THE CONSTRUCTION OF PHYSICAL PARAMETERS FROM MODAL DATA
Abstract Some analytical models of vibrating systems may be expressed as a linear combination of known connectivity matrices. The connectivity matrices depend on the modelling method and the order of the approximation chosen, while the combination factors are determined by the physical parameters of the system. The physical parameters of such models can be identified from a single natural frequency, two mode shapes and a static deflection due to a unit load. It is shown that the identification process is determined by the solution of a certain generalised eigenvalue problem, where the physical parameter vector is proportional to one of its eigenvectors. It thus follows that generally for an n -degree-of-freedom (dof) system there are n possible solutions. Realisable solutions, however, correspond only to eigenvectors with no sign change in their entries and no vanishing elements, which limits the number of possible physical solutions. The results are demonstrated by an analytical example of an axially vibrating rod and a numerical solution for a Bernoulli–Euler beam.