Frequency trends of acoustic radiation modes for cylindrical structures

Abstract

Acoustic radiation modes have become a useful and widespread analysis tool in situations involving sound radiation from vibrating structures. They have found use in applications such as active structural acoustic control, optimization of structures for minimal sound radiation, and acoustical holography. Analytical expressions for the radiation resistance matrix, from which the radiation modes are obtained, are available only for a small number of simple source geometries, while the obtaining of radiation modes for more complicated structures typically requires boundary element analysis or similar computational methods. In addition, better characterization of radiation modes could lead to rules of thumb or expressions for evaluating them more quickly, e.g. when the modes must be evaluated across a wide frequency band. This paper details the development of quasi-analytical expressions for the radiation resistance matrices of singly-curved structures such as cylinders, cylindrically curved plates, and angularly truncated cylinders. Through these expressions, radiation modes for these structures may be obtained without the use of typical computational methods. Wavenumber transforms of these modes are shown, and trends of the physical and wavenumber space representations are investigated as frequency varies. It is found that the most efficient modes morph with frequency to match the acoustic wavenumber.Acoustic radiation modes have become a useful and widespread analysis tool in situations involving sound radiation from vibrating structures. They have found use in applications such as active structural acoustic control, optimization of structures for minimal sound radiation, and acoustical holography. Analytical expressions for the radiation resistance matrix, from which the radiation modes are obtained, are available only for a small number of simple source geometries, while the obtaining of radiation modes for more complicated structures typically requires boundary element analysis or similar computational methods. In addition, better characterization of radiation modes could lead to rules of thumb or expressions for evaluating them more quickly, e.g. when the modes must be evaluated across a wide frequency band. This paper details the development of quasi-analytical expressions for the radiation resistance matrices of singly-curved structures such as cylinders, cylindrically curved plates, and angula...