Material Selection and Tone Control Mechanism of Leather Drumheads for Percussion Instruments
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Abstract
This study proposes a physics-informed neural network framework for quantitative analysis of the coupling mechanism between leather drumhead material properties and radiated acoustic wave characteristics. A transversely isotropic Ogden hyperelastic constitutive model is embedded into nonlinear shell vibration equations and incorporated as a physical constraint within the learning architecture. The proposed framework jointly utilizes transient displacement fields captured through high-speed optical measurements and acoustic wave information acquired by an array-based microphone system. Through vibration–radiation coupling modeling, structural dynamic responses are linked to farfield sound pressure distributions and spectral characteristics. Higher-order statistical moments of the Mel-frequency spectrum are employed to characterize multidimensional timbre attributes, while a differentiable material-parameter layer enables end-to-end inversion from target acoustic wave features to constitutive parameters. Experimental results demonstrate relative inversion errors of 2.3%, 2.5%, and 2.0% for Young’s modulus, shear modulus, and damping coefficient, respectively. The model further exhibits high consistency in acoustic feature reconstruction and superior capability in capturing high-frequency modal responses compared with conventional linear constitutive approaches. The results reveal a quantitative relationship among material nonlinearity, vibration behavior, and acoustic wave propagation characteristics. The proposed framework provides an engineering methodology for wave-based parameter identification, vibration– radiation analysis, and acoustic field prediction, supporting intelligent design and digital restoration of percussion instruments.
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