Doctoral Dissertations

Date of Award

12-1995

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Engineering Science

Major Professor

Remi Engles

Committee Members

John Caruthers, Louis Deken, Gary Flandro

Abstract

Factors which produce differences between analytically computed modal characteristics, such as frequency and mode shape, and those derived experimentally are many. One area of significant uncertainty, both analytically and experimentally, are the physical boundary conditions between the component under consideration and the surrounding structure or test apparatus. This work was conducted to study the extent to which the elasticity of this interface can affect the modal characteristics of flat plates. Flat plates are studied as a first step in the understanding of boundary condition effects on the modal characteristics of compressor blade structures commonly found in gas turbine engines.

A new model adjustment scheme was developed, which uses perturbation finite elements, to compute adjustments at user specified locations of an analytical model to improve the agreement between analytical and experimental results. The scheme takes advantage of the users knowledge of where modeling uncertainties are highest, such as at the boundary, and computes adjustments to the model for only these locations. The technique not only permits changes in the elasticity of the boundary, but also permits the user to affect changes in stiffness at any specified location. Further, adjustments to the mass at specific locations are permitted to account for the mass of instrumentation, lead wires or distributions in mass density of the component itself.

The technique seeks to minimize the differences between analytical and experimental results within the constraints of the finite element formulation. Consequently, the agreement between analytical and experimental results are improved; the technique does not seek to match explicitly the experimental results. The reason for this is that experimental results typically have a measure of non-repeatability in them. making "matching" of the data unrealistic. An example problem is presented for which intentionally introduced adjustments are correctly computed.

Analytical and experimental investigations of four flat plates with five different distributions of stiffness at the support in addition to the baseline were conducted to examine their effect on modal frequency, displacement and strain. Analytical results were computed using a commercially available finite element package and eight node,isoparametric brick elements. Experimental accelerations and strains measured on the plates as they were subjected to sinusoidal base excitation from a shaker table. Results were compared to quantify differences between analytical sensitivities to the various boundary stiffnesses and experimental sensitivities to the same boundary stiffnesses. The experimental method, data processing techniques, modeling techniques and other factors were evaluated to minimize potential for error. Elimination or reduction of these factors was then pursued so that the resulting experimental data and the analytical results were of the highest quality.

Results of the investigation showed that the modal characteristics of some modes of some plates were more sensitive to variations in boundary stiffness than others. This Highlights the need for a model adjustment technique that can interrogate the boundary conditions to account for potential boundary stiffness influences. Further, significant differences between analytically computed sensitivities to boundary stiffness changes and those derived experimentally were present, although both sets of results identified the same plates and modes as having the highest sensitivities.

Adjustments to a representative analytical model using the newly developed perturbation finite elements were computed to investigate potential reasons for agreements between analytical and experimental results. Adjustments to the stiffness of the elements at the boundary and the mass of elements at instrumentation locations were computed to determine if these could account for the observed differences. Up-front modeling of the instrumentation mass was not possible since precise measurement of the amount of mass added by the instrumentation adhesive as well as the mass of the instrumentation itself was not known. Computed adjustments were reasonable.Consequently, it was concluded that the observed differences between experimental and analytical results were attributable to the mass of the experimental instrumentation, and to difficulties with the experimental set-up at the boundary.

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