Reduced-Order Finite Element Models of Viscoelastically Damped Beams Through Internal Variables Projection

For a growing number of applications, the well-known passive viscoelastic constrained layer damping treatments need to be augmented by some active control technique. However, active controllers generally require time-domain modeling and are very sensitive to system changes while viscoelastic materials properties are highly frequency dependent. Hence, effective methods for time-domain modeling of viscoelastic damping are needed. This can be achieved through internal variables methods, such as the anelastic displacements fields and the Golla-Hughes-McTavish. Unfortunately, they increase considerably the order of the model as they add dissipative degrees of freedom to the system. Therefore, the dimension of the resulting augmented model must be reduced. Several researchers have presented successful methods to reduce the state space coupled system, resulting from a finite element structural model combined with an internal variables viscoelastic model. The present work presents an alternative two-step reduction method for such problems. The first reduction is applied to the second-order model, through a projection of the dissipative modes onto the structural modes. It is then followed by a second reduction applied to the resulting coupled state space model. The reduced-order models are compared in terms of performance and computational efficiency for a cantilever beam with a passive constrained layer damping treatment. Results show a reduction of up to 67% of added dissipative degrees of freedom at the first reduction step leading to much faster computations at the second reduction step.