Complex power distribution analysis in plates covered with passive constrained layer damping patches

The vibration of a plate partially covered with a passive constrained layer damping (PCLD) patch is studied from an energetic point of view. The damped plate is excited by an acoustic plane wave. The study is done with a numerical two-dimensional multilayer plate model. Results of the present model are compared to those obtained with three-dimensional finite element models. It is shown that the present model gives accurate results, even for the layerʹs inner behavior. It is less expansive in terms of computational cost; hence, it can simulate efficiently the structure for higher frequencies. Mathematical formulas for complex mechanical power are presented, and the link with strain and kinetic energies and dissipated power is detailed. Both local and global complex power balance are established, and corresponding expressions for the discretized problem are formulated. Conservative and dissipative powers are studied for the PCLD damped plate. After a global balance analysis versus frequency, a local study has been carried out in order to quantify the relative contribution of the components of strain and stress tensors to the total strain energy and dissipated power; the individual layerʹs contributions is also investigated. The in-plane distributions of powers are mapped, showing the location where dissipative phenomenon occurs and where strain energy is stored. Finally, three criteria based on the previous power quantities are proposed in order to quantify the mechanical damping efficiency of the patch.