bluuebunny/crossref_metadata_2025_split huggingface dataset:
Vibration of Triangular Cantilever Plates by the Ritz Method
Authors: Andersen B. W. 
Published: June 2021

Abstract
Using the method published by Ritz in 1909, natural frequencies and corresponding node lines have been determined for two symmetric and two antisymmetric modes of vibration of isosceles triangular plates clamped at the base and having length-to-base ratios of 1, 2, 4, and 7 and for the two lowest modes of right triangular plates clamped along one leg and having ratios of the length of the free leg to that of the clamped one of 2, 4, and 7. A nonorthogonal co-ordinate system was used which gave constant limits of integration over the area of the triangle. The co-ordinate transformation made it necessary to modify the functions used by Ritz in approximating deflections and to consider cross products in the integration. The integration was done numerically, using tables compiled by Young and Felgar in 1949. To check the accuracy of results, a solution was obtained to the problem of a vibrating cantilever beam of uniform depth and triangular plan view. The results obtained were found to be consistent with those obtained for the plates by using an eight-term series to approximate the deflections of the symmetric plates (isosceles triangles) and a six-term series to approximate the deflections of the unsymmetric plates (right triangles).
Fretting Corrosion of Mild Steel in Air and in Nitrogen
Authors: Feng I-Ming , Uhlig Herbert H. 
Published: June 2021

Abstract
Data are presented on fretting corrosion of mild steel using weight loss as a measure of damage. Relative slip was measured both by use of stroboscopic light and strain gages. Load was applied pneumatically. Humidity of ambient air was found to be a sensitive variable requiring control, a fact first discovered through discrepancies of weight-loss data obtained in winter compared with those obtained in summer. Fretting corrosion of mild steel in moist air is only 55 to 65 per cent of the weight loss in dry air, depending on duration of test. Because of this large difference, all tests were carried out in dry air. At the same time, it was observed that fretting corrosion is appreciably greater below room temperature than above room temperature (up to 150 C). Weight losses of specimens fretted at 50 C are approximately 50 per cent losses at 0 C. Rate of fretting corrosion in air is found to be constant with time after an initial run-in period during which the rate is temporarily higher. In moist or dry nitrogen, weight losses are much less, although not zero. The greater the relative slip, the greater is fretting damage, and in complete absence of slip the data indicate that no weight loss occurs. Increased pressure or load is found to increase fretting damage. Weight loss is greater the lower the frequency for the same number of test cycles. The frequency effect increases with relative slip, and in nitrogen the frequency effect disappears.
Gravitational Stresses in a Circular Ring Resting on Concentrated Support
Authors: Yu Yi-Yuan 
Published: June 2021

Abstract
Muschelišvili’s complex variable method in two-dimensional elasticity has been extended by the present author to solve a few gravitational stress problems. A further problem of a heavy circular ring resting on a concentrated support is solved by the same method in the present paper. The two analytic functions which constitute the solution of the problem are determined. A numerical example is given for a ring the radii of which are in the ratio of 1 to 2.
Remarks on Donnell’s Equations
Authors: Kempner Joseph 
Published: June 2021

Abstract
Flügge’s set of differential equations of equilibrium for circular cylindrical shells is expressed in a form analogous to the Donnell equations. The results of solutions of the two sets of equations for a simply supported cylinder under a centrally applied, uniformly distributed radial line load over a generator segment, as well as under sinusoidally applied line loads, are in very good agreement for the particular geometry investigated.
Prediction of Creep-Deflection and Stress Distribution in Beams From Creep in Tension
Authors: Findley W. N. , Poczatek J. J. 
Published: June 2021

Abstract
A method of predicting creep in bending from data on creep in tension has been derived and applied to creep of a canvas laminate. Both creep deflections and stress distribution were derived. The deflections compared favorably with test data. It was shown that the stress distribution remained constant during creep in bending when creep in tension and compression were equal and the coefficient of the time-dependent term was equal to the time-independent term. Methods of determining creep deflections of beams having nonuniform bending moments are described.
Thermal Shock on a Circular Surface of Exposure of an Elastic Half Space
Authors: Sadowsky M. A. 
Published: June 2021

Abstract
The paper presents an explicit determination of displacements and stresses in a uniform circular thermal shock. In a generalization to nonuniform shocks on surfaces of arbitrary shape, it is shown that the protrusion arising at any place is proportional to the intensity of the shock at that place.
Further Work on the General Three-Dimensional Photoelastic Problem
Authors: Frocht Max M. , Guernsey Roscoe 
Published: June 2021

Abstract
It is known that purely photoelastic procedures cannot solve the general three-dimensional stress problem. Photoelasticity furnishes data from which only the principal shears can be determined, but not the principal stresses. A new, general, and practical method of solution which has been described previously (1, 2) is reviewed briefly, and possible variations in procedure are discussed. This method combines the photoelastic data from frozen stress patterns with a numerical integration of one of the differential equations of equilibrium in Cartesian coordinates. The actual principal stresses at each point of a homogeneous and isotropic body of arbitrary shape subjected to a general system of loads are thereby determined. The method has been applied previously to a sphere subjected to diametral compressive loads of 172 lb. The present paper contains the results from a second sphere subjected to 79.6 lb which show that the degree of reproducibility of results is high. Very good agreement is also shown to exist with a theoretical solution of the same problem by Sternberg and Rosenthal (3) The paper also contains the solution of a short rectangular parallelepiped loaded through a small flat circular die. The investigation was conducted in the Photoelastic Laboratory of the Mechanics Department of Illinois Institute of Technology.
Frictional Vibrations
Authors: Sinclair David 
Published: June 2021

Abstract
Frictional vibrations, such as stick-slip motion and automobile-brake squeal, which occur when two solid bodies are rubbed together, are analyzed mathematically and observed experimentally. The conditions studied are slow uniform motion and relatively rapid simple harmonic motion of brake lining over a cast-iron base. The equations of motion show and the observations confirm that frictional vibrations are caused primarily by an inverse variation of coefficient of friction with sliding velocity, but their form and occurrence are greatly dependent upon the dynamical constants of the mechanical system. With a constant coefficient of friction, the vibration initiated whenever sliding begins is rapidly damped out, not by the friction but by the “natural” damping of all mechanical systems. The coefficient of friction of most brake linings and other organic materials was essentially invariant with velocity, except that the static coefficient was usually greater than the sliding coefficient. Most such materials usually showed a small decrease in coefficient with increasing temperature. The persistent vibrations resulting from the excess static friction were reduced or eliminated by treating the rubbing surfaces with polar organic compounds which produced a rising friction characteristic.
The Elastic-Plastic Stress Distribution Within a Wide Curved Bar Subjected to Pure Bending
Authors: Shaffer Bernard W. , House Raymond N. 
Published: June 2021

Abstract
Analytical expressions are obtained for the radial and circumferential stress distributions within a wide curved bar made of a perfectly plastic material when it is subjected to a uniformly distributed bending moment. The elastic stress distributions are based on the use of the Airy stress function, whereas the plastic stress distributions in this problem of plane strain are based on the use of the Tresca yield condition. It is found that as the bending moment increases in the direction which tends to straighten the initially curved bar, an elastic-plastic boundary develops first around the concave surface. It meets a second boundary, which starts sometime later around the convex surface, when the bar is completely plastic. The elastic region within the bar decreases at a fairly uniform rate as the bending moment increases to within approximately 90 per cent of the fully plastic bending moment but then it degenerates very much more rapidly until it no longer exists when the bar is completely plastic. The position of the neutral surface is independent of the applied bending moment when the stress distribution is within the completely elastic and the completely plastic ranges. Within the elastic-plastic range, however, it moves away from and then toward the center of curvature as the bending moment increases.
Free Oscillations of Systems Having Quadratic Damping and Arbitrary Restoring Forces
Authors: Klotter Karl 
Published: June 2021

Abstract
In this paper, systems are treated which are subjected to quadratic damping forces (of any magnitude) and to restoring forces of any type. The differential equations of motion for such systems can be transformed into linear differential equations of first order for the velocity squared, whatever the restoring forces may be. A first integral can be obtained readily. From it the exact relationships between any two consecutive maximum displacements (“amplitudes”) are derived. These relationships are discussed in detail for various types of restoring forces. Examples are worked out numerically and illustrated by graphs.
On the Nonlinear Oscillations of Viscoelastic Plates
Authors: Eringen A. Cemal 
Published: June 2021

Abstract
Equations of motion of the three-dimensional finite oscillation theory are integrated across the plate thickness to obtain a second-order theory of oscillations for plates. For this purpose, components of the displacement vector are assumed to have power-series expansions in the transverse co-ordinate, and a systematic perturbation procedure in a nondimensional thickness parameter is used. Stress-strain relations include the hereditary damping.
Forced Vibration of a Clamped Rectangular Plate in Fluid Media
Authors: Yeh Gordon C. K. , Martinek Johann 
Published: June 2021

Abstract
Forced vibration of a thin rectangular plate clamped in a rigid infinite baffle is analyzed. The plate is assumed to separate two different fluid media and the vibration is excited by a simple plane wave of high frequency (as compared with c / 2 π ab ) normally incident from one side of the plate. Using the characteristic shape functions, the Lagrange equations of motion of the plate are set up in generalized co-ordinates. The solutions of the equations render series expressions for the plate deflection and an energy-transmission coefficient. Certain numerical results are given.
Influence of Secondary Inertia Terms on Natural Frequencies of Rotating Beams
Authors: Bogdanoff J. L. 
Published: June 2021

Abstract
The equations of small motion of a straight cantilever beam attached to the rim of a rotating disk are determined assuming the Bernoulli-Euler theory of bending and the Saint Venant theory of torsion are valid, the mass and elastic axes coinciding and retaining all inertia terms. Influence of the secondary inertia terms on the fundamental torsional and lateral frequencies is then examined at two angular settings for a uniform beam having a length to disk-radius ratio in the range usually encountered in gas-turbine buckets and axial-flow compressor blades.
Large Deflections of Elliptical Plates
Authors: Weil N. A. , Newmark N. M. 
Published: June 2021

Abstract
A solution is obtained by means of the Ritz method for the “large-deflection” problem of a clamped elliptical plate of constant thickness, subjected to a uniformly distributed load. Two shapes of elliptical plate are treated, in addition to the limiting cases of the circular plate and infinite strip, for which the exact solutions are known. Center deflections as well as total stresses at the center and edge decrease as one proceeds from the infinite strip through the elliptical shapes to the circular plate, holding the width of the plates constant. The relation between edge-stress at the semiminor axis (maximum stress in the plate) and center deflection is found to be practically independent of the proportions of the elliptical plate. Hence the governing stress may be determined from a single curve for a given load on an elliptical plate of arbitrary dimensions, if the center deflection is known.
The Load-Carrying Capacity of Circular Plates at Large Deflection
Authors: Onat E. T. , Haythornthwaite R. M. 
Published: June 2021

Abstract
This paper presents an approximate analysis for the load carrying capacities of initially flat circular plates under various loading and edge conditions and subjected to slowly increasing load. As a plate deforms, the carrying capacity is increased as a result of favorable changes in geometry. In this study, the load capacity after finite deflection is estimated by assuming a velocity field based on the boundary conditions and on the incipient velocity field of the flat plate, the analysis being made for a rigid plastic, nonstrain-hardening material that yields according to the maximum shear-stress criterion. In several cases the results obtained compare favorably with test data for mild-steel plates; however, for very thin plates, better agreement is obtained by means of a purely membrane-type analysis, which also is presented.
The Pattern of Plastic Deformation in a Deeply Notched Bar With Semicircular Roots
Authors: Garr L. , Lee E. H. , Wang A. J. 
Published: June 2021

Abstract
The plastic deformation in a notched bar with deep semicircular roots pulled in plane strain is determined theoretically. The finite deformation is analyzed according to plastic-rigid theory. The motion is unsteady, and the velocity field at any instant is given in terms of the current geometry of the deformed free surface. A graphical step-by-step method is used to determine the deformation of a square grid scribed on the undeformed cross section. The deformed pattern details the regions of large plastic strain, and may be useful in considering the initiation of fracture cracks.
On Some Problems in Bending of Thick Circular Plates on an Elastic Foundation
Authors: Frederick Daniel 
Published: June 2021

Abstract
The governing equations and solutions for the nonsymmetrical bending of circular plates resting on an elastic foundation are presented using the theory developed by E. Reissner. Also included are two examples in which numerical comparisons have been made with the predictions of the classical theory. These are (a) the axially symmetric bending of a finite circular plate on an elastic foundation under a partial uniform loading, and (b) the nonsymmetric bending of an infinite plate on an elastic foundation with a rigid circular inclusion.
Effect of Hub Radius on the Vibrations of a Uniform Bar
Authors: Boyce W. E. 
Published: June 2021

Abstract
Methods are discussed for obtaining upper and lower bounds on the frequencies of a uniform beam, rotating at a constant speed about an axis at one end, and vibrating transversely to the plane of rotation. Previous results are extended to include the case of a nonzero hub radius. Bounds on the first two frequencies are given for several ratios of hub radius to beam length. These show that the frequencies depend almost linearly on the hub radius for various rotational speeds.
On the Role of Extension in the Flexural Vibrations of Rings
Authors: Philipson L. L. 
Published: June 2021

Abstract
In a generalization of the classical analysis of A. E. H. Love, equations describing the flexural vibrations of thin rings are derived without making use of the usual assumption of no extension of the central line. Direct comparison with the nonextensional formulas of Love leads to a criterion for the validity of the assumption. In the process, the forced-vibration problem is shown to require the possibility of extension in certain cases in which its neglecting in a free-vibration analysis is valid.
Impulsive Loading of Elastic-Plastic Beams
Authors: Seiler J. A. , Cotter B. A. , Symonds P. S. 
Published: June 2021

Abstract
A simply supported uniform beam of ductile material, subjected to impulsive loading such that the initial velocity is a half-sine wave, is considered in this paper. The elastic and elastic-plastic motions are discussed under the assumption that plastic flow is confined to one cross section, and the final deformations are compared with those computed from an analysis which neglects all elastic deformations. The purpose of the work is to provide further information which may help in estimating the range of validity of the latter (“rigid-plastic”) type of analysis.
An Experimental Investigation of Beam Stresses Produced by Oblique Impact of a Steel Sphere
Authors: Cunningham D. M. , Goldsmith Werner 
Published: June 2021

Abstract
An experimental investigation designed to study the phenomenaincident to the oblique collision of 1/2-in-diam steel spheres with mild-steel and annealed drill-rod beams at oblique angles of incidence has been undertaken. Initial ball velocities ranged from 30 ft/sec to 150 ft/sec, beam sizes varied from 1/4 in. × 1/4 in. to 3/4 in. × 3/4 in., angles of incidence were chosen from 85 deg to normal incidence, and simply supported, clamped, and free beams were employed. Information is reported concerning the values of maximum bending stress at various positions along the beam as function of the angle of incidence and as a function of beam size for various angles of incidence. The progressive dispersion of the initial transient has been examined in detail. The effect of end supports, effective beam length, and repetitive shots into the same hole upon stress are described.
Augmentation in Tribological Performance of Polyalphaolefins by COOH-Functionalized Multiwalled Carbon Nanotubes as an Additive in Boundary Lubrication Conditions
Authors: Kumar Homender , Harsha A. P. 
Published: June 2021

Abstract
This current study emphasized the tribological performances of COOH-functionalized multiwalled carbon nanotubes (MWCNTs) dispersed in two different grades of polyalphaolefins (i.e., PAO 4 and PAO 6). The friction and wear properties have been estimated using SRV 5 tribometer with “ball-on-disc” configuration. Prior to tribo testing, MWCNTs were characterized by X-ray diffractometer (XRD), high-resolution transmission electron microscopy (HR-TEM), and Fourier-transform infrared spectroscopy (FTIR). The varying dose of MWCNTs (0.025–0.15 wt%) was incorporated into both PAO base oils to obtain the optimized lubrication behavior. The test results revealed that PAO 4 exhibited a reduction in friction coefficient (∼27%) and wear volume (∼88%) at a dose of 0.05 wt% and 0.025 wt% MWCNTs, respectively. However, in PAO 6, the minimum coefficient of friction and wear volume was obtained at a concentration of 0.075 wt% and 0.05 wt% of the additive. The results evidenced that PAO 6 based nanolubricants demonstrated the best frictional characteristics while attained the best anti-wear performance with PAO 4 based nanolubricants. For the better unveiling of the lubrication mechanism of MWCNTs, worn surfaces were characterized using various analytical techniques such as scanning electron microscopy (SEM), scanning probe microscope (SPM), energy-dispersive X-ray spectroscopy (EDS), and X-ray photoelectron microscopy (XPS).
Drift-Flux Parameters for High-Viscous-Oil/Gas Two-Phase Upward Flow in a Large and Narrow Vertical and Inclined Annular Duct
Authors: Barbosa Marcel Cavallini , Rodriguez Oscar Mauricio Hernandez 
Published: June 2021

Abstract
Proper sizing of flow lines in the upstream energy industry depends on accurate modeling of gas–liquid flow, which has a common occurrence in production wells and has been studied thoroughly for many decades. However, data of flow in duct geometries different from circular pipes and when the liquid viscosity is much higher than that of water are scarce. Proper prediction of pressure gradient, heat and mass transfer, and corrosion depends on the accuracy of the model used to calculate the volumetric phase fraction. In pumped directional wells with inverted-shroud gravitational separators, there is flow through an annular duct formed between the wells’ casing and the separator itself that can have some tens of meters. The present work is an investigation on upward vertical/inclined high-viscous-oil/gas flow in a large and narrow annulus (30 mm hydraulic diameter with an outer diameter equal to 155 mm), using a radial geometry comparable with those found in real production systems. Air–water and air–oil mixtures, the latter with two oil viscosity ranges, were used as working fluids. The experimental test section used was 9.67 m long positioned at 90 deg (vertical) and 45 deg and made of two concentric pipes. Flow pattern transitions from the literature were analyzed and compared with the collected experimental data. Drift-flux parameters were obtained from multiple working conditions. These drift-flux parameters were used in the development of a novel flow pattern-independent correlation, compared against the present data and other data sets from the literature in which other geometries and fluids were used. The predictions of the proposed drift-flux correlation are significantly superior in comparison with correlations selected from the literature in all cases.
Variability in Submaximal Self-Paced Exercise Bouts of Different Intensity and Duration
Authors: O’Grady Ciaran , Passfield Louis , Hopker James G. 
Published: June 2021

Purpose: Rating of perceived exertion (RPE) as a training-intensity prescription has been extensively used by athletes and coaches. However, individual variability in the physiological response to exercise prescribed using RPE has not been investigated. Methods: Twenty well-trained competitive cyclists (male = 18, female = 2, maximum oxygen consumption = 55.07 [11.06] mL·kg−1·min−1) completed 3 exercise trials each consisting of 9 randomized self-paced exercise bouts of either 1, 4, or 8 minutes at RPEs of 9, 13, and 17. Within-athlete variability (WAV) and between-athletes variability (BAV) in power and physiological responses were calculated using the coefficient of variation. Total variability was calculated as the ratio of WAV to BAV. Results: Increased RPEs were associated with higher power, heart rate, work, volume of expired oxygen (VO2), volume of expired carbon dioxide (VCO2), minute ventilation (VE), deoxyhemoglobin (ΔHHb) (P < .001), and lower tissue saturation index (ΔTSI%) and ΔO2Hb (oxyhaemoglobin; P < .001). At an RPE of 9, shorter durations resulted in lower VO2 (P < .05) and decreased ΔTSI%, and the ΔHHb increased as the duration increased (P < .05). At an RPE of 13, shorter durations resulted in lower VO2, VE, and percentage of maximum oxygen consumption (P < .001), as well as higher power, heart rate, ΔHHb (P < .001), and ΔTSI% (P < .05). At an RPE of 17, power (P < .001) and ΔTSI% (P < .05) increased as duration decreased. As intensity and duration increased, WAV and BAV in power, work, heart rate, VO2, VCO2, and VE decreased, and WAV and BAV in near-infrared spectroscopy increased. Conclusions: Self-paced intensity prescriptions of high effort and long duration result in the greatest consistency on both a within- and between-athletes basis.