Improving the modal strain energy method for damped structures using a dyadic matrix perturbation approach

Abstract

A dyadic matrix based perturbation method has been developed to evaluate the natural frequencies and modal loss factors of viscoelastically damped structures. This approach improves the accuracy of the prediction given by the modal strain energy (MSE) method by making use of the modal basis of the undamped system. Examples involving lumped parameter systems and a constrained layer viscoelastic sandwich beam are presented. In each case, the solutions given by exact numerical methods, MSE and the perturbation approach are compared. Results are also correlated with performance indices to assess the damping level and type in the system. A solution involving a reduced modal basis of the original structure using the perturbation approach is also presented. This approach also gives a significant improvement over the original MSE prediction.