Spatial impulse responses from a flexible baffled circular piston.

Area of Science:

• Acoustics
• Wave Propagation
• Optical Aberrations

Background:

• Orthogonal polynomial expansions, specifically Zernike polynomials, are fundamental in optical aberration theory.
• Calculating spatial impulse responses for non-uniformly moving baffled circular pistons is crucial in acoustics and transducer analysis.
• Previous methods, like Stepanishen's, utilized Bessel functions, offering a basis for comparison.

Purpose of the Study:

• To derive semi-analytical expressions for spatial impulse responses of non-uniformly moving, baffled, circular pistons.
• To apply the theory of Zernike expansions to acoustic radiation problems.
• To compare the Zernike polynomial method with existing Bessel function-based approaches.

Main Methods:

• Application of Zernike polynomial expansions to functions on a disk.
• Derivation of spatial impulse responses based on expansion coefficients and responses of orthogonal functions.
• Formulation of impulse responses as finite series involving Legendre functions and the sinc function.

Main Results:

• Obtained semi-analytical expressions for spatial impulse responses.
• The derived expressions are in terms of non-uniformity expansion coefficients and orthogonal function responses.
• Impulse responses for orthogonal expansion functions are found in a closed form as finite series.

Conclusions:

• The Zernike polynomial expansion method provides a viable approach for analyzing acoustic radiation from complex sources.
• The derived closed-form solutions offer computational advantages.
• This method is a valuable alternative to previous techniques, particularly for non-uniform motion analysis.