ANALYSIS OF ERRORS AND APPROXIMATIONS IN THE USE OF MODAL COORDINATES

A basic operation in several updating procedures and other modal analysis applications concerns the transformation of the complex modes, identified from experimental tests, into the real ones typical of theoretical models. In this transformation several approximations are normally adopted. This paper presents a discussion of two of these approximations: the first refers to a series expansion of the complex modes into the subspace of real modes, commonly used for normalization of complex modes. The second, used in advanced modal analysis applications, relates the physical damped co-ordinates to the modal ones through the real modal matrix. An explanation of the limitations of these assumptions is given through analytical developments and numerical results obtained from a discrete model.