Modal analysis of plates with uncertain properties: Theory and applications

This dissertation is concerned with modal analysis of plates with properties which vary over the structures. The uncertain geometric and material parameters are treated as random fields which are discretized over individual regions by using a local averaging technique. These discretized properties are then combined with a random perturbation procedure based upon traditional finite element methods. The result is a stochastic finite element method (SFEM) program for modal analysis of plates. This SFEM method is applied to two problems areas.; The first application is to provide a new approach for modal analysis of printed circuit boards wherein the circuit board is modeled as an elastic plate with random spatial variation of its properties. The SFEM program is used to predict the effect of this variation on the natural frequencies and mode shapes of the board. Predicted results are compared with those obtained from modal testing of a circuit board. It is shown that variations between the measured and predicted modal parameters can be accounted for by small random variations in the board properties. This approach offers a simple, realistic, and cost-effective way for prediction of board modal properties.; The second application is on vibration control of plates by application of surface viscoelastic damping treatments. Existing works generally treat the geometric and material properties of the damping layer as deterministic parameters, although uncertainties in the values of these parameters are commonplace. No work has been done regarding surface damping treatments with uncertain properties. In this thesis, the modal properties of plates with random spatial variation of the damping layer properties are investigated. The effects of this variation on the system natural frequencies, modal loss factors, and mode shapes are calculated by the SFEM program developed. Results are presented for a cantilever aluminum plate with complete PVC surface damping treatment with uncertain properties.; In the SFEM modeling of both PC boards and plates with surface damping treatments, the effects on the system eigenvalues/eigenvectors of the correlation distance of the random property field, the correlation constant between the random fluctuations, and the magnitude of the random property variations, are investigated.