MODAL EQUATIONS OF LINEAR STRUCTURES WITH VISCOELASTIC DAMPERS

Several types of energy dissipation devices using viscoelastic materia ls have been proposed to reduce vibration in structures subjected to w ind and earthquake excitations. At constant temperature and small stra in levels, the mechanical behaviour of Viscoelastic (VE) materials can be described using linear operators. In general, the stiffness and da mping matrices of structures using VE devices are frequency dependent; this implies that the classical second-order differential equations f or the modal co-ordinates are not a complete model for this type of st ructures. In this paper, the concept of modal coupling in the frequenc y domain is addressed, expressions for diagonalizable frequency-depend ent stiffness and damping matrices are given, and an iterative techniq ue for the computation of the response of viscoelastic structures is s tudied. Necessary and sufficient conditions for convergence of the tec hnique are given and numerical examples are developed to illustrate th e application of the method.