Development of approximate methods for the analysis of patch damping design concepts

This paper develops three approximate methods for the analysis of patch damping designs. Undamped natural frequencies and modal loss factors are calculated using the Rayleigh energy method and modal strain energy technique, respectively, without explicitly solving high order differential equations or complex eigenvalue problems. Approximate Method I is developed for sandwich beams assuming that damped mode shapes are given by the Euler beam eigenfunctions. The superposition principle is then used to accommodate any arbitrary mode shape, which may be obtained from modal experiments or the finite element method. In Method II, the formulation is further simplified with the assumption of a very compliant viscoelastic core. Finally, Method III considers a compact patch problem. The modal loss factor is then expressed as a product of terms related to material properties, layer thickness, patch size and patch performance. Approximate Methods II and III are also extended to rectangular plates. Formulations are verified by conducting analogous modal measurements and by comparing predictions with those obtained using the Rayleigh-Ritz method (without making any of the above mentioned assumptions). Several example cases are presented to demonstrate the validity and utility of approximate methods for patch damping design concepts. (C) 1999 Academic Press.