  Driven by the need for describing and understanding wave propagation in
structural materials and components, several analytical, numerical, and
experimental techniques have been developed to obtain dispersion curves.
Accurate characterization of the structure (waveguide) under test is needed for
analytical and numerical approaches. Experimental approaches, on the other
hand, rely on analyzing waveforms as they propagate along the structure.
Material inhomogeneity, reflections from boundaries, and the physical
dimensions of the structure under test limit the frequency range over which
dispersion curves can be measured. In this work, a new data-driven modeling
approach for estimating dispersion curves is developed. This approach utilizes
the relatively easy-to-measure, steady-state Frequency Response Functions
(FRFs) to develop a state-space dynamical model of the structure under test.
The developed model is then used to study the transient response of the
structure and estimate its dispersion curves. This paper lays down the
foundation of this approach and demonstrates its capabilities on a
one-dimensional homogeneous beam using numerically calculated FRFs. Both
in-plane and out-of-plane FRFs corresponding, respectively, to longitudinal
(the first symmetric) and flexural (the first anti-symmetric) wave modes are
analyzed. The effects of boundary conditions on the performance of this
approach are also addressed.
