Modelling high-frequency tyre belt vibrations

The problem of tyre noise demands, among other approaches, theoretical prediction methods. A key component here is calculation of the tyre vibrations. A tyre is a complex, composite structure, especially the belt. The majority of work to date has treated this component as a thin plate, which is advantageous for computational economy. However, the fidelity of the representation is unclear, as is its relation to the belt’s component material properties. Here, these questions are addressed in the context of a problem for which exact solutions can be computed: wave propagation on a planar laminate matching the belt’s composition. Over most of the frequency range of interest — up to 2 kHz — three waves can be sustained: flexural, horizontal-shear and extensional. Approximate solutions have been obtained on the basis of the Kirchhoff and Reissner–Mindlin assumptions, layerwise polynomial expansions, and a one-dimensional finite-element discretisation. The thin-plate (Kirchhoff and Reissner–Mindlin) approaches fail to reproduce the exact solutions satisfactorily. In contrast, the methods that resolve the laminate thickness are able to do so, but need high resolutions to capture the horizontal-shear wave accurately. This observation has significant implications for the numerical cost of tyre-noise simulation, and suggests that further work on developing simplified formulations is needed. • Dispersion relations for waves on a laminate with composition representative of a tyre belt, at frequencies up to 2 kHz. • Comparison against approximate solutions arising from simplified laminate theories. • Accuracy requires formulations that resolve the through-thickness direction. • Adverse implications for the numerical cost of tyre-noise simulation.