Moiré interferometry for thermal expansion of composites

Techniques were developed for high-sensitivity moiré interferometry by reflection, using a real reference grating of 1200 lines/mm (30,000 /in.). Coefficients of thermal expansion of selected graphite-epoxy laminates were determined in the temperature range of 297 K (75°F) to 422 K (300°F). Very good precision was achieved for a wide range of thermal-expansion coefficients, from approximately zero to 27 /K.D.E. Bowles was a Graduate Student at Virginia Polytechnic Institute and State University when this research was conducted; is currently Materials Engineer at NASA-Langley Research Center, Hampton, VA 23665Paper was presented at 1981 SESA Spring Meeting held in Dearborn, MI on May 31–June 4.     

Corneal studies by photoelasticity

Freshly enucleated andin vivo eyes of cats were analyzed to determine the detailed distribution of birefringence across the cornea and through its thickness, and to determine the change of birefringence with intraocular pressure. Scattered light and oblique-incidence photoelasticity were used. The experiments are summarized and special considerations are discussed. These include the necessity for a laser-light source; diffraction limitation in producing a narrow ribbon of light; rotation of the plane of polarization; inequalities in reflected components of polarized light.     

A localized hybrid method of stress analysis: A combination of moiré interferometry and FEM

A method of combining moiré interferometry and the finite-element method to effect localized stress analysis is presented. The displacement data from local regions of interest in the optical experiment are used as boundary conditions for the finite-element stress analysis. The stability of the method is examined with data from simple numerical models one of which corresponded to the stress analysis of a pin-loaded plate with friction. These studies show that the method requires the sensivity of moiré interferometry for successful implementation, i.e., displacement data accuracy within 0.1 μm or 4 μin. This localized hybrid method of stress analysis provides a powerful and efficient method for the reduction of experimental data.     

Stable crack growth in aluminum tensile specimens

Post's white-light moiré interferometry was used to obtain sequential records of the transientU _y -displacement fields associated with stable crack growth in 7075-T6 and 2024-0, single-edge-notched (SEN) specimens with fatigued cracks. TheU _y -displacement fields are used to evaluate the crack-tip opening displacement (CTOD), far- and near-fieldJ-integral values, Dugdale-strip-yield model, William's polynomial function and the HRR field. Paper was presented at 1985 SEM Spring Converence on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

The Stark effect in the 6snf Rydberg series of barium

The Stark effect has been studied in the odd-parity 6snf^1,3F₃ Rydberg series of barium with high-resolution laser-atomic-beam spectroscopy. Scalar and tensor polarizabilities have been measured of 6snf¹F₃ levels with n=11–30 and of 6snf³F₃ levels withn = 12 ? 40. The contributions of the adjacent even-parity Rydberg levels to these polarizabilities have been calculated as far as data are available. This results in important additional information on the only partly known 6sng^1,3G₄ series and confirms the perturbation of these series atn = 24 by a 5d7dJ= 4 level. A tentative three-channel quantum-defect-theory analysis of the^1,3G₄ series has been performed. It is shown that reported level energies of the 6snd^1,3D₂ series are systematically 0.14 cm^?1 too high.     

Stress Evaluation Using Ultrasonic Interference Spectrum of Leaky Lamb Waves

This paper presents a nondestructive stress evaluation technique using the ultrasonic interference spectrum of leaky Lamb waves. By using a specific pitch-catch ultrasonic setup, the symmetric and antisymmetric modes of Lamb waves in a finite plate are decoupled, leading to simple relationships between the modal frequency spacing of two adjacent modes in the interference spectrum and the acoustic wave velocities that are functions of stress. As a result, the stress in the plate can be determined by measuring the modal frequency spacing instead of the relative flight times to calculate the acoustic wave velocity. Extensive experiments were carried out to verify the viability and robustness of the new technique using a simple testing system. It has been demonstrated that the new technique is about 25 times more accurate than existing flight-time approaches using the same testing system. The experimental results agree well with the results obtained by other ultrasonic methods using expensive equipment.     

Continuity properties of the integrated density of states on manifolds

We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS. Subsequently, alloy-type perturbations of the periodic operator are considered. The randomness may enter both via the potential and the metric. A Wegner estimate is proven which implies the continuity of the corresponding IDS. This gives an example of a discontinuous “periodic” IDS which is regularized by a random perturbation.     

An algebraic interpretation of the multivariate <Emphasis Type="Italic">q</Emphasis>-Krawtchouk polynomials

The multivariate quantum q-Krawtchouk polynomials are shown to arise as matrix elements of “q-rotations” acting on the state vectors of many q-oscillators. The focus is put on the two-variable case. The algebraic interpretation is used to derive the main properties of the polynomials: orthogonality, duality, structure relations, difference equations, and recurrence relations. The extension to an arbitrary number of variables is presented.     

Quadratic data envelopment analysis

Data Envelopment Analysis (DEA) offers a piece-wise linear approximation of the production frontier. The approximation tends to be poor if the true frontier is not concave, eg in case of economies of scale or of specialisation. To improve the flexibility of the DEA frontier and to gain in empirical fit, we propose to extend DEA towards a more general piece-wise quadratic approximation, called Quadratic Data Envelopment Analysis (QDEA). We show that QDEA gives statistically consistent estimates for all production frontiers with bounded Hessian eigenvalues. Our Monte-Carlo simulations suggest that QDEA can substantially improve efficiency estimation in finite samples relative to standard DEA models.