ABSTRACT
In this chapter, the author considers discrete system models of continuous systems such as beams and finds their isospectral counterparts. It allows us to use matrix theory to determine the isospectral systems. Livingston et al. introduced a non-linear least squares parameter estimation technique applied to experimental modal data to estimate axial load on a square rod loaded in uniaxial tension. Piana performed an experimental study on the fundamental frequency evolution in slender elastic beams subjected to displacements imposed on one end (to each value of imposed displacement corresponds an internal compressive axial load). The discrete model can also be used for determining critical combinations of loading parameters that cause the onset of dynamic instability in a beam. Discrete models for analysis of longitudinal and transverse vibrations of bars and beams are constructed based on dimensions and material-properties of these structures.
