An INverse COnvolution MEthod for wavenumber extraction (INCOME): Formulations and applications

Identification of partial differential equations in structural mechanics theory through k-space analysis and design

“…Then wavenumbers have to be extracted from the given solution fields using k-space method. The methods used are the Inhomogeneous wave correlation method (IWC) [25,24] and the INverse COnvolution MEthod (INCOME) [26,27] they are described in Appendix A. For each solution field, a set of n θ wavenumbers are calculated in different directions θ i : k ref (f, θ i ).…”

“…The INverse COnvolution MEthod, INCOME, [26,27] is an other method to get the k-space from a displacement field. u is the discrete displacement field at a given frequency known on a grid.…”

“…In two dimension, this wave is parameterized by the angle and the wavenumber at this angle. INCOME, [26,27] is an other method to get the k-space from a displacement field. The aim of the method is to find a convolution kernel such that the convolution between it ant the discrete field is minimized.…”

Computing dispersion diagrams and forced responses of arbitrarily varying waveguides

“…There is still a gap in the experimental and numerical techniques for these periodic structures when compared to "conventional structures" [16,17]. Recently, for example, some methodologies were expanded or developed for wavenumber identification [18,19,20,21], for dealing with damping [21,22,23], and non-linearity in periodic structures [24,25,26].…”

Algebraic wavenumber identification method in presence of uncertainty

“…Moreover, the IWC is not able to provide accurate wavenumbers in the low frequency range due to the requirement of many wavelengths presented in the displacement field. Comparatively, linear Prony family methods, such as High Resolution Wavenumber Analysis (HRWA) [7] and INverse COnvolution MEthod (INCOME) [8], have the advantage of requiring a low computational cost and providing accurate wavenumbers in the wide frequency range, while they require that frequency response are measured by periodic sampling and they are sensitive to small perturbation of coordinates. The small perturbation problem is common in experiments and it leads to the mismatching problem between frequency response and each measuring point's coordinate.…”