REDUCING THE COMPLEXITY WHEN MODELLING DAMPING IN VIBRATING SYSTEMS

If a frequency spectra or frequency response function is known for a structure what physical model can be. generated to represent it? This is an important question for computer based simulations where a translation must be made between a spectra and a computer model. This is particularly difficult if damping is to be modelled. Investigation of electrical theory shows that this problem has been examined in detail due to the need to construct circuits that have specific spectra. However, before ideas can be borrowed from electrical theory it is necessary to develop vibration theory so that it aligns perfectly with electrical theory. To achieve this a method for representing mass is suggested which is a generalisation of the usual method and involves using a system of levers so that force is equal to mass times the derivative of relative velocity rather than absolute velocity. It is then shown that following electrical theory a damped spectra may be represented by an undamped sequence of masses and springs terminated by just one dashpot. Such a model is of considerable theoretical interest as well as having utility in computer simulations.