Critical elastic parameters motivating divergence instability of frictional composite infinitely long media

Abstract

The current study addresses the occurrence of smooth dynamic paths which rapidly diverge the mechanical system away from equilibrium configuration in an exponentially (non-oscillatory) path. The explored paths begin arbitrarily in the neighborhood of equilibrium states of an infinite orthotropic composite elastic layer. The subject treated here is handled from both the analytical and the numerical models. The divergence instability problem is reformulated as a nonlinear constrained optimization problem. Fortran implementation of sequential quadratic programming optimization algorithm for finding the minimum coefficient of friction for the onset of instability and the corresponding parameters is exploited. A finite element model is worked out to approximate the continuum. The results of several sets of numerical experiments for finding the minimum coefficient of friction for the onset of instability and the corresponding parameters are presented. The finite element method results were computed and compared with the analytic solutions: A very good matching between numerical and analytical results was obtained. It is concluded that, for normal relationships among elastic material properties and specific orthotropic directions, significantly surprising very low thresholds of the coefficient of friction were required for the onset of divergence instability.