Vibration analysis of beams and rectangular plates with multiple constrained layer damping patches

This dissertation examines the damped vibration characteristics of beams and rectangular plates treated with multiple constrained-layer viscoelastic patches. Each damping patch consists of a metallic constraining layer and an adhesive viscoelastic layer with spectrally-varying shear modulus and loss factor properties. A new analytical model based on the Rayleigh-Ritz scheme is developed first. Motion variables of all layers are expressed in terms of the flexural displacement of the base structure (beam or plate). Then the flexural shape function sets are incorporated in the Rayleigh-Ritz minimization scheme to obtain a complex eigenvalue problem. This method allows for the visualization of complex modes of all deformation variables including shear deformation of the viscoelastic core that is the major contributor to the overall energy dissipation. Results of the proposed method compare well with those reported in the literature on simply supported sandwich beams and plates with single patches. Analytical predictions of natural frequencies, modal loss factors and complex modes are in excellent agreement with modal measurements. Effect of patch boundary conditions, patch cutouts and locations, and mismatched patch combinations are also analytically and experimentally examined. A refined technique to estimate unknown spectrally-varying properties of viscoelastic materials, by combining theory and experiment, has also been developed.;Subsequently, three simpler analytical formulations are successfully developed 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 superposition of Euler beam eigenfunctions. 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 and modal loss factor is expressed as a product of terms related to material properties, layer thickness, patch size and location. Approximate Methods II and III are also extended to rectangular plates. These methods yield reasonably accurate results in a computationally efficient manner while providing much insight into patch damping design concepts. Approximate formulations have been verified by comparing results with modal measurements.