Reconstructing the vibroacoustic response of thin isotropic plates under distorted similitude: A wavenumber-based approach

Similitude methods are widely used across engineering fields to reduce cost and setup complexity in experimental testing. Several approaches have been proposed in the literature, all relying on specified similitude conditions whose satisfaction is necessary to accurately reconstruct the vibroacoustic response of a structure. When these conditions are violated, the reconstruction fails because the order and spacing of resonance modes differ from those of the reference prototype, producing a distorted similitude. To address this, a wavenumber-based method is proposed, assigning mode-dependent scale factors to natural frequencies and to the vibroacoustic response, expressed in terms of the modal wavevector components. The key idea is that wavenumber information enables direct identification and reconstruction of the prototype's resonance mode shapes, independent of their ordering. Numerical and experimental validations on thin isotropic plates show accurate reconstructions of natural frequencies, mobility, and radiated acoustic-power peaks, paving the way for applications to more complex structural configurations.