Acoustic Resonator Design via Eigenvalue Analysis

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Solution Overview

Problem

Conventional computational acoustic design methods for wind instruments are inefficient and time-consuming, particularly for free-form resonant cavities, as they require iterative simulations across a wide frequency range and often result in inaccurate three-dimensional designs due to the use of two-dimensional simulations.

Innovation Solution

A method for simulating the audio output of a three-dimensional object with a resonant cavity, involving the reception of a 3D mesh and hole configuration, computation of an air pressure coefficient matrix, and determination of a minimum non-zero eigenvalue to find resonant frequencies, allowing for interactive manipulation of the shape and hole placement to produce targeted tones.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If conventional iterative simulations are used to determine resonant frequencies of free-form resonant cavities, then measurement precision is improved, but loss of time increases significantly

Engineering Contradiction:

Improveresonant frequency determination accuracyVSAvoidsimulation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent replaces conventional iterative mechanical simulation methods with an analytical mathematical approach. By formulating the acoustic resonance problem as an eigenvalue problem based on the wave equation, the system directly calculates resonant frequencies without requiring time-consuming iterative simulations across frequency spectra.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent performs preliminary discretization of the resonant cavity into finite elements and pre-calculates the mass matrix and stiffness matrix. This preliminary setup enables direct eigenvalue analysis that quickly determines resonant frequencies without requiring iterative sweeping through frequency ranges during the actual measurement process.

Inventive Principle:

Principle #10Preliminary action

2Device complexity

If two-dimensional simulations are used for wind instrument design, then device complexity is reduced, but manufacturing precision deteriorates due to inaccurate three-dimensional translation

Engineering Contradiction:

Improvesimulation model complexityVSAvoidthree-dimensional design accuracy

Core Design Contradiction:

Device complexityVSManufacturing precision

Solution Approach 1:

The patent transitions from two-dimensional simulation models to a genuine three-dimensional analytical model by discretizing the 3D resonant cavity volume into finite elements. This allows direct calculation of three-dimensional resonant frequencies and acoustic modes without requiring translation or approximation from 2D models, thereby maintaining manufacturing precision while managing complexity through automated meshing procedures.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This approach enables fast simulation of multiple frequencies for free-form cavities, facilitating the design and fabrication of free-form wind instruments by allowing users to easily find and produce resonant frequencies, thus overcoming the limitations of traditional methods.

Implementation Method 1

a wind instrument produces tones through acoustic resonance within the resonant cavity of the instrument

Methodology Applied

Scientific EffectAcoustic resonance: Resonance

Implementation Method 2

computing a minimum non-zero eigenvalue for the air pressure coefficient matrix. The method further includes determining an output resonant frequency for the resonant cavity based on the minimum non-zero eigenvalue

Methodology Applied

Scientific EffectEigenvalue analysis:

Data Source

PatentUS11798521B2Computation design of acoustic resonators

Publication Date: 2023.10.24 AUTODESK INC

AI summary

One embodiment of the present application sets forth a method for simulating an audio output of a three-dimensional object that includes a resonant cavity. The method includes receiving an input mesh of a three-dimensional shape and a hole configuration. The input mesh has an outer surface and an internal cavity, and the hole configuration includes one or more holes. The method further includes adding the one or more holes to the three-dimensional shape based on the hole configuration to generate a modified three-dimensional shape having a resonant cavity. The resonant cavity includes the one or more holes and the internal cavity. The method further includes determining an air pressure coefficient matrix for the resonant cavity. The method further includes computing a minimum non-zero eigenvalue for the air pressure coefficient matrix. The method further includes determining an output resonant frequency for the resonant cavity based on the minimum non-zero eigenvalue.