A stochastic operator for interface dynamics and the canonical relation between compliance update and modal frequency variation—II. Non-deterministic evolution of modal frequency changes engendered by compliance influenced state-space variations

Abstract

This paper presents an analytical description of the non-deterministic evolution of modal frequency changes that are engendered by compliance influence state-space variations in a disturbed elastic microstructured medium. In order to access the inner foundation of the random compliance update process which is known to influence predictions on modal frequency state-space variations, the analysis invokes the concept of stochastic stretch-shear-rotation operator which characterizes the microstructure interface dynamics. The analytical results indicate that treating the pathology inherent in the random compliance update process as uncorrelated white and colored noise processes leads to a canonical decomposition that partitions the modal frequency variation as a linear manifold with deterministic and non-deterministic complements. In particular, the formulation shows that the “Paley-Wiener Criterion” can serve as a means of checking the nature of the drift towards non-determinism, once the structure and intensity of the noise-induced transition probability controlling the time-evolution of the modal frequency changes are well defined.