A waveguide finite element model with geometric nonlinearity and orthotropy to analyse broadband vibrations in a reinforced radial tyre

In this work, we present a Waveguide Finite Element (WFE) model to predict the dynamic response of tyres, especially at high frequencies. The model developed here offers significant improvements over earlier ones as it accounts for geometric nonlinearities, material anisotropy, a multi-layered structure of the tyre, and prestress due to inflation pressure. Our formulation adopts a Total Lagrangian approach to establish the weak form of equilibrium equations, utilising the initial undeformed state as a reference frame. Further, we have linearised the problem using the Newton-Raphson iterative approach. The WFE method is then applied to formulate a linear eigenvalue problem corresponding to a given wavenumber. Forced vibration analysis is facilitated by using a proportional viscous damping model, enabling the assignment of damping factors to each natural mode while maintaining the symmetry of the undamped problem. The model developed was duly validated against results from a 3D FEA (Finite Element Analysis) model developed in commercial FEA software. Such validation exercises were conducted for both statically loaded and dynamically loaded tyres. Finally, the application of the waveguide finite element model is demonstrated through a case study involving vibration analysis of an inflated tyre. As part of this analysis, we carefully examined the FRF response and the dispersion diagram of the tyre. While the former helped us understand the tyre behaviour at low frequencies, the latter was found to be very useful for understanding wave propagation in the tyre at higher frequencies. Our investigation clearly shows that the WFE model developed in this work can be a very useful tool in designing tyres with better vibrational attributes speedily.