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Sensitivity analysis of acoustic eigenfrequencies by using a boundary element method.

Changjun Zheng1, Wenchang Zhao2, Haifeng Gao3

  • 1Institute of Sound and Vibration Research, Hefei University of Technology, Hefei, Anhui 230009, People's Republic of China.

The Journal of the Acoustical Society of America
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Summary
This summary is machine-generated.

This study introduces a boundary element method for analyzing acoustic eigenfrequency sensitivity in interior and exterior systems. The approach efficiently solves generalized eigenvalue problems, enhancing accuracy and applicability for acoustic system design.

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Area of Science:

  • Computational mechanics
  • Acoustics engineering
  • Numerical analysis

Background:

  • Acoustic eigenfrequency analysis is crucial for designing enclosed spaces and external structures.
  • Sensitivity analysis of acoustic eigenfrequencies helps optimize system performance and identify critical parameters.
  • Existing boundary element methods (BEM) face challenges with computational burden and spurious solutions.

Purpose of the Study:

  • To develop an efficient boundary element-based scheme for sensitivity analysis of acoustic eigenfrequencies.
  • To reformulate nonlinear eigenvalue problems into a reduced-dimension generalized eigenvalue problem.
  • To address and mitigate spurious eigenfrequencies and their sensitivities.

Main Methods:

  • Reformulation of nonlinear eigenvalue problems using contour integral approach.
  • Adjoint method utilizing right and left eigenvectors for sensitivity derivation.
  • Adaptive cross approximation and hierarchical matrices for computational efficiency.
  • Burton-Miller-type combined formulation to handle spurious solutions.

Main Results:

  • A validated boundary element-based scheme for acoustic eigenfrequency sensitivity analysis.
  • Efficient reduction of boundary element systems through advanced matrix techniques.
  • Successful identification and mitigation of spurious eigenfrequencies and their sensitivities.
  • Demonstrated accuracy and applicability via three numerical examples.

Conclusions:

  • The developed scheme provides an accurate and efficient method for acoustic eigenfrequency sensitivity analysis.
  • The integration of advanced numerical techniques enhances the robustness and applicability of BEM in acoustics.
  • This work offers a valuable tool for the design and optimization of acoustic systems.