Calculated Pressure Distributions and Shock Shapes on Conical Wings with Attached Shock Waves

1968 ◽  
Vol 19 (1) ◽  
pp. 31-50 ◽  
Author(s):  
L. C. Squire
Keyword(s):  
Shock Waves ◽  
Exact Solutions ◽  
Pressure Distribution ◽  
Newtonian Theory ◽  
First Order ◽  
Pressure Distributions ◽  
Present Solution ◽  
Design Behaviour ◽  
First Order Correction ◽  
Good Agreement

SummaryRecently Messiter has proposed a first-order correction to simple Newtonian theory for the pressure distribution on the lower (compression) surfaces of lifting conical bodies. Although the basic theory holds for bodies with and without attached shock waves, solutions have so far only been obtained for bodies with detached shocks. In the present paper an approximate method of applying the theory to bodies with attached shocks is given. In spite of the approximations involved the calculated shock shapes and pressure distributions are in good agreement with some exact solutions for flat wings, except near the incidence for shock detachment. Like the detached shock case, the present solution can be applied to Nonweiler wings in certain off-design conditions. The combined results for the detached shock and for the attached shock enable the off-design behaviour of Nonweiler wings to be discussed in a systematic manner.

Calculated Pressure Distributions and Shock Shapes on Thick Conical Wings at High Supersonic Speeds

1967 ◽  
Vol 18 (2) ◽  
pp. 185-206 ◽  
Author(s):  
L. C. Squire
Keyword(s):  
Integral Equation ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Poor Agreement ◽  
Delta Wings ◽  
Newtonian Theory ◽  
Pressure Distributions ◽  
First Order Correction ◽  
Good Agreement

SummaryIn recent papers Messiter and Hida have proposed a first-order correction to simple Newtonian theory for the pressure distributions on the lower surfaces of lifting conical bodies with detached shocks. The method involves the solution of an integral equation which Messiter solved numerically for thin delta wings, while Hida gave an approximate solution for thick wings with diamond and bi-convex cross-sections. It is shown in the present paper that Hida’s approximate solutions give poor agreement with experiment, and a series of more precise numerical solutions of the equation are given for wings with diamond cross-sections. The pressures, and shock shapes, obtained from these solutions are in very good agreement with experiment at Mach numbers as low as 4·0.The method has also been extended to Nonweiler wings at off-design when the shock wave is detached from the leading edges. Again the agreement with experiment is good provided the integral equation is solved numerically.

The Effects of Yaw on Conical Wings at High Supersonic Speeds

1970 ◽  
Vol 21 (3) ◽  
pp. 199-210 ◽  
Author(s):  
R. Hillier
Keyword(s):  
Pressure Distribution ◽  
Lower Surface ◽  
Order Correction ◽  
Newtonian Theory ◽  
First Order ◽  
First Order Correction ◽  
Leading Edges

SummaryIn recent papers Squire has presented results for the shock shape and pressure distribution on the lower surface of unyawed, lifing, conical bodies with sharp leading edges. The work, a development of Messiter’s first-order correction to Newtonian theory, was successfully applied to wings of diamond and caret section. This paper shows how the method may be used to include the effects of yaw. Results are presented here for the flat wing and some biconvex sections. Comparisons are made with experiment for both the flat and biconvex wings and agreement is shown to be good.

First-Order Perturbations of Laminar Free-Convection Boundary Layers on a Vertical Plate

1964 ◽  
Vol 86 (1) ◽  
pp. 107-114 ◽  
Author(s):  
Kwang-Tzu Yang ◽  
Edward W. Jerger
Keyword(s):  
Free Convection ◽  
Vertical Plate ◽  
Order Approximation ◽  
Leading Edge ◽  
Temperature Fields ◽  
First Order ◽  
Present Solution ◽  
Classical Boundary ◽  
Prandtl Numbers ◽  
Good Agreement

A perturbation analysis for laminar free convection along a vertical plate, utilizing the classical boundary-layer solution as the zeroth-order approximation, is presented. First-order perturbations for the velocity and temperature fields have been calculated in detail for Prandtl numbers of 0.72 and 10.0. The propagation of leading-edge singularity into the first-order perturbations is examined and discussed. Good agreement is found between the present solution and experimental data.

Approximate Solutions for Symmetrically Loaded Thick-Walled Cylinders

1947 ◽  
Vol 14 (4) ◽  
pp. A301-A311
Author(s):  
C. W. MacGregor ◽  
L. F. Coffin
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Approximate Solutions ◽  
Fourier Integral ◽  
Integral Methods ◽  
Pressure Distributions ◽  
Internal Strains ◽  
Walled Cylinder ◽  
Simple Approximate Solution ◽  
Good Agreement

Abstract Based upon an extension of the theory of a bar on an elastic foundation, a simple approximate solution is given in closed form for the analysis of the stresses and strains in a thick-walled cylinder loaded either internally or externally by an axially symmetrical system of forces. The analysis avoids the tedious computation of stresses inherent in exact solutions of this problem by the Fourier series or Fourier integral methods and is in a form which can easily be used by designers. The approximate solution for both semi-infinite pressure distributions and shorter bands of internal pressure are compared with the mathematically exact solutions and with experiment. Good agreement is found in all cases for external strains, while for internal strains the agreement is good except very close to the discontinuity in pressure. Since it is doubtful in practice that an abrupt discontinuity in pressure is often realized in such cases, the approximate solution may also be useful near this discontinuity. More important, however, is the fact that the effective stresses (based upon the distortion-energy theory of yielding), as determined both by the exact and approximate solutions, are in close agreement.

THE EFFECT OF SURFACES ON THE ORIENTATIONAL PROPERTIES AND PHASE TRANSITIONS PECULIARITIES OF A NONPOLAR SMECTOGEN

2010 ◽  
Vol 24 (22) ◽  
pp. 4305-4323 ◽  
Author(s):  
SEVTAP YILDIZ ◽  
ESRA ÖZKAN ZAYIM ◽  
ÖNDER PEKCAN ◽  
HALUK ÖZBEK
Keyword(s):  
Thin Films ◽  
Compression Modulus ◽  
Transmission Method ◽  
Polarizing Microscopy ◽  
First Order ◽  
Smectic A ◽  
Phase Transition Temperatures ◽  
Correction To Scaling ◽  
First Order Correction ◽  
Good Agreement

The effect of thin films on the orientational and optical properties of nonpolar monolayer smectogen 4-butoxyphenyl-4′-decyloxybenzoate [Formula: see text] liquid crystal has been studied by polarizing microscopy and high-resolution photon transmission method. The uniform planar textures of [Formula: see text] on the surfaces coated with WO3, VO2, and WO3– VO2mixture thin films have been obtained. No significant shifts in the phase transition temperatures to lower values under the influence of the surfaces have been observed. We have also presented the new experimental data on the critical behavior of the layer compression modulus B near the nematic–smectic A transition. It was observed that the data in the vicinity of the transition can be described by a power law expression after the introduction of a first-order correction-to-scaling term within the limit of experimental error. The resulting critical exponent was found to be 0.34∓0.01 which is good agreement with the previously reported values for other investigated compounds in literature.

scholarly journals NEWMAN–PENROSE FORMALISM FOR GRAVITATIONAL SHOCK WAVES

1996 ◽  
Vol 11 (12) ◽  
pp. 1023-1030 ◽  
Author(s):  
KOICHI HAYASHI ◽  
TOSHIHARU SAMURA
Keyword(s):  
Shock Waves ◽  
Exact Solutions ◽  
Particle Physics ◽  
First Order ◽  
Planck Energy ◽  
Perturbation Equations

First-order perturbations for the fields with spin on the background metric of the gravitational shock waves are discussed. Applying the Newman–Penrose formalism, exact solutions of the perturbation equations are obtained. For particle physics, this would be an approach to the problem of scattering particle at Planck energy.

Computer Modeling of a Tire under Cornering Loads

1989 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
I. Gardner ◽  
M. Theves
Keyword(s):  
Finite Element Analysis ◽  
Geometric Approach ◽  
Lateral Force ◽  
Slip Angle ◽  
Element Analysis ◽  
Pressure Distributions ◽  
Slip Effects ◽  
Improved Accuracy ◽  
Nonlinear Geometric ◽  
Good Agreement

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.

Analysis of the Contact Deformation of a Radial Tire with Camber Angle

1995 ◽  
Vol 23 (1) ◽  
pp. 26-51 ◽  
Author(s):  
S. Kagami ◽  
T. Akasaka ◽  
H. Shiobara ◽  
A. Hasegawa
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Region ◽  
Contact Deformation ◽  
Contact Pressure Distribution ◽  
Radial Tire ◽  
Ring Model ◽  
Camber Angle ◽  
Contact Free ◽  
Good Agreement

Abstract The contact deformation of a radial tire with a camber angle, has been an important problem closely related to the cornering characteristics of radial tires. The analysis of this problem has been considered to be so difficult mathematically in describing the asymmetric deformation of a radial tire contacting with the roadway, that few papers have been published. In this paper, we present an analytical approach to this problem by using a spring bedded ring model consisting of sidewall spring systems in the radial, the lateral, and the circumferential directions and a spring bed of the tread rubber, together with a ring strip of the composite belt. Analytical solutions for each belt deformation in the contact and the contact-free regions are connected by appropriate boundary conditions at both ends. Galerkin's method is used for solving the additional deflection function defined in the contact region. This function plays an important role in determining the contact pressure distribution. Numerical calculations and experiments are conducted for a radial tire of 175SR14. Good agreement between the predicted and the measured results was obtained for two dimensional contact pressure distribution and the camber thrust characterized by the camber angle.

scholarly journals Effect of Pressure Distribution on the Energy Dissipation of Lap Joints under Equal Pre-tension Force

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 320-328
Author(s):  
Delin Sun ◽  
Minggao Zhu
Keyword(s):  
Energy Dissipation ◽  
Pressure Distribution ◽  
Theoretical Basis ◽  
Lap Joints ◽  
Power Exponent ◽  
Lap Joint ◽  
Stick Slip ◽  
Pressure Distributions ◽  
Hysteretic Characteristics ◽  
Effective Use

Abstract In this paper, the energy dissipation in a bolted lap joint is studied using a continuum microslip model. Five contact pressure distributions compliant with the power law are considered, and all of them have equal pretension forces. The effects of different pressure distributions on the interface stick-slip transitions and hysteretic characteristics are presented. The calculation formulation of the energy dissipation is introduced. The energy dissipation results are plotted on linear and log-log coordinates to investigate the effect of the pressure distribution on the energy distribution. It is shown that the energy dissipations of the lap joints are related to the minimum pressure in the overlapped area, the size of the contact area and the value of the power exponent. The work provides a theoretical basis for further effective use of the joint energy dissipation.

scholarly journals Superconformal boundaries in 4 − ϵ dimensions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Aleix Gimenez-Grau ◽  
Pedro Liendo ◽  
Philine van Vliet
Keyword(s):  
Three Dimensional ◽  
Spacetime Dimension ◽  
Perfect Agreement ◽  
Bootstrap Analysis ◽  
First Order ◽  
Free Theory ◽  
First Order Correction ◽  
Free Parameters ◽  
Superconformal Theories ◽  
Zumino Model

Abstract Boundaries in three-dimensional $$ \mathcal{N} $$ N = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits $$ \mathcal{N} $$ N = (0, 2) or $$ \mathcal{N} $$ N = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $$ \mathcal{N} $$ N = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

Sign in / Sign up

Export Citation Format

Share Document