Abstract

A new approach to operator identification is proposed for a class of conservative linear dynamic systems whose characteristic equation can be represented in terms of the spatial spectral parameter and the excitation frequency. The inverse problem is reformulated as a problem of recognizing spectral branches in the transformed variables z=λ² and q=ω². In this formulation, spectral geometry becomes a carrier of information about the structure of the governing operator. The approach is demonstrated using a gradient porous cantilever beam model. A characteristic equation is derived, the role of the full spatial parameter λ(ω) is discussed, and a numerical experiment is performed for several configurations of spectral branches. The main result is formulated as an identification theorem: under the considered assumptions, recovering the parameters of the model is equivalent to recognizing central second-order curves associated with the spectral branches of the system.

Keywords: Operator identification; Spectral branch recognition; Inverse problems; Gradient porous media; Dispersion analysis; Spectral geometry