Inverse method identification of thermophysical properties based on solotone effect analysis for discontinuous Sturm–Liouville systems

Abstract

We consider one-dimensional Sturm–Liouville systems where conditions for the existence of oscillatory terms within the distribution of the eigenvalues have been established. This so-called solotone effect arises when the underlying partial differential equations contain discontinuities within their coefficients. Models of the Earth contain such discontinuities and research into solotones was originally motivated by vibration problems in geophysics. In this paper, we consider heat conduction in a layered composite and provide what is probably the first example of the presence of a solotone effect within a heat transfer context. Furthermore, we devise a novel method whereby relative values of the specific heat capacity and thermal conductivity of a composite rod may be accurately estimated from oscillations within the eigenvalue spectra. That is, we show how the solotone effect may be used to solve a particular heat transfer inverse problem. The method we present could be used to determine thermophysical properties of bonds or welds, for example when developing new adhesives or solders.