Free vibrations of rectangular orthotropic shallow shells with varying thickness

The paper proposes a numerical-analytic approach to studying the free vibrations of orthotropic shallow shells with double curvature and rectangular planform. The approach is based on the spline-approximation of unknown functions. Calculations are carried out for different types of boundary conditions. The influence of the mid-surface curvature and variable thickness on the behavior of dynamic characteristics is studied __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 102–115, June 2007.     

Validating a GIS-based multi-criteria method for potential road identification

This paper investigated the validation of a multi-criteria method for identifying potential roads, and demonstrated the capability of analyzing GPS vehicle tracking data for identifying vehicle movement patterns and potential roads. The multi-criteria method was evaluated by comparing the predictions to the site visit results on 34 selected road segments meeting different criteria levels. Results show that locations meeting higher criteria levels have higher possibilities to be roads: an approximately 91% possibility of road existence for the locations meeting all five criteria; 55% for the locations meeting four criteria; and 14% for those meeting criteria level two or three. This approach provides an opportunity for land managers to update existing GIS roads map, or identify newly formed roads that may need either rehabilitation or inclusion into the roads maintenance program.     

Change in the structure of a polymer solution in a longitudinal hydrodynamic field

There are two qualitatively different conditions for the stretching of liquid fibers formed by moderately concentrated polymer solutions [1]. If the longitudinal gradient of the drawing rate is rather small the structure of the solution remains unchanged. If this gradient exceeds a certain critical value, some of the solvent is expressed from the solution in and the liquid filament is converted into a slightly swollen fiber. The solvent released settles as droplets on the filament surface. This effect is of very great importance for a number of industrial processes pertaining to the production of filaments and films from polymer solutions. In addition, as was reported in [1], the drawing of a liquid filament, accomapnied by orientational formation of the solid phase, can serve as a most simple imitation of the formation of silk and gossamer filaments in nature.This paper presents a qualitative theory for this phenomenon, based on investigation of the thermodynamic stability of a polymer solution in a longitudinal hydrodynamic field.In conclusion the author thanks S. Ya. Frenkel for kindly providing information about the experiments conducted in his laboratory.     

Vibrations of a Floating Elastic Plate Due to Periodic Displacements of a Bottom Segment

The problem of the behavior of a floating elastic thin plate under periodic vibrations of a bottom segment is solved using a numerical procedure based on the Wiener-Hopf technique. The effects of the vibration frequency, the position of the vibrating bottom segment, and the fluid depth on the vibration frequencies of the fluid and plate are studied numerically.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 166–179, September–October, 2005.     

Nonlinear problem of flow past a source with the formation of a stagnant zone given different Bernoulli constants

The problem of free flow past a point source is considered for two streams with different Bernoulli constants whose encounter creates a bounded region of constant pressure. The theory and method of solving problems of plane ideal jet flows with different Bernoulli constants in the jets were developed in [1]. Here, in conformity with [1], a nonlinear system of equations is derived, the question of the construction of a high-accuracy numerical solution is considered, and certain calculation results are presented for various values of the Bernoulli and cavitation numbers, which are dimensionless parameters of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 55–60, May–June, 1986.     

Three-dimensional static problem for an elliptical crack in an elastic body with initial stress

Conclusions Thus, the influence of the initial stress on the displacement distribution in the crack plane is significant. In [6], it was concluded that, for a shear crack, it is impossible to show in the general case that the initial stress has no influence on the stress-intensity coefficients (which is the case for a normal-rupture crack). For the example of an elliptical shear crack, it is shown that the initial stress influences the stress distribution close to the crack and hence the stress-intensity coefficient, in contrast to the plane and axisymmetric problems.Close to the value of ₁ equal to the surface instability of the half space, as follows from a consideration of quantitative dependences, its influence is sharply expressed.The stress and displacement distribution in a body with initial stress (y ₃0) will differ from the corresponding distribution in a linear isotropic and transversally isotropic elastic body with no initial stress.Institute of Mechanics. Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 20, No. 10, pp. 22–31, October, 1984.     

Properties of vortices in the self-similar turbulent jet

Instantaneous, two-dimensional velocity measurements were conducted in the axial plane of a self-similar turbulent axisymmetric jet. The velocity fields were high-pass filtered to expose the vortical structures. An automated method was used to identify the radial and axial coordinates of the vortex centers and rotational sense, and to measure their size, circulation, vorticity, and energy. New insights into turbulent jets are obtained by plotting statistical distributions for vortex properties as functions of Reynolds number and radial position. While the probability of finding a vortex is uniform up to the edge of the jet, the strongest eddies in the high-pass filtered field occur near the jet axis. The average circulation is directly proportional to the vortex size. The Reynolds number strongly affects the average vorticity, circulation, and energy of the eddies. However, the normalized curves show a good collapse implying that the jet is indeed self-similar. Results for the left and right half-planes of the jet are also presented. Interestingly, we find that contrary to customary drawings of jet flows, a substantial number of both clockwise and counter-clockwise rotating eddies exist on both sides of the jet axis, with almost equal numbers of oppositely rotating vortices close to the jet axis. Further, the disparity in the number of oppositely rotating eddies in each half-plane increases with the eddy size. Nevertheless, these results are consistent with the well-known radial vorticity distribution of axisymmetric jets.     

Nonlinear response of a parametrically excited buckled beam

A nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented. The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using a digital computer and are compared with those obtained via an analog-computer simulation. The complicated dynamic behaviors that were found include period-multiplying and period-demultiplying bifurcations, period-three and period-six motions, jump phenomena, and chaos. In some cases, multiple periodic attractors coexist, and a chaotic attractor coexists with a periodic attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented.     

Experimental study of large-diameter thin-wall pressure vessels

An experimental stress analysis of three cylindrical pressure vessels with radius/thickness ratios ranging from 100 to 238 and different head closures is described. Brittle coatings and electrical strain gages were employed to determine stress distributions over the entire outer surface of the vessels. Electrical strain gages alone were used to determine stresses on the inside surface of the vessels. Particular emphasis was placed on determining stress concentrations and on nonlinear effects produced by geometric imperfections. An attempt was also made to correlate the failure, which started in the cylindrical portion of the three vessels, with the elastic-stress distribution. It was found that the imperfections in the cylinder were not significant if the vessel was fabricated from a ductile steel. However, if the vessel was constructed from a high-strength but brittle steel, the imperfections significantly lower the bursting strength of the vessel.