Topic
The oscillation of elasto-mechanical systems involves the exchange of kinetic and potential energies as well as the dissipation of energy by damping. Methods are generally well established for modelling the inertial and stiffness properties of most systems but often there remains very considerable doubt on how the damping behaviour should be represented. The most common method is to assume viscous damping, which is attractive computationally because it results in systems of second-order differential equations with solutions that are readily available by well-understood techniques. A regular approach is to simplify the assumption of viscous damping still further by selecting a damping matrix, C, diagonalizable by the classical normal modes of the system. This form of damping, usually known as classical damping, includes proportional damping as a special case.
The viscous damping approximation may not be very representative of reality, since the mechanisms that remove energy from a system (material damping, friction, gas pumping at interfaces, energy radiation, etc.) are very different both in nature and amplitude, and they could be often nonlinear. However, if the damping is light the dynamical behavior is principally determined by the relatively large elastic or inertial forces so this approach can represent a valid approximation in many cases.
The literature on the subject includes several different methods to identify the linear viscous damping matrix in multiple degree-of-freedoms systems. In the recent review paper [1] we compare the philosophy and performances of the main strategies in the identification of linear viscous damping, namely the perturbation method, Lancaster formula, the imaginary part of the inverse receptance matrix and the energy method. In [1] is shown that the last two strategies are in principle identical when dealing with linear viscous damping only and they perform better than the others when modal incompleteness is present in the measurements.
For these reasons, a method is developed based on the energy strategy with some variations that allow the identification of damping without the need to estimate the mass and the stiffness matrices.
The energy-based method is able to locate the main sources of damping and it is intended to be used practically in real structures and to be able to identify both viscous and non-viscous damping. The method is validated by a numerical simulation [2] and gives good results in the first experimental tests [3]. Further tests are currently running to confirm the good performance of the method for both viscous damping and Coulomb friction identification.
This work is being carried out in collaboration with our project partners at Politechnico di Torino.
Progress
PhD Thesis
References
- Prandina, M., Mottershead, J.E., and Bonisoli, E., An assessment of damping identification methods, Journal of Sound and Vibration 323(3-5), 2009, pages 662-676.
- Prandina, M., Mottershead, J.E., and Bonisoli, E., Location and identification of damping parameters, IMAC XXVII Conference and Exposition on Structural Dynamics, Orlando, Florida, USA, 2009.
- Prandina, M., Mottershead, J.E., and Bonisoli, E., Damping identification in multiple degree-of-freedom systems using an energy balance approach, Journal of Physics: Conference Series, 181, 2009, 012006.
Contact
Marco Prandina
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