Similitude laws under the bending approximation for the vibroacoustic response of fluid-loaded, thin cylindrical shells

The objective of similitude theory is to establish scaling conditions and laws by which the response of a given system can be scaled to infer that of another, distinct system. Exact similitude laws for the structural acoustic response of thin cylindrical shells exist only in the trivial case where length, radius and thickness are scaled equally, because of the coupling between in-plane and transverse deformations. However, under the bending approximation, which applies when bending wavelengths are one order of magnitude smaller than the length and radius of the shell, thickness can be scaled differently to length and radius. This work focuses on similitude laws and conditions for the structural acoustic response of fluid-loaded cylindrical shells, under the bending approximation. The scaling parameters include the shell dimensions, material parameters and the properties of the acoustic domain. A criterion for validity of the bending approximation based on ring frequencies of the reference and scaled in vacuo shells is proposed. In the case of fluid-loaded cylindrical shells, new similitude conditions and laws are derived for exact scaling of the modal radiation impedance. When these conditions are satisfied, satisfactory re-scaling of both the spatially-averaged vibration response and the radiated sound power is obtained.