Frequency domain analysis of continuous systems with viscous generalized damping

This paper deals with the effects of generalized damping distributions on vibrating linear systems. The attention is focused on continuous linear systems with distributed and possibly non-proportional viscous damping, which are studied in terms of modal analysis, defining and discussing the orthogonality properties of their eigenfunctions. Exact expressions of the frequency response functions obtained by direct integration of the equations of motion are compared with the analogous formulas based on the superposition of modes. In addition, approximate expressions of the frequency response functions of both continuous and discrete (finite element models) systems in terms of their undamped eigenfunctions / eigenvectors are also considered and discussed. The presented methods are explained, compared and validated by means of numerical examples on a clamped-free Euler-Bernoulli beam.