DOI: 10.1007/s10915-005-9028-x Journal of Scientific Computing, Vol. 27, Nos. 1–3, June 2006 (© 2005) Pseudo Spectral Methods Applied to Problems in Elasticity Chris Talbot 1 and Andrew Crampton 1 Received October 14, 2004; accepted (in revised form) September 13, 2005; Published online January 4, 2006 Pseudo spectral methods offer an attractive alternative to finite element proce- dures for the solution of problems in elasticity. Especially for simple domains, questions involving both two and three dimensional elasticity (Navier’s Equa- tions or their non-linear generalisations) would seem to be reasonable candidates for a pseudo spectral approach. This paper examines some simple vibrational eigenvalue type problems, demonstrating how Navier’s equations can be recast into pseudo- spectral format, including first derivative boundary conditions representing zero traction. Fourier–Chebyshev methods are shown to give solu- tions with typical spectral accuracy, with the addition of pole conditions being necessary for the case of a two dimensional disc. There is also consideration given to time-stepping solutions of elastodynamic problems, especially those involving non-linear friction effects, the authors particular interest being the study of disc brake noise. It is shown that, at least for relatively simple cases, it is possible to model systems in such a way that animated graphical output can be provided as the system of partial differential equations is numerically inte- grated. This provides a useful tool for engineers to rapidly examine the effect of parameter changes on a system model. KEY WORDS: Pseudo spectral; elasticity; brake noise; vibration. 1. INTRODUCTION For simpler problems on regular domains, problems in solid mechanics can be modelled by Fourier–Chebyshev collocation methods that enable both eigenvalue and time-stepping problems to be solved efficiently with simple code. Application of pseudo-spectral (PS) methods to elasticity, using the 2D or 3D Navier equations with periodic boundary conditions, 1 School of Computing and Engineering, University of Huddersfield, Huddersfield, UK. E-mail: c.j.talbot@hud.ac.uk 443 0885-7474/06/0600-0443/0 © 2005 Springer Science+Business Media, Inc.