Determinination of the acoustic characteristics of the ligno cellulose plates by non-invasion method.

Stanciu, Mariana Domnica ; Curtu, Ioan ; Luca, Dana Motoc 等

1. INTRODUCTION

Vibration damping of composite ligno-cellulose plates is the phenomenon that occurs as a result of sound losses of sound energy dissipated in the material being an interdependent phenomenon of internal friction (expressed as logarithmic decrement of vibrations damping), the contributions of constituents, their combination of architecture and the stages between phases (Alamoreanu, 2005). Depreciation of the internal mechanisms of wood plates are dependent on their own frequencies, estimating the specific characteristics is also difficult because of the non-isotropy of wood species, density and wood as being an non-homogeneous material. Unlike the homogeneous and isotropic materials, where wood is used for relations theory and applied experimental Beldie (1965), Beldeanu (1996), Vladimirovich (2004), Bucur (2006) and so on, presented below. Thus, internal friction is expressed by the logarithmic decrement or quality factor of vibration damping, Q (Beldie, 1965, Bucur 2006). In the case of forced vibration, the logarithmic decrement (8) is calculated with relation (6.1)--after Beldeanu (1996, 2001):

[delta] = [pi] [[DELTA].sub.F]/[f.sub.r] = [pi] [f.sub.2] - [f.sub.2]/[f.sub.r] (1)

where [f.sub.r] is the resonance frequency in Hz and [f.sub.1], [f.sub.2]--frequencies corresponding vibration amplitudes, [A.sub.1], 2 = 0,707 * [A.sub.max], as Fig. 1 .

[FIGURE 1 OMITTED]

The value of internal friction depends on the moisture content, species, anisotropic direction, size and structure of sample (beam, plate), the regularity and continuity of the wood structure, the mode of fixation and method of investigation.

2. MATERIALS AND METHOD

In the case of the undertaken research were tested ligno-cellulose plates from spruce, sycamore, mahogany, walnut, cherry and alder. Physical characteristics, elastic taken from literature (Bucur 2006; Curtu 1984) and the average values of moisture content of wood and the thickness of plates were measured using ultrasonic device type Merlin PM1-E. The vibration damping was assessed by determining the logarithmic decrement according to relationship of calculation (1). Based on the resonance frequency curve shown in Fig.1 was determined the logarithmic decrement for each plate tested. The experimental setup is presented in Fig. 2.

[FIGURE 2 OMITTED]

3. RESULTS AND DISCUSSION

It was noticed that average values of logarithmic decrements depending on the particular characteristics of wood, even in the same species. These structural differences of the macro and microscopic wood to print the more acoustic characteristics--they are the result of the interaction of nanostructured material. In Fig. 3 are shown the result in terms of logarithmic decrement of different species which are comparable with those in literature. Thus Vladimirovici (2004) recorded values of logarithmic decrement between 0157 / 0377 on similar structures with present test. Given the complex nature of the resonance phenomenon, as a result of interaction of different factors--biochemical, elastic, geometric techniques, sound, a. o., Beldeanu and Pescarus (1996) introduced the concept of sound quality grade, making statistical studies on spruce bars valued as resonance wood.

Thus they established the following groups of values of logarithmic decrement expressed as 2*[pi]*tan[delta], for a sound quality of spruce resonance: very good (0.0175--0.0197), good values (0.0197--0.0219) and failure values (more than 0022). Other studies in the international literature (Bucur, 2006) using ultrasound performed on wood resonance bars shows that the optimum in the range 0.02 0026.

To determine the frequency response of the plate was used Fast Fourier Transform (FFT noted) in the graphics processed with Microcal Origin soft. Thus were obtained the natural frequencies of analyzed plates. It was noticed that the wood species present multiple frequencies which contribute to specific timber. These acoustical properties influence the acouytical quality of musical instruments.

The results led to the grouping of analyzed species by the range of the fundamental frequency. Thus, in terms of classifying species as the fundamental frequency (Fig. 4) species can be grouped in low fundamental frequency (121 Hz-as in the mahogany case) and species with high fundamental frequency (295 Hz--where the cherry case is assigned).

[FIGURE 4 OMITTED]

Spruce is placed between the extreme natural frequencies which makes it able to be combined with different species within the resonance guitar body for instance.

The current research aimed to explain scientific resultant of the acoustic musical instrument--the sound, enriching and improving the quality of the acoustic instrument by theoretical and experimental research undertaken To validate the experimental results obtained, they were compared with those determined by finite element method as can be shown in Fig. 5 (Curtu, Stanciu 2008). It was obtained similarly values which validate both invastigation methods. These results confirm that the mathematical models used are correctly estimated, the parameters and assumptions used are approaching the real values. In this sense, it can be said that numerical method used is a viable way to shape the structures of plates being used with confidence in studies on optimizing the structure of the guitar body.

4. CONCLUSION

In conclusion, the impact hammer used to provide relevant results for the current study, on the acoustic characteristics of wood of different species. Each species presents its the macro and microstructure, for which appreciation acoustic characteristics requires a very rigorous statistical study, which is not subject to present research. Even within the same species, there were differences due non-homogenisity sensitive material timber and method of cutting a semi-plates used in construction.

5. ACKNOWLEDGEMENT

This work was accomplished under the following grants: CNCSIS ID135/2007, project responsible dr. eng. Luca Motoc Dana and researches Curtu Ioan, University Transilvania of Brasov, Stanciu Mariana Domnica, University Transilvania of Brasov, Romania.

6. REFERENCES

Alamoreanu, E., Constantinescu, D. M., (2005). Proiectarea placilor composite laminate (The design of laminated composite plates), Bucuresti, Ed. Academiei Romana, p. 11-30

Beldeanu, E., Pescarus, P. (1996). Research on the Acoustic Quality Classes of Resonance Spruce Wood of Romania. In Proceedings of 10th International Symposium on Nondistructive Testing of Wood, Sopron, Hungary;

Beldeanu, E. (2001). Produse forestiere si studiul lemnului I (Forest and Wood Products Study I), Editia a II a, Editura Universitatii Transilvania din Brasov

Beldie, I. P., (1965). Determinarea frecventelor proprii ale placii viorii, in vederea acordarii acestora. In Rev. Industria Lemnului, nr. 4

Bucur, V. (2006). Acoustic of wood. Springer-Verlag Berlin Heidelberg New York, ISBN-13 978-3-540-26123-0, p.173-216

Curtu, I., Ghelmeziu, N. (1984). Mecanica lemnului si a materialelor pe baza de lemn (Mechanics of wood and wooden materials on the wood), Ed. Tehnica, Bucuresti, Romania (in Romanian)

Curtu I., Stanciu M. D. & Savin A. (2008). The propagation of forced vibrations in coupled plates of guitars, Proceeding of the 19th International DAAAM Symposium "Intelligent Manufacturing & Automation: Focus on Next Generation of Intelligent Systems and Solutions" ISSN 1726-9679, Trnava, Slovacia 22-25 Octombrie 2008, pp 345-346.

Vladimirovici, S. (2004). Calculation Method for the Component Elements of Guitar, PhD Thesis. Technical State Institute Marii, 2004

Fig. 3. Variation of logarithmic decrement depending on
the wood species

Logarithmic decremtn [delta]

Walnut 0.17
Hornbeam 0.208
Cherry 0.214
Spruce 0.268
Maple 0.3165
Mahogany 0.363

Note: Table made from bar graph.

Fig. 5 Comparison between experimental results and results
obtained with finit element method

 FEM, H=3 mm EXP h-28 mm

100 00 202 226
120 00 222 226
14 000 239 226

Note: Table made from bar graph.