A Numerical Method-Based Analysis of the Structural Deformation Behaviour of a Turkish String Instrument (Cura Baglama) under Varying String Tensions
Abstract
:1. Introduction
2. Materials and Methods
2.1. Cura Baglama and Three-Dimensional Modelling Procedure
2.2. Frequency Measurement and Calculations for String Tension Force
2.3. Finite Element Analysis Procedure
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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String Group | Playing Tuning (End Tune) | String Diameter | String Note | Measured Fequency (FFT Size 1024-Blackman-Haarris) | Corresponding String Tension Force | Corresponding Cross Section String Stress |
---|---|---|---|---|---|---|
(Reference Tune: A4 (LA) @ 440 Hz) | (mm) | (-) | (Hz) | (N) | (MPa) | |
Lower String Group (S1 and S2) | B2 (SI) (123.5 Hz) | 0.16 | B4 (SI) | 493.14 ± 0.10 | 30.194 | 1502.488 |
C3 (DO) (130.8 Hz) | 0.16 | C5 (DO) | 523.54 ± 3.24 | 34.032 | 1693.471 | |
D3 (RE) (146.8 Hz) | 0.16 | D5 (RE) | 587.42 ± 0.43 | 42.843 | 2131.917 | |
Middle String Group (S3 and S4) | B2 (SI) (123.5 Hz) | 0.25 | E4 (MI) | 329.10 ± 0.25 | 32.831 | 669.160 |
C3 (DO) (130.8 Hz) | 0.25 | F4 (FA) | 349.9 ± 2.15 | 37.112 | 756.415 | |
D3 (RE) (146.8 Hz) | 0.25 | G4 (SOL) | 392.78 ± 1.95 | 46.765 | 953.162 | |
Upper String Group (S5 and S6) | B2 (SI) (123.5 Hz) | 0.16 | A4 (LA) | 440.5 ± 0.20 | 24.092 | 1198.846 |
C3 (DO) (130.8 Hz) | 0.16 | B4b (SI b) | 466.11 ± 3.30 | 26.975 | 1342.307 | |
D3 (RE) (146.8 Hz) | 0.16 | C5 (DO) | 523.32 ± 0.14 | 34.003 | 1692.028 |
Component No. | Component of the Instrument | Material | Component Coordinates | Modulus of Elasticity | Poisson’s Ratio | Density | Crushing/Tensile Yield Strength |
---|---|---|---|---|---|---|---|
(GPa) | (-) | (kg m−3) | (MPa) | ||||
1 | Soundboard | Spruce | (Orthotropic) | EL (X): 9.800 | Vxy: 0.462 | 385 | 31.50 |
ET (Y): 0.580 | Vyz: 0.422 | ||||||
ER (Z): 1.250 | Vxz: 0.255 | ||||||
2 | Soundbox | Mulberry | (Isotropic) | 9.32 | 0.33 | 690 | 48.20 |
3 | Neck | Beech | (Orthotropic) | EL (X): 13.900 | Vxy: 0.24 | 710 | 57.00 |
ET (Y): 0.606 | Vyz: 0.27 | ||||||
ER (Z): 1.900 | Vxz: 0.27 | ||||||
4 | Neck head | (Isotropic) | 13.90 | 0.24 | |||
5 | Tunning keys/Pegs | Rosewood | (Isotropic) | 13.93 | 0.37 | 835 | 67.20 |
6 | String tie (String holder) | ||||||
7 | Bridge | Maple | (Isotropic) | 12.62 | 0.35 | 705 | 54.00 |
8 | Nut | Hornbeam | (Isotropic) | 12.10 | 0.38 | 735 | 50.50 |
9 | Frets | Nylon 6/Fishing line | (Isotropic) | 1.3–4.2 | 0.39 | 1110–1170 | 40–100 |
10 | Lower string group (Dia:0.16 mm) | ASTM A228 Steel (UNS K08500) | (Isotropic) | 210.00 | 0.31 | 7800 | 2860–3165 |
11 | Middle string group (Dia:0.25 mm) | ASTM A228 Steel (UNS K08500) | 2670–2950 | ||||
12 | Upper string group (Dia:0.16 mm) | ASTM A228 Steel (UNS K08500) | 2860–3165 |
Playing Tuning (End Tune) | Related Strings | Corresponding String Tension Force | Tension Force Components on the Bridge | Resultant Tension Force on Bridge by Single String | Total Resultant Tension Force on the Bridge | Resultant Tension Force Angle on the Bridge | |
---|---|---|---|---|---|---|---|
(T) | T.FX (←) | T.FY (↓) | |||||
(N) | (N) | (N) | (N) | (N) | (o) | ||
B2 (SI) (123.5 Hz) | S1 = S2 | 30.194 | 0.069 | 2.233 | 2.234 | 12.89 | 1.77 |
S3 = S4 | 32.831 | 0.075 | 2.428 | 2.429 | |||
S5 = S6 | 24.092 | 0.055 | 1.782 | 1.782 | |||
C3 (DO) (130.8 Hz) | S1 = S2 | 34.032 | 0.078 | 2.517 | 2.518 | 14.52 | 1.77 |
S3 = S4 | 37.112 | 0.085 | 2.744 | 2.746 | |||
S5 = S6 | 26.975 | 0.062 | 1.995 | 1.996 | |||
D3 (RE) (146.8 Hz) | S1 = S2 | 42.843 | 0.098 | 3.168 | 3.170 | 18.29 | 1.77 |
S3 = S4 | 46.765 | 0.107 | 3.458 | 3.460 | |||
S5 = S6 | 34.003 | 0.078 | 2.515 | 2.516 |
Structural Components | Material Reference to Failure | Playing Tuning (End Tune) | |||||
---|---|---|---|---|---|---|---|
B2 (SI) (123.5 Hz) | C3 (DO) (130.8 Hz) | D3 (RE) (146.8 Hz) | |||||
FEA Eq. Stress Output | Factor of Safety (FoS) | FEA Eq. Stress Output | Factor of Safety (FoS) | FEA Eq. Stress Output | Factor of Safety (FoS) | ||
(MPa) | (MPa) | (-) | (MPa) | (-) | (MPa) | (-) | |
Soundbox | 48.20 | 1.675 | 28.78 | 1.856 | 25.97 | 2.249 | 21.43 |
Soundboard | 31.50 | 3.111 | 10.12 | 3.559 | 8.85 | 4.616 | 6.82 |
Neck | 57.00 | 0.532 | 107.16 | 0.575 | 99.06 | 0.677 | 84.20 |
String tie (String holder) | 67.20 | 12.822 | 5.24 | 14.440 | 4.65 | 18.264 | 3.68 |
Bridge | 54.00 | 12.883 | 4.19 | 14.545 | 3.71 | 18.325 | 2.95 |
Nut | 50.50 | 10.179 | 4.96 | 10.993 | 4.59 | 12.879 | 3.92 |
Strings (ASTM A228 Steel (UNS K08500)) | Material Reference to Failure | Playing Tuning (End Tune) | |||||
B2 (SI) (123.5 Hz) | C3 (DO) (130.8 Hz) | D3 (RE) (146.8 Hz) | |||||
Section Stress | Factor of Safety (FoS) | Section Stress | Factor of Safety (FoS) | Section Stress | Factor of Safety (FoS) | ||
(MPa) | (MPa) | (-) | (MPa) | (-) | (MPa) | (-) | |
Lower string group (Dia:0.16 mm) | 2860 | 1502.49 | 1.90 | 1693.47 | 1.69 | 2131.92 | 1.34 |
Middle string group (Dia:0.25 mm) | 2670 | 669.16 | 3.99 | 756.42 | 3.53 | 953.16 | 2.80 |
Upper string group (Dia:0.16 mm) | 2860 | 1198.85 | 2.39 | 1342.31 | 2.13 | 1692.03 | 1.69 |
Component | Playing Tuning (End Tune) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
B2 (SI) (123.5 Hz) | C3 (DO) (130.8 Hz) | D3 (RE) (146.8 Hz) | ||||||||||
RX | RY | RResultant | Resultant Reaction Force Angle | RX | RY | RResultant | Resultant Reaction Force Angle | RX | RY | RResultant | Resultant Reaction Force Angle | |
(N) | (N) | (N) | (o) | (N) | (N) | (N) | (o) | (N) | (N) | (N) | (o) | |
String tie (String holder) | 7.940 | 13.600 | 15.75 | 30.28 | 8.670 | 15.100 | 17.41 | 29.86 | 10.400 | 18.500 | 21.22 | 29.34 |
Nut | 7.540 | 3.830 | 8.46 | 63.07 | 8.220 | 3.990 | 9.14 | 64.11 | 9.800 | 4.350 | 10.72 | 66.06 |
Bridge-Contact surface | 0.398 | 12.900 | 12.91 | 1.77 | 0.45 | 14.500 | 14.51 | 1.77 | 0.566 | 18.300 | 18.31 | 1.77 |
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Celik, H.K.; Gok, S.; Caglayan, N.; Rennie, A.E.W. A Numerical Method-Based Analysis of the Structural Deformation Behaviour of a Turkish String Instrument (Cura Baglama) under Varying String Tensions. Appl. Sci. 2023, 13, 9682. https://doi.org/10.3390/app13179682
Celik HK, Gok S, Caglayan N, Rennie AEW. A Numerical Method-Based Analysis of the Structural Deformation Behaviour of a Turkish String Instrument (Cura Baglama) under Varying String Tensions. Applied Sciences. 2023; 13(17):9682. https://doi.org/10.3390/app13179682
Chicago/Turabian StyleCelik, H. Kursat, Sevilay Gok, Nuri Caglayan, and Allan E. W. Rennie. 2023. "A Numerical Method-Based Analysis of the Structural Deformation Behaviour of a Turkish String Instrument (Cura Baglama) under Varying String Tensions" Applied Sciences 13, no. 17: 9682. https://doi.org/10.3390/app13179682