Purpose Present a unified, engineering-oriented modal framework for the vibro-acoustic behaviour of flexible, fluid-filled shells under external transducer forcing, and to identify how geometry, source localization and dissipation mechanisms (boundary-layer shear, interfacial friction and viscoelastic fillings) control resonance, modal content and insertion-loss performance. Methods Starting from the linearized coupled fluid–structure PDEs, the study projects the fields onto suitable modal bases (1-D axial modes, 2-D circumferential/axial Fourier modes, and 3-D spherical harmonics) and reduces the problem to per-mode scalar impedance relations that combine radiation/added mass with frequency-dependent viscous and frictional terms. Closed-form modal scattering and structural response expressions are derived, and extensive parametric numerical panels (modal spectra, truncation convergence, energy-balance checks and rheological sweeps including Maxwell-type fluids and two-layer fillings) are produced with accompanying Octave code. Results The analysis demonstrates that (i) near-field, localized excitation (monopole) markedly increases the effective modal bandwidth (Bmodal), populating high-order modes compared with far-field plane waves; (ii) geometry (sphere vs finite cylinder vs spheroid) redistributes modal density, directivity and insertion-loss proxies in ways that materially affect damper efficacy; and (iii) viscous and viscoelastic fillings shift resonance frequencies and reduce Q, producing predictable frequency-dependent attenuation and broadening. Convergence and energy residual diagnostics establish practical truncation rules (recommended ℓmax for engineering studies) and validate the sign and magnitude of dissipative closures used in the modal algebra. Conclusions The unified modal toolkit furnishes rapid, transparent design diagnostics for passive and active damper strategies and clarifies when surface-coupled dissipation (porosity, boundary-layer coupling) is required versus bulk viscous approaches. For regimes where transient, broadband or strong memory effects are important, we recommend complementing the frequency-domain modal predictions with structure-preserving time-domain simulations (multi-symplectic / structure-preserving iterative methods) to validate dissipative closures and long-time energy budgets. The paper provides reproducible code and a road-map for such high-fidelity validation.

Vibro-Acoustic Coupling of Flexible Fluid-Filled Shells Under Transducer Forcing: Modal Models, Geometry Effects and Dissipation Strategies

期刊论文
发表日期：

2026年1月5日

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Jacob Nagler

摘要

Purpose

Present a unified, engineering-oriented modal framework for the vibro-acoustic behaviour of flexible, fluid-filled shells under external transducer forcing, and to identify how geometry, source localization and dissipation mechanisms (boundary-layer shear, interfacial friction and viscoelastic fillings) control resonance, modal content and insertion-loss performance.

Methods

Starting from the linearized coupled fluid–structure PDEs, the study projects the fields onto suitable modal bases (1-D axial modes, 2-D circumferential/axial Fourier modes, and 3-D spherical harmonics) and reduces the problem to per-mode scalar impedance relations that combine radiation/added mass with frequency-dependent viscous and frictional terms. Closed-form modal scattering and structural response expressions are derived, and extensive parametric numerical panels (modal spectra, truncation convergence, energy-balance checks and rheological sweeps including Maxwell-type fluids and two-layer fillings) are produced with accompanying Octave code.

Results

The analysis demonstrates that (i) near-field, localized excitation (monopole) markedly increases the effective modal bandwidth (B_modal), populating high-order modes compared with far-field plane waves; (ii) geometry (sphere vs finite cylinder vs spheroid) redistributes modal density, directivity and insertion-loss proxies in ways that materially affect damper efficacy; and (iii) viscous and viscoelastic fillings shift resonance frequencies and reduce Q, producing predictable frequency-dependent attenuation and broadening. Convergence and energy residual diagnostics establish practical truncation rules (recommended ℓ_max for engineering studies) and validate the sign and magnitude of dissipative closures used in the modal algebra.

Conclusions

The unified modal toolkit furnishes rapid, transparent design diagnostics for passive and active damper strategies and clarifies when surface-coupled dissipation (porosity, boundary-layer coupling) is required versus bulk viscous approaches. For regimes where transient, broadband or strong memory effects are important, we recommend complementing the frequency-domain modal predictions with structure-preserving time-domain simulations (multi-symplectic / structure-preserving iterative methods) to validate dissipative closures and long-time energy budgets. The paper provides reproducible code and a road-map for such high-fidelity validation.