Stability of circular-section bonded rubber blocks subjected to compression and bending

2006 ◽  
Vol 220 (10) ◽  
pp. 1489-1496
Author(s):  
J M Horton ◽  
G E Tupholme
Keyword(s):  
Cross Section ◽  
Critical Loads ◽  
Circular Cross Section ◽  
Numerical Data ◽  
Theory Of Elasticity ◽  
Circular Section ◽  
Typical Representative ◽  
Parallel Surfaces ◽  
Explicit Representations ◽  
Implicit Expressions

Rubber blocks of circular cross-section whose ends are bonded to rigid plates are studied under compression between either flat parallel surfaces or central parallel knife-edges. Implicit expressions are derived exactly in each case for the critical values of the loads at which the blocks begin to bend, based upon the classical theory of elasticity. Convenient very good approximate explicit representations are additionally deduced for these first critical loads. Some typical representative numerical data are compared and presented graphically in both situations.

scholarly journals The torsion and flexure of shafting with keyways or cracks

1932 ◽  
Vol 138 (836) ◽  
pp. 607-634 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Circular Cross Section ◽  
Transverse Load ◽  
Torsion Problem ◽  
Circular Section ◽  
Physical Conditions ◽  
The Cross ◽  
Straight Lines

The object of the paper is to investigate the properties of shafts of circular cross-section into which keyways or slits have been cut, first when subjected to torsion, and second when bent by a transverse load at one end. The torsion problem for similar cases has been treated by several writers. Filon has worked out an approximation to the case of a circular section with one or two keyways ; in his method the boundary of the cross-section was a nearly circular ellipse and the boundaries of the keyways were confocal hyperbolas. In particular he considered the case when the hyperbola degenerated into straight lines starting from the foci. The solution for a circular section with one keyway in the form of an orthogonal circle has been obtained by Gronwall. In each case the solution has been obtained by the use of a conformal trans­formation and this method is again used in this paper, the transformations used being ρ = k sn 2 t . ρ = k 1/2 sn t , ρ = k 1/2 sn 1/2 t where ρ = x + iy , t = ξ + i η. No work appears to have been done on the flexure problem which is here worked out for several cases of shafts with slits. 2. Summary of the Problems Treated . We first consider the torsional properties of shafts with one and with two indentations. In particular cases numerical results have been obtained for the stresses at particular points and for the torsional rigidity. The results for one indentation and for two indentations of the same width and approximately the same depth have been compared. We next consider the solution of the torsion problem for one, two or four equal slits of any depth from the surface towards the axis. The values of the stresses have not been worked out in these cases since the stress is infinite at the bottom of the slits. This in stress occurs because the physical conditions are not satisfied at the bottom of the slits, but as had been pointed out by Filon this does not affect the validity of the values of the torsional rigidity. We compare the effect on the torsional rigidity of the shaft of one, two and four slits of the same depth in particular cases. We also compare the results for one slit with those obtained by Filon by another method, and find very good agreement which is illustrated by a graph. The reduction in torsional rigidity due to a semicircular keyway is compared with that due to a slit of approximately the same depth. Finally the distortion of the cross-sections at right angles to the planes is investigated, and in this, several interesting and perhaps unexpected features appear. The relative shift of the two sides of the slits is calculated in several cases.

Resonant Gas Oscillations in a Linear Area Variation Cavity: Rectangular Versus Circular Cross Section

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sonu K. Thomas ◽  
T. M. Muruganandam
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Second Harmonic ◽  
Circular Cross Section ◽  
High Amplitude ◽  
Rectangular Section ◽  
Closed Cavity ◽  
Circular Section ◽  
Resonance Frequencies ◽  
Area Variation

Resonant gas oscillations in a linear area variation closed cavity are investigated, for two duct cross sections: rectangular and circular. The resonance frequencies were similar for both the ducts. Increased drive amplitude produced higher distortions in the waveform. It was found that both resonators exhibited commensurate behavior. This is opposed to noncommensurate behavior observed in nonuniform circular cross section resonators. The rectangular section duct had higher energy than circular section duct, in second harmonic for the same drive amplitude. The results reveal that in order to achieve shockless high amplitude pressure oscillations in a duct, both nonuniform area variation and circular cross section are required.

Helical Springs of Hollow Circular Cross Section

1959 ◽  
Vol 81 (1) ◽  
pp. 30-35
Author(s):  
C. W. Bert
Keyword(s):  
Experimental Investigation ◽  
Elasticity Theory ◽  
Cross Section ◽  
Circular Cross Section ◽  
Shear Stresses ◽  
Helical Spring ◽  
Circular Section ◽  
Helical Springs ◽  
Elastic Shear ◽  
Theory Solution

A theoretical and experimental investigation of elastic shear stresses and deflection in an axially loaded helical spring having a hollow circular section is reported in this paper. Two analyses are presented: An approximation of the stresses by strength-of-materials theory and a more accurate elasticity-theory solution for stresses and deflection. The results are compared with strain and deflection measurements on an actual tubular spring.

Axial Loading of Bonded Rubber Blocks

2002 ◽  
Vol 69 (6) ◽  
pp. 836-843 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme ◽  
M. J. C. Gover
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Closed Form ◽  
Cross Section ◽  
Shape Factor ◽  
Circular Cross Section ◽  
Axial Loading ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Lateral Profile

Axially loaded rubber blocks of long, thin rectangular and circular cross section whose ends are bonded to rigid plates are studied. Closed-form expressions, which satisfy exactly the governing equations and conditions based upon the classical theory of elasticity, are derived for the total axial deflection and stress distribution using a superposition approach. The corresponding relations are presented for readily calculating the apparent Young’s modulus, Ea, the modified modulus, Ea′, and the deformed lateral profiles of the blocks. From these, improved approximate elementary expressions for evaluating Ea and Ea′ are deduced. These estimates, and the precisely found values, agree for large values of the shape factor, S, with those previously suggested, but also fit the experimental data more closely for small values of S. Confirmation is provided that the assumption of a parabolic lateral profile is invalid for small values of S.

Optimal Assembly Problem of Rotor Blades : A Heuristic Approach

2005 ◽  
Vol 57 (1-2) ◽  
pp. 1-18
Author(s):  
R. Dasgupta ◽  
J. K. Ghosh
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Statistical Properties ◽  
Rotor Blades ◽  
Optimal Arrangement ◽  
Circular Section ◽  
Heuristic Approaches ◽  
Assembly Problem ◽  
High Degree ◽  
Optimal Assembly

Consider the optimal assembly problem of assigning blades of different but known momenta to fixed positions of a rotor of circular cross section used in hydroturbine. The assembly has to be such that the resultant imbalance of the rotor after assembly is a minimum and the momenta are more or less uniformly spread over the circular section. When the number of blades and consequently the number of possible permutations is also large , the optimal assembly is difficult to obtain. A few heuristic approaches for the assembly are suggested and the statistical properties for the assembly arc studied under an appropriate data based model (for the distribution of momenta). We compare the performance of the proposed techniques with the optimal arrangement when the number of blades is small. It is also found that the imbalance arising out of the proposed assembly can be predicted with a high degree of accuracy. based only on first a few large momenta spacings when the blade momenta follow sowe standard distributions.

A General Model for Predicting Low Reynolds Number Flow Pressure Drop in Non-Uniform Microchannels of Non-Circular Cross Section in Continuum and Slip-Flow Regimes

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
M. Akbari ◽  
A. Tamayol ◽  
M. Bahrami
Keyword(s):  
Pressure Drop ◽  
Cross Section ◽  
General Model ◽  
Circular Cross Section ◽  
Numerical Data ◽  
Creeping Flow ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Flow Pressure ◽  
The Cross

A general model that predicts single-phase creeping flow pressure drop in microchannels of a noncircular cross section under slip and no-slip regimes is proposed. The model accounts for gradual variations in the cross section and relates the pressure drop to geometrical parameters of the cross section, i.e., area, perimeter, and polar moment of inertia. The accuracy of the proposed model is assessed by comparing the results against experimental and numerical data collected from various studies in the literature for a wide variety of cross-sectional shapes. The suggested model can be used for the design and optimization of microsystems that contain networks of microchannels with noncircular cross sections resulting from different fabrication techniques.

Circulation Control and its Application to Stopped Rotor Aircraft

1968 ◽  
Vol 72 (691) ◽  
pp. 635-646 ◽  
Author(s):  
I. C. Cheeseman
Keyword(s):  
Cross Section ◽  
Rotor Blade ◽  
Circular Cross Section ◽  
Scale Model ◽  
Circulation Control ◽  
Thrust Coefficient ◽  
Circular Section ◽  
Typical Performance ◽  
Blade Section ◽  
Cyclic Control

Summary The problems associated with the design of a stopped rotor aircraft are summarised. The decision to attempt to overcome the aerodynamic difficulties by the choice of a rotor blade section which is basically insensitive to atmospheric gusts dictates a largely circular cross section. During the rotor lifting phases of the flight the circular section is constrained to lift by a technique called circulation control by blowing — this technique is described and some results presented. A scale model hingeless rotor has been tested at the National Gas Turbine Establishment. Typical performance figures are presented and their implications discussed. In particular, it is shown that operating rotors at high values of thrust coefficient per blade leads to high induced power factors. Cyclic control of rotor lift is achieved by hub throttling the air to the circulation control slots —a simple mechanism to achieve this result is described. Two possible schemes for a VTOL circulation control stopped rotor transport are discussed and compared.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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