414 / 2022-07-31 12:53:19

Wave Localization in Two-dimensional Membranes Coupled to Continuous Viscoelastic Supports

Circular/rectangular membrane, continuous viscoelastic supports, nonclassical damping, traveling and standing waves, wave localization

We present some recently obtained results on the localization of travelling and standing waves in circular and rectangular membranes in the presence of continuous viscoelastic line supports when the systems undergo harmonic boundary excitation. An analytical approach is developed to determine the stiffness and damping properties of the supports that lead to directional transfer of energy, in the form of traveling waves, from harmonic displacement excitation of the outer edge to the region bounded by the interior line supports, where the response is converted to standing waves. The results show that the weak eccentric configuration for a circular membrane and a ring-type viscoelastic support exhibit perfect wave localization with nonuniformly distributed spring stiffness and damping of the support. For strong nonsymmetric coupling between a rectangular membrane and two viscoelastic line supports, nearly perfect traveling waves can prevail in part of the membrane, while the remaining subdomains are dominated by a superposition of standing waves.  Wave patterns of spatial localization are examined using a power-flow analysis.  This work will be useful for passive vibration control using a wave approach in two-dimensional continua.