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Purpose <p>This paper aims to establish a comprehensive mathematical framework for simulating the vibro-acoustic behavior of guitar systems that directly links fundamental physical string parameters (diameter, tension, stiffness, density, and viscoelastic loss) to perceptually relevant tonal attributes such as sustain, brightness, warmth, and inharmonicity, thereby enabling predictive evaluation and optimization of instrument performance.</p> Methods <p>A fully coupled string-body-acoustic model is developed, integrating internal viscoelastic string damping, geometric stiffness, aerodynamic damping, body modal dynamics, and acoustic radiation via Rayleigh integral formulation. The model employs modal truncation (15 string modes, 10 body modes) and a partitioned time-integration scheme (implicit Newmark-β for the body, explicit RK4 for the string). Validation is performed through two complementary approaches: verification of string dynamics against classical theory and Kodama’s experiments, and quantitative comparison of bridge admittance with experimental datasets. Multi-objective optimization using CMA-ES and Gaussian process surrogate modeling, together with global sensitivity analysis, is applied to quantify trade-offs among sustain, brightness, and inharmonicity across nylon-like, fluorocarbon, and steel-like material classes.</p> Results <p>The model achieves excellent agreement with experimental bridge admittance (R² = 0.87, RMSE = 3.8×10⁻⁴ m/sN). Distinct spectral signatures are observed: nylon-like polymers exhibit long decay (up to 3.60 s optimized vs. 2.43 s baseline) and strong low-frequency content (warmth 58.7%), steel-like alloys achieve high brightness (0.376) and extended high-frequency harmonics with moderate sustain (3.14 s), while fluorocarbon strings provide balanced performance (sustain ~3.51 s, inharmonicity as low as 0.04%). Sensitivity analysis reveals diameter as the dominant parameter for polymer strings (scaled variance contribution &gt;4.0), whereas body damping exerts significant influence on sustain for steel strings (0.669). Pareto-optimal fronts quantify inherent trade-offs: increasing brightness reduces sustain, and minimizing inharmonicity favors intermediate stiffness and diameter. The Pareto front remains robust under ±20% variations in body damping and loss modulus, with bridge stiffness identified as the most sensitive parameter. </p> Conclusions <p>The proposed framework provides actionable, physics-based guidance for engineering guitar strings with tailored tonal outcomes. Nylon-like polymers can be optimized for warm, sustained tones; steel-like alloys for bright, brilliant spectra; and fluorocarbon for clear, articulate, balanced performance. The identified Pareto-optimal regions and sensitivity hierarchies offer a rational design map for instrument makers, demonstrating that systematic vibro-acoustic modeling enables predictive, materially grounded string design. Future work includes experimental time-domain validation, listener studies, and extension to wound strings and nonlinear dynamics.</p>

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A Coupled Vibro-Acoustic Model for Guitar String-Body Interaction: Integrating Viscoelastic Damping, Modal Dynamics, and Perceptual Design

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Qinhan Jin

摘要

Purpose

This paper aims to establish a comprehensive mathematical framework for simulating the vibro-acoustic behavior of guitar systems that directly links fundamental physical string parameters (diameter, tension, stiffness, density, and viscoelastic loss) to perceptually relevant tonal attributes such as sustain, brightness, warmth, and inharmonicity, thereby enabling predictive evaluation and optimization of instrument performance.

Methods

A fully coupled string-body-acoustic model is developed, integrating internal viscoelastic string damping, geometric stiffness, aerodynamic damping, body modal dynamics, and acoustic radiation via Rayleigh integral formulation. The model employs modal truncation (15 string modes, 10 body modes) and a partitioned time-integration scheme (implicit Newmark-β for the body, explicit RK4 for the string). Validation is performed through two complementary approaches: verification of string dynamics against classical theory and Kodama’s experiments, and quantitative comparison of bridge admittance with experimental datasets. Multi-objective optimization using CMA-ES and Gaussian process surrogate modeling, together with global sensitivity analysis, is applied to quantify trade-offs among sustain, brightness, and inharmonicity across nylon-like, fluorocarbon, and steel-like material classes.

Results

The model achieves excellent agreement with experimental bridge admittance (R² = 0.87, RMSE = 3.8×10⁻⁴ m/sN). Distinct spectral signatures are observed: nylon-like polymers exhibit long decay (up to 3.60 s optimized vs. 2.43 s baseline) and strong low-frequency content (warmth 58.7%), steel-like alloys achieve high brightness (0.376) and extended high-frequency harmonics with moderate sustain (3.14 s), while fluorocarbon strings provide balanced performance (sustain ~3.51 s, inharmonicity as low as 0.04%). Sensitivity analysis reveals diameter as the dominant parameter for polymer strings (scaled variance contribution >4.0), whereas body damping exerts significant influence on sustain for steel strings (0.669). Pareto-optimal fronts quantify inherent trade-offs: increasing brightness reduces sustain, and minimizing inharmonicity favors intermediate stiffness and diameter. The Pareto front remains robust under ±20% variations in body damping and loss modulus, with bridge stiffness identified as the most sensitive parameter.

Conclusions

The proposed framework provides actionable, physics-based guidance for engineering guitar strings with tailored tonal outcomes. Nylon-like polymers can be optimized for warm, sustained tones; steel-like alloys for bright, brilliant spectra; and fluorocarbon for clear, articulate, balanced performance. The identified Pareto-optimal regions and sensitivity hierarchies offer a rational design map for instrument makers, demonstrating that systematic vibro-acoustic modeling enables predictive, materially grounded string design. Future work includes experimental time-domain validation, listener studies, and extension to wound strings and nonlinear dynamics.