2 0.0 s to s 0.0389 4 74 3 δ L3 s to 0.03 s 0.0388 2 63 Table 4. verage Value of the tteuatio Coefficiet i Differet Time Periods (300 mm Specimes) Paulowia elogata Picea jezoesis 300 S.Y.Hu 300 Specimes tteuatio Stadard tteuatio Stadard Coefficiet Deviatio Coefficiet Deviatio Expoetial δ S s to s 25 28 25 36 fuctio fittig δ S2 s to s 4 4 6 80 Logarithmic δ s to s 23 06 65 07 average δ 2 s to s 33 02 0.036 06 Logarithmic δ L s to s 0 22 08 36 regressio of slope δ L2 s to s 2 25 2 0.056 Correlatioal alysis of the tteuatio Coefficiet by Differet Computatioal Methods Correlatio aalysis of the atteuatio coefficiet i the etire period The logarithmic average, logarithmic regressio of slope, ad expoetial fuctio fittig methods were used to calculate the wood vibratioal eergy atteuatio coefficiet for 33 P. jezoesis specimes ad 33 P. elogata S.Y.Hu specimes. The quatities δs, δ, ad were regarded as the correspodig atteuatio coefficiets. The oe-variable liear regressio equatio was used to solve the questio of the correlatio aalysis of the atteuatio coefficiet. Figures 2 ad 3 show that δs, δ, ad represeted the liear correlatios i these specimes. These atteuatio coefficiet values showed sigificat correlatio, with values greater tha 0.9. The correlatio coefficiet values of P. jezoesis were greater tha those of P. elogata S.Y.Hu. For P. elogata S.Y.Hu, the correlatio coefficiets of δ ad were highest (R 2 = 0.9664), ad the correlatio coefficiets of δs ad δ were lowest (R 2 = 0.990). For P. jezoesis, the correlatio coefficiets of δs ad were highest (R 2 = 0.9997), ad the correlatio coefficiets of δs ad δ were lowest (R 2 = 0.974). Takig these factors ito accout ad give that the correlatio coefficiets of δs ad were closer to, the differeces ad correlatios of the atteuatio coefficiets of δ ad were compared ad aalyzed. Miao et al. (205). Wood vibratio atteuatio, BioResources 0(), 272-28. 277
PEER-REVIEWED RTICLE 0.0 δs ad δ δs ad y = 0.8772x + 65 R 2 = 0.99 y = 0.9769x + 04 R 2 = 0.965 0.0 0.0 y = 0.9029x + 6 R 2 = 0.9664 δ δ δs (a) Fig. 2. Correlatio aalysis of δ δ L ad δ S for Paulowia elogata S.Y.Hu (b) δ 0.0 δs ad δ y = 0.86x + 54 R 2 = 0.974 0.0 0.0 δs ad y = 0.9924x + 02 R 2 = 0.9997 y = 0.8678x + 53 R 2 = 0.9748 δ δs (a) Fig. 3. Correlatio aalysis of δ δ L ad δ S for P. jezoesis (b) Correlatio aalysis of δ ad i differet time periods Usig differet badwidths to determie vibratio sigal i the experimet, the 30 mm specimes were differet from the 300 mm specimes with regard to the vibratio sigals obtaied durig differet time periods of data acquisitio. For more scietific results, differet atteuatio coefficiets were compared usig differet legths of specimes. time period of s was employed for data acquisitio i the test for the 30 mm specimes. The specimes were compared ad aalyzed values for three time periods. period of s was used for data acquisitio i the test for the 300 mm specimes. Data were the compared ad aalyzed values for two time periods, amely, s to s ad s to s. Figures 4 to 7 show that δ ad represeted the liear correlatios i these specimes i differet time periods. The smallest correlatio coefficiets were obtaied i the s to 0.03 s period of the 30 mm P. elogata S.Y.Hu, s to s period of the 300 mm P. elogata S.Y.Hu, ad s to s period of the 300 mm P. jezoesis. The other correlatio coefficiet values were greater tha 0.9. I the s to 0.03 s period, the correlatio coefficiet of the 30 mm P. elogata S.Y.Hu was lower tha that of the 30 mm P. elogata S.Y.Hu. Miao et al. (205). Wood vibratio atteuatio, BioResources 0(), 272-28. 278
PEER-REVIEWED RTICLE 0.0 y =.083x - 4 R 2 = 0.9807 y = 0.9603x + 24 R 2 = 0.9638 y = 0.865x + 6 R 2 = 0.53 0.03 0.05 0.07 0.09 δ -0.0s 0.0-s -0.03s 线性 (-0.0s) 线性 (0.0-s) 线性 (-0.03s) Fig. 4. Correlatio aalysis of δ ad δ L for the 30 mm Paulowia elogata S.Y.Hu y = 0.9757x + 2 R 2 = 0.9093 y = 0.973x + 06 R 2 = 0.9822 y = 0.9603x + 4 R 2 = 0.922 0.03 0.05 0.07 δ -0.0s 0.0-s -0.03s Fig. 5. Correlatio aalysis of δ ad δ L for the 30 mm P. jezoesis y = 0.7279x + 5 R 2 = 0.5298 0.03 y =.065x - 47 R 2 = 0.5983 y = 0.4994x + 04 R 2 = 0.9386 0.0 y = 0.5255x - 6E-05 R 2 = 0.969 0.0 0.03 δ -s -s -s δ -s Fig. 6. Correlatio aalysis of δ ad δ L for the 300 mm Paulowia elogata S.Y. Hu Fig. 7. Correlatio aalysis of δ ad δ L for the 300 mm P. jezoesis The other correlatio coefficiet values were similar i other time periods. Differet tree species have differet atteuatio amplitudes. The 300 mm P. elogata Miao et al. (205). Wood vibratio atteuatio, BioResources 0(), 272-28. 279
PEER-REVIEWED RTICLE S.Y. Hu ad 300 mm P. jezoesis had low correlatio coefficiets (R 2 = 0.52 to 0.60) for δ ad. These results show that the atteuatio image was sigificatly chaged at the iitial stage. s such, a suitable computatioal method had to be selected. CONCLUSIONS The logarithmic average, logarithmic regressio of slope, ad expoetial fuctio fittig methods were used to calculate the wood vibratioal eergy atteuatio coefficiet of frictio eergy i the full time ad differet time periods. By aalyzig these differet atteuatio coefficiets, the followig coclusios could be draw:. Geerally, cosiderig the average value of the atteuatio coefficiet obtaied usig the three methods, δ was similar to δs, whereas was sigificatly differet from the other two values. For the etire period, the logarithmic average method was selected as the most suitable way to compute the atteuatio coefficiet whe the vibratio image shows a liear correlatio. 2. For the etire time period, values computed usig the expoetial fuctio fittig, logarithmic average, ad logarithmic regressio of slope methods had sigificat correlatio coefficiet values close to. This result showed slight differeces betwee these three methods. 3. By comparig ad aalyzig the correlatio coefficiet values, a sigificat chage was observed i the vibratio sigal of time domai at the iitial stage. For the oliear vibratio sigal, the logarithmic regressio of slope or expoetial fuctio fittig method should be selected. For the liear vibratio sigal, the logarithmic average method is recommeded. CKNOWLEDGMENTS The authors are grateful for the support by the Fudametal Research Fuds for the Cetral Uiversities (DL2EB03-0), ad the special fud project of Harbi sciece ad techology iovatio talets research (RC202LX-00200) for this research. REFERENCES CITED Cui, Y. Y., ad Zhag, H. J. (2006). Research o the relatioship betwee the umber of kots ad wood modal parameters, Beijig Istitute of Mechaics, The 2 th ual Coferece, 84-86. Cui, Y. Y., ad Zhag, H. J. (2009). Lateral vibratio measuremet structural timber modulus of elasticity, Practical Forestry Techology (2), 57-59. Ilic J. (200). Relatioship amog the dyamic ad static elastic properties of air dry Eucalyptus delegatesis R. Baker, Holz als Roh-ud Werkstoff 59(3), 69-75. DOI: 7/s000700098. Miao et al. (205). Wood vibratio atteuatio, BioResources 0(), 272-28. 280
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