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Modal equations of linear structures with viscoelastic dampers
Author(s) -
Inaudi José A.,
Kelly James M.
Publication year - 1995
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290240111
Subject(s) - viscoelasticity , dissipation , modal , damper , stiffness , vibration , modal testing , structural engineering , frequency domain , computation , modal analysis using fem , damping matrix , frequency response , mathematical analysis , modal analysis , stiffness matrix , mathematics , physics , engineering , materials science , acoustics , algorithm , electrical engineering , polymer chemistry , thermodynamics
Several types of energy dissipation devices using viscoelastic materials have been proposed to reduce vibration in structures subjected to wind and earthquake excitations. At constant temperature and small strain levels, the mechanical behaviour of Viscoelastic (VE) materials can be described using linear operators. In general, the stiffness and damping matrices of structures using VE devices are frequency dependent; this implies that the classical second‐order differential equations for the modal co‐ordinates are not a complete model for this type of structures. In this paper, the concept of modal coupling in the frequency domain is addressed, expressions for diagonalizable frequency‐dependent stiffness and damping matrices are given, and an iterative technique for the computation of the response of viscoelastic structures is studied. Necessary and sufficient conditions for convergence of the technique are given and numerical examples are developed to illustrate the application of the method.