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; Danekʹs (D) reconstruction from complex eigenvalues and 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.