Stevens, Karl K.

A theoretical analysis for predicting the system loss factors and
natural frequencies of rectangular plates with complete and partial
constrained-layer damping treatments has been presented. This analysis
is based upon an energy approach to the free vibration of plates.
Results predicted were compared with those from experiments. Satisfactory
agreement has been reached. Both the theoretical and the
experimental results presented in this thesis indicate clearly that
partial constrained-layer damping treatments can provide effective, or
even superior, amounts of damping, and that their use can lead to
significant savings in material costs and weight.

An energy method for predicting the natural frequencies and loss factors
of Rectangular Plates with Complete Constrained-Layer Damping Treatments
has been presented. Results obtained using the method developed were
compared with those of two former theories. The agreement between the
current theory and these two theories was generally good. There is a
serious need for carefully conducted experimental work to verify the
applicability of the current theory and of the various other laminated
plate theories in existence. It is believed that the method of analysis
presented can be extended to handle plates with partial constrainedlayer
damping treatments.

A method of analysis is presented to determine the natural
frequencies and loss factors of a plate covered with viscoelastic
coating, using experimentally obtained mode shapes.
The mode shapes for a square plate clamped on all edges are
determined using an HP 5423 A Structural Dynamics Analyzer.
A computer program, based on the method of analysis, is
developed to determine the natural frequencies and loss
factors of a rectangular plate covered with viscoelastic
material, and clamped on all edges. It was found that,
for a fully coated plate, and for a mesh with twenty-five
mesh points, the error in the fundamental frequency was
approximately 5 percent. A comparison between the mode
shapes for the bare plate and for the fully coated plate
revealed no significant difference. It was also found
that increasing the number of measurement points would
not significantly improve the results.

An energy method for predicting the natural frequency and loss
factor for square plates with partial and complete coatings is
developed. Both simply-supported and edge-fixed bonndary conditions
are considered. An impulse testing technique is used to
provide an experimental verification of the analysis for the case
of an edge-fixed square plate. The analytical and experimental
results are in close agreement, and indicate that partial coatings
can provide effective damping treatments.

A fatigue machine was rebuilt to investigate the wear of mild steel and
AISI Type 304 stainless steel while undergoing cyclic relative motions
in air and sea water environments. Wear curves were obtained for both
materials by measuring specimen weight loss as a function of the number
of cycles of relative motion, and surface damage of the specimens was
photographed. The results indicate that a sea water environment has a
strong influence upon the wear characteristics of mild steel and 304
stainless steel. For the mild steel, the corrosive effects of the sea
water contributed to severe pitting and cracking of the wear surface
and resulted in a significant increase in wear; after approximately
2.5 million cycles the amount of wear in sea water was approximately
three times that in air. For the stainless steel, the sea water acted
primarily as a lubricant and coolant, and served to reduce the amount
of wear after 2.5 million cycles to about one-tenth of that in air.

A static stress analysis of a common chain link and a pear-shaped
nng ivas performed using the finite element structural analysis
program SAP IV. The required finite element mesh and loading
inputs were generated by the pre-processing program PRE-SAP- LINK.
This procedure was used to determine the midplane stresses and
displacements in a link and ring of typical sizes and subject to
concentrated fcrces. Stress distributions and displacements were
drawn by hand and by using a Tektronix 4662 Interactive Digital
Plotter, respectively. The results obtained show that for both
link and ring, the numerically largest principal stress and maximum
in-plane shear stress occur on the element directly under an
applied load . The entire procedure was verified by comparing
the results obtained for the common link with experimental results
in the literature and with analytical results obtained using a
mechanics of materials approach. All of the results were in close
agreement.

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.

The feasibility of using structural modification techniques to determine the effect of added viscoelastic damping treatments on the modal properties of a distinct eigenvalue system and a degenerate system is investigated. Linear perturbation equations for the changes introduced into the system eigenproperties are derived and applied to several examples involving the flexural vibration of beams and square plates with varying degrees of damping treatment. Both large and small perturbations are considered. An FEM code has been developed to compute the dynamic system parameters which are subsequently used in an iterative method to determine the modal properties. The perturbation approach described can accommodate temperature and frequency-dependent material properties, and the procedures involved are illustrated in the examples considered. Results obtained for these examples are compared with those available from closed form or finite element solutions, or from experiments. Excellent agreement of the results of the present method with those of other contemporary methods demonstrates the validity, overall accuracy, efficiency and convergence rate of this technique. The perturbation approach appears to be particularly well suited for systems with temperature and frequency dependent material properties, and for design situations where a number of damping configurations must be investigated.