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Dictums for problem solving and approximation in mathematical acoustics: examples involving low-frequency vibration
Allan D Pierce1, Amadou G Thiam
1Department of Mechanical Engineering Boston University, Boston, Massachusetts 02215, USA. adp@bu.edu
The Journal of the Acoustical Society of America
|March 20, 2012
Summary
This study presents authoritative dictums for mathematical acoustics, detailing solutions for cylinder vibrations on compliant surfaces. Findings include apparent entrained mass and radiation resistance for low-frequency forced vibrations.
Area of Science:
- Mathematical Acoustics
- Vibrational Mechanics
Background:
- The study addresses forced vibrations of a long cylinder partially embedded in a compliant half-space.
- It considers limiting cases, including a cylinder in a rigid baffle and on an incompressible fluid surface.
Purpose of the Study:
- To provide authoritative dictums for solving mathematical acoustics problems.
- To detail the forced vibration of a cylinder on an impedance boundary at low frequencies.
- To address and overcome challenges in ensuring causal solutions.
Main Methods:
- Application of complex variable theory.
- Utilizing the method of matched asymptotic expansions.
- Analysis of low-frequency vibrations and limiting cases.
Main Results:
- Derivation of solutions for cylinder vibrations on compliant surfaces.
- Calculation of apparent entrained mass in the cylinder's near field.
- Determination of radiation resistance per unit length for the vibrating cylinder.
Conclusions:
- The study offers a framework for understanding cylinder vibrations in acoustic fields.
- It highlights the importance of causal solutions and approximation techniques.
- Results provide key parameters for vibrational analysis in related physical systems.
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