Application of holographic interferometry to predict long-time torsional relaxation

The objective of the work described in this paper was to develop techniques to predict long-term relaxation in torsional springs based on short-time data. The torsional springs examined in this study were torsion bars fabricated from 300M steel (280–300-ksi tensile strength). A holographic technique was utilized to perform very precise measurements of relaxation in torsion bars. The technique utilizes real-time holographic interferometry and was capable of resolving relaxation (torque losses) as small as. 01 in.-lb for a bar initially torqued to 825 in.-lb. The holographically determined torque-logs data were used to develop a model to estimate the relaxation behavior of the torsion bars. The model determined to best fit the data is described by: ΔT=0.32(t+50)^0.4?qt ^?1 wheret = time in hours ΔT = total change in torque (in.-lb) The model was developed to fit the holographic data from 0 to 5000 h. Excellent agreement between the torque-loss rate predicted by the model and that actually measured holographically at 10,000 h was obtained. This further indicates that long-time relaxation behavior of the torsion bars can be accurately predicted from short-time tests. Using the model, it is now a simple matter to holographically measure and evaluate the relaxation of other lots of torsion bars to predict their long-time relaxation behavior. The measurement period can be as short as 100 h to show the comparison with baseline data. The long-time prediction can be compared with the acceptable engineering-energy requirements to determine suitability for service.     

Converging flow of a viscoelastic liquid

Two-dimensional creeping sink flow of a Maxwell fluid is an accurate approximation to a bounded converging flow of contraction ratio at least 5 : 1 and covergence half-angles of up to 45°. In this range, a perturbation expansion in Weissenberg number can be used over most of the flow field in the range where stable processing can be carried out.     

On patched variational principles with application to elliptic and mixed elliptic-hyperbolic problems

Summary Variational principles are important tools for the approximate solution of boundary-value problems. There are many types of variational principles, and each has its advantages and disadvantages. In this paper we show how to use a combination of variational principles, each for a given subregion of the underlying region of space, so as to best utilize the chief benefits of the individual principles. Such a patched principle is particularly useful in solving transonic flow problems, where we use different principles in the elliptic and hyperbolic regions. We present the results of some numerical experiments for the Tricomi problem. These seem to indicate that our patched principle, when used in conjunction with the finite element method, leads to accuracy which is second-order in the mesh spacing, as compared to the standard numerical methods of solving this problem, which are only first-order.     

On graphs with a constant link,II

We study the following problem: For which finite graphs L do there exist graphs G such that the link (i.e., the neighborhood subgraph) of each vertex of G is isomorphic to L? We give a complete solution for the cases (i) L is a disjoint union of arcs, (ii) L is a tree with only one vertex of degree greater than two, (iii) L is a circle of prescribed length. Some other cases are also discussed. An interesting case is whether the situation is changed if we require G also to be finite. It transpires (see for example, Corollaries VII.3 and VII.4) that this is indeed the case.Part I of this paper will appear in [3]. It provides the basic definitions used in both part I and part II. Section III provides the basic tool, an identification procedure, that is used throughout the rest of the paper. Section IV sets up the basic building technique for the construction of more complicated graphs. It is shown how to build graphs such that the link of each vertex is an arc (of non-constant length), and how to control the proportional number of vertices with links of various lengths.