Modelling and identification of structures with rate-independent linear damping
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In the present paper, a linear model for multi-degree-of-freedom systems with rate-independent damping is proposed to the purposes of dynamic response prediction and identification. A viscoelastic model with memory, equivalent to the ideal hysteretic model as for the energy dissipation properties, but causal and physically consistent in both the time and the frequency domain, is developed by adopting the Maxwell–Wiechert kernel function and by requiring the loss modulus to be substantially independent of frequency in a specified range of interest. The finite element model of the equivalent viscoelastic system is constructed and its equations of motion are shown to be uncoupled, in terms of modal coordinates, by the real-valued eigenvectors of the conservative system. An augmented state-space formulation, which encompasses, besides the customary displacements and velocites, a number of internal variables devoted to represent the viscoelastic memory, is then provided for the sake of system identification. Mechanical and modal properties of the equivalent viscoelastic model are finally illustrated by means of numerical examples.
KeywordsRate-independent damping Ideal hysteretic model Maxwell-Wiechert model Multi-degree-of-freedom systems Modal uncoupling Internal variables
Anna Reggio is beneficiary of an AXA Research Post-Doctoral Grant, whose generous support is gratefully acknowledged. Maurizio De Angelis thanks the Italian Ministry of Education, University and Research (PRIN Grant 2010MBJK5B).
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