Waveguide finite element modelling for broadband vibration analysis of tyres including rotation and prestress

In the framework of tyre/road noise prediction, our aim is to introduce a waveguide finite element (WFE) method for broadband vibration analysis of rotating inflated structures of arbitrary cross-section. Approximating the geometry as perfectly circular, the finite element discretization is restricted to the two-dimensional cross-section, enabling fast and high-frequency computations. Tyres are particularly challenging to model due to various complicating effects, often approximated or neglected in WFE models : rotation, inflation, structural anisotropy, heterogenetity, damping among others. Our formulation uses Lagrangian perturbations of displacement in Eulerian coordinates, providing a concise way to express equilibrium equations in vibrating media initially moving, prestressed and subjected to fixed point forces (typically, contact excitations in rotating tyres). The method comprises three steps: computing the steady rolling state (including rotation, inflation and centrifugal force), determining the undamped vibration modes superimposed onto the steady state (solving an eigenvalue problem of quadratic type owing to Coriolis acceleration), and obtaining the forced response of the damped structure through specific orthogonality relationships (considering a specific form of damping). The WFE method is compared with a rotating shell analytical model from existing literature and is subsequently applied to a rotating tyre with heterogeneous cross-section up to 4kHz.