Influence of Cross-Section Distortion on the Bending Vibration of Thin-Walled Beams of H Section

1964 ◽  
Vol 6 (3) ◽  
pp. 211-218 ◽  
Author(s):  
A. D. S. Barr ◽  
T. Duthie
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Reasonable Agreement ◽  
Experimental Results ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Bending Vibration ◽  
Cross Sectional ◽  
Thin Walled ◽  
The Cross

Approximate differential equations describing the bending vibration of beams of thin-walled H section, in which the distortion of the cross-section in its own plane is taken into account, are derived from Hamilton's principle using an assumed form for the cross-section deformation. Only the simplest of the cross-sectional deformation configurations which will couple with ordinary bending is considered. The variation with wavelength of the two spectra of frequencies which result from this coupling of the bending and cross-sectional motions is shown for several section geometries. Theoretical curves show reasonable agreement with experimental results from free beams.

Collapse of Thin-Walled Elliptical Tubes for High Values of Major-to-Minor Axis Ratio

1993 ◽  
Vol 115 (4A) ◽  
pp. 432-440 ◽  
Author(s):  
C. Ribreau ◽  
S. Naili ◽  
M. Bonis ◽  
A. Langlet
Keyword(s):  
Contact Pressure ◽  
Cross Section ◽  
External Pressure ◽  
Straight Line Segment ◽  
Minor Axis ◽  
Cross Sectional ◽  
Axis Ratio ◽  
Straight Line ◽  
Thin Walled ◽  
The Cross

The topic of this study concerns principally representative models of some elliptical thin-walled anatomic vessels and polymeric tubes under uniform negative transmural pressure p (internal pressure minus external pressure). The ellipse’s ellipticity ko, defined as the major-to-minor axis ratio, varies from 1 up to 10. As p decreases from zero, at first the cross-section becomes somewhat oval, then the opposite sides touch in one point at the first-contact pressure pc. If p is lowered beneath pc, the curvature of the cross-section at the point of contact decreases until it becomes zero at the osculation pressure or the first line-contact pressure p1. For p<p1, the contact occurs along a straight-line segment, the length of which increases as p decreases. The pressures pc and p1 are determined numerically for various values of the wall thickness of the tubes. The nature of contact is especially described. The solution of the related nonlinear, two-boundary-values problem is compared with previous experimental results which give the luminal cross-sectional area (from two tubes), and the area of the mid-cross-section (from a third tube).

Cross-Section Deformation Effects in the Vibration of Thin-Walled Beams of Arc Section

1965 ◽  
Vol 7 (3) ◽  
pp. 292-299 ◽  
Author(s):  
S. A. Hasan ◽  
A. D. S. Barr
Keyword(s):  
Cross Section ◽  
Reasonable Agreement ◽  
Natural Frequencies ◽  
Characteristic Functions ◽  
Curved Beam ◽  
Cross Sectional ◽  
Frequency Spectra ◽  
Circular Arc ◽  
Beam Geometry ◽  
Thin Walled

Differential equations describing the coupling of ordinary bending motion with cross-sectional distortion are obtained for thin-walled beams of circular-arc cross-section using Hamilton's principle. In deriving the theory the cross-sectional deformation is assumed to take the form of the characteristic functions of a curved beam of the shape of the section. The variation with wavelength of the frequency spectra which result from the coupling is obtained. Experimental results showing the effects of the variation of the parameters of the beam geometry on the natural frequencies are in reasonable agreement with the theory.

Experimental Study on Residual Cross-Sectional Flattening of Thin-Walled Pipes Under Pure Plastic Bending

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Ziqian Zhang
Keyword(s):  
Cross Section ◽  
Wall Thickness ◽  
Residual Deformation ◽  
Outer Diameter ◽  
Cross Sectional ◽  
Plastic Bending ◽  
Thin Walled Pipe ◽  
Bending Radius ◽  
Thin Walled ◽  
The Cross

Abstract Cross-sectional ovalization (ovalization) usually occurs when thin-walled pipe is subjected to large plastic bending. This paper is concerned with residual deformation of thin-walled pipe's cross section in a radial direction when external bending moment is removed. In order to clarify the fundamental ovalization characteristics, find out what factors influence the residual flattening (value of ovalization), the ovalization behavior is investigated experimentally. The experiments are carried out on 21 stainless steel specimens with different geometric parameters under different bending radii by means of a four-point pure bending device. The residual cross-sectional flattenings are monitored continuously by scanning the cross section periodically along the circumferential direction. From the experimental results, it is observed that the cross-sectional shape of the thin-walled pipe is not perfect standard ellipse, and the appearance of the maximum residual flattening is usually found in the direction normal to the neutral surface. It is also revealed the relationships between the residual flattening and the bending radius, the wall thickness, and the pipe outer diameter, i.e., the residual flattening increases as the bending radius and the wall thickness reduce, but it increases as the outer diameter increases. These results are expected to find their potential application in thin-walled pipe bending operation.

scholarly journals Experimental and Numerical Study on the Lateral-Torsional Buckling of Steel C-Beams with Variable Cross-Section

Metals ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 941
Author(s):  
Ida Mascolo ◽  
Mariano Modano ◽  
Antimo Fiorillo ◽  
Marcello Fulgione ◽  
Vittorio Pasquino ◽  
...  
Keyword(s):  
Cross Section ◽  
Numerical Study ◽  
Numerical Approach ◽  
Computational Effort ◽  
Experimental Results ◽  
Variable Cross ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Cross Sectional ◽  
Thin Walled

Metallic thin-walled beams with continuously varying cross-sections loaded in compression are particularly sensitive to instability problems due to lateral-torsional buckling. Such a phenomenon depends on several parameters, including the cross-sectional properties along the entire length, material properties, load distribution, support, and restraint conditions. Due to the difficulty of obtaining analytic solutions for the problem under consideration, the present study takes a numerical approach based on a variational formulation of the lateral-torsional buckling problem of tapered C-beams. Numerical simulations are compared with experimental results on the buckling of a physical model of at thin-walled beam with uniformly varying cross-section, with the aim of assessing the accuracy of the proposed approach. The good agreement between numerical and experimental results and the reduced computational effort highlight that the proposed variational approach is a powerful tool, provided that the geometry of the structure and the boundary conditions are accurately modeled.

Converting Helicopter Rotor Blades From D-Spar to C-Spar: Allowing for Aeromorphing Structures

2014 ◽  
Author(s):  
Nathan S. Hosking ◽  
Zahra Sotoudeh
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Leading Edge ◽  
Honeycomb Structure ◽  
Rotor Blades ◽  
Cross Sectional ◽  
Helicopter Blades ◽  
Helicopter Rotor Blades ◽  
Thin Walled ◽  
The Cross

Modern helicopter blades are designed as thin-walled hollow structures in form of either C-spar or D-spar cross-sections. With the advent of new materials hollow designs have been implemented to reduce the overall weight of the structure. A D-spar is a rotor blade cross-section that is hollow in nature with a single vertical spar used to carry a large portion of the stresses otherwise carried by the skin [1]. The vertical spar is normally located between the leading edge and half of the chord length. The remaining volume aft of the vertical spar can either be hollow or filled with a honeycomb structure. The honeycomb structure increases the cross-sectional stiffness. Figure 1. shows an example of a common D-spar with a honeycomb structure aft of the vertical spar [2]. Due to new manufacturing methods the D-spar has now become common place in helicopter design [3]. A C-spar cross-section is very similar to the D-spar cross-section in design and construction. The C-spar cross-section does not have the honeycomb structure and the spar. The structural load is offset by more lamina layers towards the leading edge of the cross-section [4,5]. The thin-walled structure is comprised of many layers of composite materials such as fiberglass or carbon fibers. There has been extensive research into D-spar cross-section while there is a lack of studies for C-spar cross-sections [1,3,4].

Explicit Solutions for the Stability of No-Tension Beam-Columns

2003 ◽  
Vol 03 (02) ◽  
pp. 195-213 ◽  
Author(s):  
A. de Falco ◽  
M. Lucchesi
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Axial Load ◽  
Explicit Solutions ◽  
Cross Sectional ◽  
Beam Columns ◽  
The Cross ◽  
The Stability ◽  
No Tension Material ◽  
Explicit Relation

This work concerns the stability of rectangular cross-sectional piles made of a no-tension material and subjected to an axial load acting at the extremities within the middle third of the cross section. The resulting differential equations are solved, and an explicit relation between the load and a suitable deformability parameter obtained.

Automated Diagonal Slice and View Solution for 3D Device Structure Analysis

2018 ◽  
Author(s):  
Sang Hoon Lee ◽  
Jeff Blackwood ◽  
Stacey Stone ◽  
Michael Schmidt ◽  
Mark Williamson ◽  
...  
Keyword(s):  
Cross Section ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Image Data ◽  
Planar Surface ◽  
Device Structure ◽  
Cross Sectional ◽  
Device Structures ◽  
The Cross ◽  
Planar Analysis

Abstract The cross-sectional and planar analysis of current generation 3D device structures can be analyzed using a single Focused Ion Beam (FIB) mill. This is achieved using a diagonal milling technique that exposes a multilayer planar surface as well as the cross-section. this provides image data allowing for an efficient method to monitor the fabrication process and find device design errors. This process saves tremendous sample-to-data time, decreasing it from days to hours while still providing precise defect and structure data.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

The influence of the nuclear and atomic form factors on the muon bremsstrahlung cross section

1968 ◽  
Vol 46 (10) ◽  
pp. S377-S380 ◽  
Author(s):  
A. A. Petrukhin ◽  
V. V. Shestakov
Keyword(s):  
Form Factor ◽  
Cross Section ◽  
Born Approximation ◽  
Form Factors ◽  
Experimental Results ◽  
Simple Analytical Expression ◽  
Nuclear Form Factor ◽  
The Cross ◽  
Atomic Electrons ◽  
Bremsstrahlung Process

The cross section for the muon bremsstrahlung process is calculated as a function of the nuclear form factor in the Born approximation following the Bethe and Heitler theory. The influence of the nuclear form factor is greater than that taken by Christy and Kusaka. The simple analytical expression for the effect of the screening of the atomic electrons is found. The influence of a decrease in the cross section upon the interpretation of some experimental results is estimated.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

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