Modeling of a passive distributed vibration control device using a superposition technique

The modeling of a distributed vibration control device is considered for use in predicting the vibration attenuation benefits and best design practices when such devices are attached to vibrating structures. Three-dimensional (3D) finite element (FE) analysis is possible but the geometric intricacies of the distributed spring layer and potential lack of symmetries of the device placement on a host structure make such a model expensive to compute, particularly for optimization purposes. Thus, an equivalent 2D model is desirable, whereby conventional Ritz-method solution forms may be implemented. This paper describes the continuum domain model of interest and explores the applicability of a superposition approach by which a non-continuous distributed spring layer is homogenized into a 2D continuum. Simple FE models are described which allow computation of the required elasticity parameters of the spring layer. An eigenfrequency analysis comparing 3D FE and 2D model results show good agreement in the lowest order natural frequencies over a range of typical device design parameters. Experimental measurements further validate the modeling approach by comparison of FRF results. The superposition method is found to accurately model non-continuous materials such as the corrugated distributed spring layer of interest and should therefore be applicable to other embodiments of such layers.