Reinforcing effect of birefringent coatings

Birefringent coatings carry a portion of the load that would otherwise be carried by the structure. Thus, strains at the structure-coating interface are somewhat less than those in an uncoated part. In addition, strain gradients through the coating thickness must be taken into account to determine the surface strains that would be developed in an uncoated part. Correction factors are derived for plane stress, flexure of plates, torsion of shafts and cylindrical pressure vessels, and the case of combined plane and flexural loads is treated. For plane and flexural loading, the correction factors are equally applicable to regions surrounding common geometrical discontinuities.     

Strain measurement with asymmetric oblique-incidence polariscope for birefringent coatings

A method for measuring principal-strain components is presented. Retardation in the birefringent coatings is measured with a compensator in normal and oblique-incidence. In order to reduce the errors and increase the angle of oblique incidence, a prism made of optically homogeneous material with an asymmetric polariscope is used. The plane of incidence of light is arbitrarily chosen and does not have to be changed during the measurement. Jones calculus is used to analyze the light transformation in the polariscope and in birefringent coatings.     

Application of birefringent coatings to glass-fiber-reinforced plastics

The application of birefringent coatings to plane-stress problems associated with orthotropic-glassreinforced plastic materials is treated. The improvement in the sensitivity of the birefringent-coating method due to the high strength and low modulus of the glassfiber-reinforced plastic materials is noted. Next, the effect of a mismatch in Poisson's ratio between the specimen material and coating is examined and a correction factor is developed which permits determination of boundary stresses even when the mismatch is large. Finally, the stress-strain relations for an orthotropic material are reviewed and an example of a nonsymmetric stress distribution associated with a symmetric fringe pattern is covered.     

Effects of the thickness of birefringent coatings

It is known that birefringent coatings are a powerful experimental technique for the determination of surface strains of metals or other opaque bodies. In this paper the complete state of strain in such a coating is determined for an arbitrary one-dimensional variation of the displacement at the metal surface. It is shown that strain gradients or curvature of the surface have a pronounced effect on the observed birefringence, and must be taken into consideration. This can be done by means of two correction factors derived in the paper which take into account the elastic properties of the coating and its thickness. An experimental procedure is outlined for determining an unknown distribution of strain at the metal surface on the basis of the observed photoelastic pattern.     

Bonding of birefringent coatings to composite flat-belt-drive materials

The bonding of birefringent coatings to composite flat-belt-drive materials is described. The belts were subsequently subjected to tension tests without apparent disassociation of the coating from the belt. Additionally, lengths of photoelastic coating bonded to endless flat belts run at speeds approaching 50 m/s exhibited no evidence of disassociation.     

On reinforcing effect of birefringent coatings on plate structures

A mathematical model is introduced and used to obtain a correction factor of the reinforcing effect of birefringent coatings on structures. The bending effect introduced to the coated structure due to the shifting of neutral surface is considered in the derivation of the correction factor. The photoelastic data corrected by this correction factor are found to be in good agreement with the theoretical calculations.     

An experimental investigation of cog-root strains in V-belts using birefringent coatings

A birefringent photoelastic coating was used in conjunction with a linear-elastic finite-element analysis in order to deline critical regions of cogged V-belts subjected to a purely geometric loading. The results indicate that cord-ply delamination in the midcog region adjacent to the cog root is a probable mode of failure.     

Measurements of thermally induced stress waves in a thin rod using birefringent coatings

When an elastic body is heated rapidly, significant inertial stresses are developed if the imposed heating rates cause a substantial temperature change in times which are short relative to the mechanical response time of the body. This work describes a method for inducing and measuring the thermally induced elastic stress waves in an unrestrained thin rod. Rapid heating was accomplished electrically by discharging a low-inductance capacitor bank (0.1 μH, 2800 J) through the rod. Utilizing the frozen-stress technique, an initial fringe pattern was introduced into thin strips of a birefringent material securely bonded to each side of the rod. The longitudinal strain oscillations were measured by direct observation of the movement of the fringe patterns with a high-speed framing camera. Interpretation of these measurements required a dynamic calibration and application of a dynamic correction factor for the reinforcing effect of the coating. Oscillations with periods from 35 to 250 μsec and stress amplitudes up to 900 psi were measured and compared with the uncoupled thermoelastic theory. Good agreement was obtained, and it was concluded that this technique is suitable for transient measurements in the presence of large magnetic fields which normally restrict the use of electronic methods.     

Fringe multiplication and thickness effects in birefringent coating

The feasibility of applying fringe-multiplication technique in birefringent-coating analysis is studied, and the conditions under which this technique can be used are discussed. The fringe-multiplication technique is then applied to birefringent-coating analysis of a plate with a central circular hole under uniaxial tension. The experimental results are then compared with Howland's analytical results for the shear-stress distribution along the minimum cross section and for normal stress distribution along the edge of the plate. Duffy's correction factors for curvatures and strain gradients are used to estimate the correction in the latter experimental results.     

Dynamic stability and phase planar property for radial sector cyclotrons with N-folded symmetry

The particle nonlinear motion equation for a radial sector cyclotron with N-folded symmetry was derived. The betatron oscillations frequency with N=4, 5, 6, 8, 10 and the phase planar properties before and after v_x=4/3 resonance with N=4, f=0.578 were analyzed, by using numerical method. The dynamic stabilities and nonlinear properties were discussed, the result compared with those of ref. [1] shows that both are consistent when nonlinear terms are neglected.     

New method for the determination of oblique-incidence coefficients for birefringent coatings and models

Results are developed which may enable the direct determination of oblique-incidence coefficients in coatings or models, thereby virtually eliminating errors due to Poisson's ratio, the oblique angle and the relative index of refraction.     

The application of birefringent coatings to metal surfaces which are to undergo large plastic strains

A direct-casting method is proposed for applying a birefringent coating to a flat metallic surface which will enable strains of at least 10 percent to be examined. This technique will assist the investigation of such problems as sheet-metal forming and plastic anisotropy.     

On the asymptotic behavior and radial symmetry of positive solutions of semilinear elliptic equations in R n II. Radial symmetry

Communicated by J. Serrin     

Propagation of acoustoelectric waves in a hollow cylinder whose physicomechanical properties have a radial symmetry axis

The general case of off-axis propagation of acoustoelectric waves in hollow cylinders made of a piezoelectric material such as a crystal of the class mm2 orthorhombic system with a two-fold radial symmetry axis is investigated. The basic system of equations for the wave problem in circular cylindrical coordinates is reduced to eight equations of the Hamiltonian type in the radial coordinate. A solution of the generalized spectral problem for harmonic waves is found by numerical methods. Special cases of the general problem are considered. The results of solving specific problems are analyzed. Taras Shevchenko National University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp 49–58, July, 1999     

Unsteady-state rarefaction flows with symmetry

The article considers unsteady-state isentropic rarefaction flows having either axial or central symmetry. Using the canonical form for writing the relationships which are satisfied along the characteristics, it is shown that, under determined conditions, rarefaction flows may contain a characteristic along which the velocity and the speed of sound vary as in a flow from some stationary source.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 34–39, November–December, 1970.In conclusion, the author thanks A. A. Nikol'skii for posing the problem.