Frequency-dependent damping in structural vibration analysis by use of complex series expansion of transfer functions and numerical Fourier transformation

The response of damped linear finite systems (discrete and continuous) to harmonic, stationary random, and transient excitations is studied. The assumed damping may be light or heavy, viscous and/or hysteretic (the latter being frequency-independent or frequency-dependent), and proportionally or non-proportionally distributed over the structure. Closed-form analytic transfer functions are derived for beam systems. In order to rationalize subsequent numerical calculations, the transfer functions are approximated by using truncated series. Complex eigenfrequencies of the structure and complex residues of the actual transfer function are used. Special interest is paid to the mathematical modelling of experimentally measured damping. Causality requirements are considered. Numerical examples are given. An efficient method (by which aliasing is eliminated) for numerical Fourier transformation has been developed and applied.