Proportional damping approximation for structures with added viscoelastic dampers
Installation of viscoelastic dampers in structures is one of the most widely used ways of enhancing structural performance against dynamic loads. Finite element dynamic analysis of structures with added viscoelastic dampers can be computationally costly. In general, to cope with non-proportional damping either complex modes or direct integration must be used, and neither of these two methods is free of complicated or time-consuming numerical procedures. This paper describes two efficient alternative methods to calculate some approximate proportional damping in order to simplify dynamic analyses and achieve reductions in computation times. Both methods approximate the effects of the added viscoelastic dampers with a damping matrix in the form of a generalised Rayleigh damping matrix as proposed by Caughey, which can be diagonalised through a modal transformation using real modes. This enables the use of modal superposition techniques with real modes to solve dynamic analyses. The accuracy and limitations of the proposed methods are later verified through case studies on a sample structure.
viscoelastic dampers non-proportional damping finite element analysis modal energy method dissipated energies method caughey damping matrix