Disk harmonics based on Fourier-Bessel basis functions are used to analyze self-affine rough surfaces. The method provides an efficient way to characterize surface morphology without introducing biases from boundary conditions or surface discretization. The approach is demonstrated to successfully measure fractal dimensions and Hurst exponents, paving the way for contact mechanics studies based on the Fourier-Bessel spectral representation of curved and rough surface morphologies.
When two bodies come into contact, only a small portion of the apparent area is involved in producing contact and friction forces due to surface roughness. Accurately describing the morphology of rough surfaces is crucial, involving extracting fractal dimensions and Hurst exponents. Harmonic decomposition using disk harmonics simplifies this task for open single-edge genus-0 surfaces by employing Fourier-Bessel basis functions.
Analytical relationships between power spectrum density decay and Hurst exponent are derived through an extension of the Wiener-Khinchin theorem. The method successfully measures fractal dimensions and Hurst exponents without introducing biases from boundary conditions or curvature of surface patches.
Disk harmonics have been used in various engineering applications but not previously employed for studying surface morphology. The method offers stability for any input, solving issues encountered with other harmonic analyses methods like spherical harmonics.
Surface morphology analysis using Fourier-Bessel basis functions provides insights into understanding frictional behavior exerted by non-closed surfaces in mechanical engineering applications. The method allows for accurate measurement of fractal dimensions and Hurst exponents without being influenced by boundary conditions or curvature of the surfaces.
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by Mahmoud Shaq... at arxiv.org 03-13-2024
https://arxiv.org/pdf/2403.07001.pdfDeeper Inquiries