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Gliga, V. G., Stanciu, M. D., Nastac, S. M., and Campean, M. (2020). "Modal analysis of violin bodies with back plates made of different wood species," BioRes. 15(4), 7687-7713.

Abstract

This research investigated the potential of some European wood species for use in the manufacturing of the back plates of violins as an alternative to the quite rare curly maple wood. An experimental modal analysis was employed for this purpose using the impact hammer method. The modal analysis was performed both on the top and back plates, as individual structures, and then after being integrated into the violin body. The modal analysis envisaged the determination of the eigenfrequencies (natural frequencies), the number of spectral components, and the quality factor, as important indicators of the acoustic performances of a musical instrument. A multi-criteria analysis based on the values obtained for these indicators allowed interesting findings concerning the acoustic properties of the selected wood species (hornbeam, willow, ash, bird-eye maple, walnut, and poplar). Same as curly maple, they all have special aesthetics, but only hornbeam, willow, and ash wood proved to have acoustic potential as well.


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Modal Analysis of Violin Bodies with Back Plates Made of Different Wood Species

Vasile Ghiorghe Gliga,a Mariana Domnica Stanciu,Silviu Marian Nastac,c,b and Mihaela Campean a,*

This research investigated the potential of some European wood species for use in the manufacturing of the back plates of violins as an alternative to the quite rare curly maple wood. An experimental modal analysis was employed for this purpose using the impact hammer method. The modal analysis was performed both on the top and back plates, as individual structures, and then after being integrated into the violin body. The modal analysis envisaged the determination of the eigenfrequencies (natural frequencies), the number of spectral components, and the quality factor, as important indicators of the acoustic performances of a musical instrument. A multi-criteria analysis based on the values obtained for these indicators allowed interesting findings concerning the acoustic properties of the selected wood species (hornbeam, willow, ash, bird-eye maple, walnut, and poplar). Same as curly maple, they all have special aesthetics, but only hornbeam, willow, and ash wood proved to have acoustic potential as well.

Keywords: Violin; Top plate; Back plate; Violin body; Modal analysis; Fundamental frequency; Number of spectral components; Quality factor

Contact information: a: Transilvania University of Brasov, Faculty of Wood Engineering, Universitatii Str. 1, 500036 Brasov, Romania; b: Transilvania University of Brasov, Faculty of Mechanical Engineering, Politehnicii Str. 1, 500024 Brasov, Romania; c: Dunarea de Jos University of Galati, Faculty of Engineering and Agronomy in Braila, MECMET Research Center, Calea Calarasilor Nr. 29, 810017 Braila, Romania; *Corresponding author: campean@unitbv.ro

Graphical Abstract 

INTRODUCTION

The violin is a “fundamental tool of human expression that reveals and reflects the historical, technological, social, and cultural aspects of time and people” (Perez and Marconi 2018). Created at the beginning of the 16th century in the northern part of Italy (Hutchins 1983), the violin is still considered to be one of the most exquisite musical instruments, not only due to its major role, sometimes as a solo instrument in the orchestra and in a wide variety of musical genres, but also due to the fact that each violin actually represents a fine work of art made from wood.

Spruce and maple are the two most favored wood species used by luthiers for the crafting of violins. The top plate with the specific f-holes, the soundpost, and the bass bar (placed inside the violin body) are made of resonance spruce wood (Picea abies), while the back plate, the ribs, and the neck are usually made of curly maple (Acer pseudoplatanus). The bridge and the fingerboard are made of ebony. Lime or willow wood are used for some elements of the counter-ribs.

As far as the raw material for the violin top plate is concerned, no other wood species could ever surpass the characteristics and acoustic performances of resonance spruce wood. Its main features are the homogeneous structure, with narrow (1 to 3 mm), regular annual rings, with a low latewood proportion (less than 20 to 35% of the annual ring width), which gives a light coloration of the wood, fine narrow rays, relatively low density (below 450 kg/m3), low resin content (without resin pockets), uniform color, the white, golden-white, and silky gloss of the wood, and straight grain (Bucur 2006; Beldeanu 2008; Stanciu and Curtu 2012).

The resonance spruce is harvested during the vegetative rest period because in the vegetation season with the presence of sap, which contains resin as well, the acoustic characteristics of the wood are depreciated. The tree diameter must be chosen to obtain logs with diameters of 400 to 600 mm (Dinulica et al. 2019). This diameter range is required for the radial cutting of the elements used for musical instruments. The trees are felled when the outside temperature is 3 to 5 °C, under heavy snow conditions, to avoid deterioration during felling.

An important aspect regarding the raw material preparation technology is the drying method used and its duration. The resonance wood is usually naturally dried until a moisture content of 15% is reached. To dry further, kiln-drying must be employed, considering that in the temperate climate zone, the moisture bound by adsorption inside the wooden cell walls cannot be eliminated from wood at ambient temperature (Campean and Marinescu 2012). It is true that kiln-drying must be avoided, as much as possible, because even mild kiln-drying conditions cause internal stresses and phenomena at the microcellular level that destroy the acoustic qualities of the resonance wood (Stanciu and Curtu 2007; Obataya et al. 2020). As a consequence, the drying duration of wood for musical instruments might last from 3 to 12 years or even more, depending on the quality class of the violin (Dinulica et al. 2015).

When it comes to choosing the material for the back plate of the violin body, luthiers have a higher degree of freedom than for the top plate. Although the back plate also plays an important acoustic role as part of the resonance body (where the top and back plate assembly must operate as a membrane, capable to transmit vibrations and to amplify them), the material characteristics imposed for this part of the violin are not as strict anymore. Thus, Hutchins (1981) considered that, from the acoustical point of view, the top plate and the back plate of a violin must have the same tone, and the frequency of mode 2 in the top plate should be within 1.4 % of that in the back. The tuning of the two plates can be obtained even if different wood species are used, but the tuning effect can be sensed only after assembling the two plates and creating the violin body.

Fig. 1. Violin back plate made of curly maple (manufactured by Gliga Instruments, Reghin, Romania)

Fiber-reinforced polymers or composites can be also used as an alternative for manufacturing the violin plates (e.g. Damodaran et al. 2015; Duerinck et al. 2018; Philips and Lessard 2018).

Coming back to the choice of the wooden raw material for the violin back plate, curly maple (Acer pseudoplatanus) is the favorite, due to its decorative pattern (Fig. 1). The wavy grain in maple is a natural “defect” that increases not only the aesthetic value, but also the acoustical properties of this wood species (Bucur 2006; Stanciu 2020).

Even if curly maple is the favorite choice, alternative wood species are worth being investigated as well, considering the scarcity of curly maple resources in the world’s forests and the fact that this species is also in demand in the furniture industry.

However, reference literature provides only minimal information on attempts of using alternative wood species in the construction of musical instruments. For example, Bond (1976) (cited by Bucur 2006) proposed the tropical wood called merbau or mirabou (Intsia bakeri) for the back of the violin. Another option could be balsa wood (Waltham 2009), or mansonia as well as many other species from the tropical regions of South America (Delgado et al. 1983; De Souza 1983) or from Australia (Bucur and Chivers 1991). A study performed by Torres and Torres-Martinez (2015) revealed that the use of alternative woods (e.g.Cupressus lindleyi, Dalbergia paloescrito, Dalbergia granadillo Pittier, and Cordia dodecandra DC.) for the back plate and ribs of a guitar does not cause considerable variations in the middle and high-frequency ranges of its vibratory response. This finding was also confirmed by Carcagno et al. (2018), who tested guitars with back plates made of Brazilian rosewood, Indian rosewood, mahogany, sapele, and walnut.

Therefore, the authors considered that a study in this direction would be most welcome, and they decided to investigate the opportunity to use alternative European wood species instead of the quite rare curly maple wood, for the back plate of violins. The modal analysis was performed both on the individual top and back plates (Fig. 2a and 2b) and on the violin body (Fig. 2c), obtained after assembling each pair of plates.

 

Fig. 2. Tested material: a) Violin top plate; b) Violin back plate; and c) Violin bodies obtained by assembling a pair of top and back plates

As a novelty, the modal analysis envisaged the determination of the mechanical (vibratory) behavior of the violin resonance box within the spectrum of low and medium frequencies, for different wood species. The eigenfrequencies (natural frequencies), the number of spectral components, and the quality factor, as important indicators of the acoustic performances of a musical instrument.

Significant contributions regarding modal analyses on violins or violin components were previously brought by e.g. Marshall (1985), Bissinger and Olivier (2007), and Pyrkosz and Van Karsen (2013).

The first eigenfrequency (f0), usually called fundamental frequency, is essential for the tuning of the musical instrument. For violins, the fundamental frequency is within the range 270 to 280 Hz (Donoso et al. 2008).

The second eigenfrequency (also called, second vibration mode) reflects the contribution of the top plate within the violin body that acts like a Helmholtz-type resonator, and the fifth eigenfrequency (which usually is the frequency with the highest amplitude) reflects the contribution of the back plate. The latter one characterizes the sound intensity: for a violin to produce a strong sound, the amplitude of the vibrational response of the sound plate should be as high as possible (Barlow 1997; Wegst 2006). According to reference literature (Hutchins 1981; Jansson 2002; Donoso et al. 2008), this frequency, which is below 1000 Hz, gives the violin its musical timbre and it acts as a fingerprint/signature for each instrument.

The number of eigenfrequencies varies from one wood species to another. It depends on the wood structure, its density, and its elastic properties. The number of eigenfrequencies determines the number of spectral components that give the violin its musical timbre. The higher this number, the larger the sound spectre covered by the violin. The maximum frequency (fmax) together with the fundamental frequency (f0) define the limits of the spectral domain of the violin acoustics.

The quality factor (Q) is one of the most important parameters for evaluating the acoustic quality of resonance wood (Wegst 2006). It characterizes the time needed for the sound to fade away after the excitation has stopped. For musical instruments, the quality factor should be as high as possible (to ensure slow sound damping). Reference literature indicates: = 105 for resonance spruce wood (Filipovici 1964) and Q = 80 to 105 for curly maple wood (Bucur 2006).

The comparative analysis of the values for these indicators on violin bodies with back plates made from different wood species allowed interesting findings concerning the acoustic potential of some species to be used for the manufacturing of musical instruments.

EXPERIMENTAL

Materials

The material used within this research consisted of 14 violin top plates made of resonance spruce wood (Picea abies), without f-holes (at this stage) (Fig. 2a) and with identical geometrical features (shape and dimensions specific to 4/4 violins). Additionally, 14 violin back plates (two of each species) with identical geometrical features (shape and dimensions specific to 4/4 violins), two reference back plates made of curly maple wood (Acer pseudoplatanus) (Fig. 2b), and six alternative wood species: hornbeam (Carpinus betulus), walnut (Juglans regia), willow (Salix alba), ash (Fraxinus excelsior), poplar (Populus nigra), and bird-eye maple wood (Acer saccharinum) (Fig. 3) were utilized in this study. Lastly, 14 violin bodies (without neck, bridge, and soundpost), obtained by assembling each top plate with a back plate, so that two violin bodies for each combination of species resulted were also used.

All violin components used within this experimental research were manufactured at Gliga Musical Instruments, Reghin (Romania).

Fig. 3. Experimental violin back plates made of alternative wood species

Table 1 presents the values of the density and the modulus of elasticity along the grain direction (EL) of the eight wood species used as raw materials for the manufacturing of the experimental violin parts, these being the most relevant physical and mechanical properties that influence the acoustic properties of wood.

Table 1. Density and MOE of the Wood Species Used for the Manufacturing of the Experimental Violin Plates

Sources: * Bucur 2006; ** Wagenführ 2008; *** The Wood Database (2020)

As one may notice, two categories of alternative species were used: some dense ones, with a density close to the one of maple wood (e.g., hornbeam, walnut, ash, and bird-eye maple), and a second category of softer hardwoods, with a similar density to spruce (e.g., willow and poplar).

However, it is important to emphasize that the main selection criterion for the alternative wood species for the back plates was the aesthetic value. Different cutting modes and some natural defects were admitted to obtain violin back plates with special visual impact, similar to the way in which curly maple was chosen by the old school violin makers (its acoustic properties being proved only later on).

Methods and Equipment

The experimental modal analysis (EMA) applied (Giron-Sierra 2017; Nastac and Debeleac 2018; Nastac 2019) involved two steps. In the first, the 28 plates were tested as individual structures (Fig. 4a). Then, the 14 violin bodies (Fig. 4b) were tested, where the output signals were captured from both coupled plates (top and back) simultaneously.

After weighing each violin component, the modal analysis by the dynamic method was applied consecutively to the top and back plates, and then to the violin bodies, one by one. Each sample (violin component) was supported with spring elements, to simulate the free structure (Fig. 4). Then, the sample was excited by an impact hammer type B&K 8204, and its response was captured by an accelerometer type B&K 4517-002 for the violin bodies two identical accelerometers were used, one placed on the top plate and the other on the back plate).

The technical data of the accelerometers are given below:

– Sensitivity: 10 mV/g,

– Measurement range: 500 g pk,

– Frequency range 2 to 10,000 Hz,

– Resonant Frequency ≥ 55 kHz,

– Size (height x length x width): 10.2 mm x 10.2 mm x 10.2 mm,

– Weight 4 g.

Both the hammer and the accelerometers were obtained from Brüel & Kjær (Nærum, Denmark).