Dynamic identification of structural systems with viscous and friction damping

The response function of a dynamic system with viscous and friction damping is derived in the time domain and in the frequency domain, under a prescribed initial displacement. The response function in the frequency domain appears as the summation of three terms, each associated to a particular physical parameter of the dynamical system. Each of these functions is then used as a building block for an approximation function, which is used in an iteration procedure to identify the physical parameters of the dynamical system considered. At first, the solution in the frequency domain to a set of parameters, including the initial condition, is used as data for an identification procedure based on the least squares method. It is shown that the identification procedure provides the exact physical parameters of the system, including the initial displacement. Then an approximation to the frequency response function (FRF) is calculated through Discrete Fourier Transform (DFT) from the exact time response and is used in the identification procedure. The identified parameters are only an approximation, though a good one, to the original ones because of the errors introduced in the FRF by the DFT. Finally the procedure is applied to real acceleration data recorded during free-vibration tests on a base-isolated building. In spite of problems related to the complex nature of damping and stiffness in isolation systems with coupled sliding and rubber bearings, the identified parameters are reasonable and compare favourably with values obtained by other methods.