Stochastic Finite Element Analysis of Plates with Damping Layers with Uncertain Properties

摘要

Vibration control of structures by application of surface viscoelastic damping treatments has received considerable attention. Existing works generally treat the geometric and material properties of the damping layer as deterministic parameters. Little work has been done regarding surface damping treatments with variable properties. In this paper we consider the modal properties of plates with random spatial variation of the damping layer properties. The effects of this variation on the system natural frequencies, modal loss factors, and mode shapes are investigated. The analysis makes use of stochastic finite element modeling. In this approach, the continuously varying random parameters are discretized using a local averaging technique. These results are then combined with a random perturbation procedure based upon traditional finite element methods. Results are presented for the example of a cantilever plate. Variations in the natural frequencies and modal loss factors are reported in the form of mean values and standard deviations. Results obtained for the natural frequencies are similar to those for an undamped plate, as described in a companion paper. Standard deviations of the modal loss factors are found to vary from mode to mode. They do not increase monotonically with increasing mode number, as do the natural frequencies.