On the reconstruction of a damped vibrating system from two complex spectra, part 2:: Experiment

This experimental-theoretical paper discusses whether. and how accurately. the mass, damping and stiffness matrices For a purportedly two-degree-of-freedom (2-d.o.f.) system may be reconstructed from the measured complex eigenvalues and/or eigenvectors. The system consists of two parallel cantilevered beams with end masses connected by a third, curved beam. Three procedures are used to reconstruct the matrices: the modal(M) method using real natural frequencies, real modes and modal damping factors: Danek's (D) reconstruction from complex eigenvalues acid eigenvectors: a reconstruction (E) from complex eigenvalues of the original and constrained system. it is shown that the damping matrix constructed via D is extremely sensitive to errors in the phases of the complex eigenvectors. The reconstruction via E uses only eigenvalues which can be measured much more reliably than eigenvectors. (C) 2001 Academic Press.