THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

History of Polymer Education-USA

Prior to 1940 there was little or no education directed toward polymer chemistry. With the contributions of Carothers and others that transformed the practice of polymers into a science-and the leadership of Herman Mark and others in formal graduate and postgraduate education-polymer education took root but rapid expansion and general acceptance by more traditionally oriented academic institutions was slowed by many barriers. Only since 1974 has there been a concerted effort to include education in the basic concepts of polymer chemistry into the undergraduate curriculum. Emphasis is on the development of polymer education in the United States.     

Simulation of three-phase displacement experiments

Three-phase displacement experiments for a water-benzyl alcohol-decane system are simulated. Literature experimental three-phase relative permeabilities for the system are used to describe the relative permeabilities in the three-phase region for different three-phase relative permeability models. Saturation trajectories and elliptical regions are mapped in the three-phase region. Simulations are performed to model displacement experiments including breakthrough and the formation of multiple shocks. The model can be used to predict the results for other displacements. In an experiment where significant gravity segregation is present, the displacement is more accurately modeled by assuming a uniform initial condition than by using the actual vertical saturation and assuming no cross flow. It is shown how different residual saturation values can be measured in the laboratory depending on the initial saturation conditions in the core. The experimental residual saturations can be significantly different than the ‘theoretical’ or model values.     

Applicability of generic linear scoring mosels in the U.S. credit-union environment

Although credit-scoring models represent a widely used managerialaid for large financial intermediaries, the vast majority ofU.S. credit unions—relatively small cooperatively ownedretail intermediaries, constrained by sample and funding limitations—haveyet to adopt such techniques. Lovie & Lovie (1986) havetheorized that the flat-maximum effect or curve of insensitivityassociated with linear scoring models could be advantageousin areas of applied prediction such as credit scoring. In thiscontext, we reported the relative predictive power of genericcredit-scoring models versus customized models in an earlierpaper (Overstreet et al. 1992). Unfortunately, these findingswere not readily adaptable to the credit-union industry dueto a dated sample with incomplete credit-bureau information.Consequently, from 1988 to 1991, we gathered a refined databasefrom which to further develop and field-test generic scoringmodels in the credit-union environment. The results reportedherein not only confirm, but amplify, the relative predictivepower of such models found earlier. Relative costs and benefitsof generic versus customized models are modelled for a representativecredit union. Future research directions are set forth in theconclusions.     

Short-Chain Branching in Polyethylene and Poly(vinyl Chloride) Using Pyrolysis Hydrogenation Gas Chromatography and 13C Nuclear Magnetic Resonance Analysis

This study compares the use of pyrolysis hydrogenation gas chromatography (PHGC) and ¹³C Fourier transform nuclear magnetic resonance (FTNMR) methods for the analysis of reference polyethylene (PE) samples, ethylene-α-olefin copolymers, and specially prepared poly(vinyl chloride) (PVC) samples which were reduced to their PE skeletal structures. The nature and relative quantities of the short branches along the polymer chains were determined using both techniques. Improved high-resolution PHGC data, obtained with a fused silica capillary separation column, gave results which were in satisfactory agreement with the ¹³C FTNMR data. This approach confirms that detailed microstructural information can be obtained with these methods by using carefully controlled experimental conditions and appropriate reference systems.