Abstract
Wood remains the material of choice for stringed musical instruments. However, as supplies of suitable wood decrease, a need to maximize the use of available timber arises. Since large variations exist within a species, manufacturing processes require direct measurements of the mechanical properties of a given specimen in order to construct acoustically consistent instruments. This paper reports on the application of non-destructive mechanical property tests developed to be used on a single wooden specimen. In this way, relationships between mechanical properties of clear, straight-grained, quartersawn timber can be investigated and the number of measurements during manufacturing can be reduced. Measured properties include density, moisture content, radial and longitudinal Young’s moduli, shear modulus and Poisson’s ratios in the longitudinal–radial plane. Furthermore, natural frequencies of theses specimens have been measured for the rectangular plates having simply supported boundary conditions. Sitka spruce (Picea sitchensis) has been studied. Relationships between various mechanical properties are found, and suggestions for using Poisson’s ratios are proposed. These relationships are shown to reduce the number of measurements required to construct acoustically consistent instruments in musical instrument manufacturing. In particular, it is shown that measurements of the Young’s moduli in both the radial and longitudinal directions would be suitable for describing the important mechanical properties of such soundboard wood. The natural frequencies of the tested plates were also calculated from the measured properties and compared to values obtained experimentally. Great correlation is found between the theoretical model and experimental results for the simply supported rectangular plates.
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References
Amabili M (2004) Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments. Comput Struct 82:2587–2605
Amabili M (2006) Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections. J Sound Vib 291:539–565
ASTM D2395-07ae1 (2007) Test methods for specific gravity of wood and wood-based materials. ASTM International, Philadelphia
ASTM D3043-00 (2011) test methods for structural panels in flexure. ASTM International, Philadelphia
ASTM D3044–94 (2011) Test method for shear modulus of wood-based structural panels. ASTM International, Philadelphia
Canadian Wood Council (2010) Wood design manual 2010. Canadian Wood Council, Ottawa
Carrington H (1923) CV. The elastic constants of spruce. Philos Mag Ser 6(45):1055–1057
Dumond P, Baddour N (2012) Effects of using scalloped shape braces on the natural frequencies of a brace-soundboard system. Appl Acoust 73:1168–1173
Forest Products Laboratory (US) (1999) Wood handbook, wood as an engineering material. U.S. Department of Agriculture, Forest Service, Madison
French RM (2008) Engineering the guitar: theory and practice, 1st edn. Springer, New York
Godin R (2007) Godin guitars factory visit. Princeville, QC
Gommers B, Verpoest I, Van Houtte P (1996) Further developments in testing and analysis of the plate twist test for in-plane shear modulus measurements. Compos A Appl Sci Manuf 27:1085–1087
Haines ME (1979) On musical instrument wood. J Catgut Acoust Soc 31:23–32
ISO 15310–1999 (1999) Fibre-reinforced plastic composites—determination of the in-plane shear modulus by the plate twist method. International Organization for Standardization, Geneva
Kahle E, Woodhouse J (1994) The influence of cell geometry on the elasticity of softwood. J Mater Sci 29:1250–1259
McIntyre ME, Woodhouse J (1985) On measuring wood properties, Part 2. J Catgut Acoust Soc 43:18–24
McIntyre ME, Woodhouse J (1986) On measuring wood properties, Part 3. J Catgut Acoust Soc 45:14–23
McIntyre ME, Woodhouse J (1988) On measuring the elastic and damping constants of orthotropic sheet materials. Acta Metall 36:1397–1416
Mishnaevsky L Jr, Qing H (2008) Micromechanical modelling of mechanical behaviour and strength of wood: state-of-the-art review. Comput Mater Sci 44:363–370
Ogorkiewicz RM, Mucci PER (1971) Testing of fibre-plastics composites in three-point bending. Composites 2:139–145
Schleske M (1990) Speed of Sound and damping of spruce in relation to the direction of grains and rays. J Catgut Acoust Soc 1(6 Series II):16–20
Sims GD, Nimmo W, Johnson AF, Ferriss DH (1994) Analysis of plate-twist test for in-plane shear modulus of composite materials (revised). NPL Report DMM(A)54, National Physical Laboratory, Teddington
Sliker A (1972) Measuring Poisson’s ratios in wood. Exp Mech 12:239–242
Tarnopol’skii YM, Kincis T (1985) Static test methods for composites. Van Nostrand Reinhold Co., New York, p 192
Leissa AW (1969) Vibration of plates. Nasa Sp-160. NASA, Washington, D.C.
Yoshihara H, Sawamura Y (2006) Measurement of the shear modulus of wood by the square-plate twist method. Holzforschung 60:543–548
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The authors would like to acknowledge the generous support provided by the Natural Science and Engineering Research Council of Canada.
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Dumond, P., Baddour, N. Experimental investigation of the mechanical properties and natural frequencies of simply supported Sitka spruce plates. Wood Sci Technol 49, 1137–1155 (2015). https://doi.org/10.1007/s00226-015-0759-z
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DOI: https://doi.org/10.1007/s00226-015-0759-z