Component-Wise Method Applied to Vibration of Wing Structures

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
E. Carrera ◽  
A. Pagani ◽  
M. Petrolo
Keyword(s):  
Cross Section ◽  
Eigenvalue Problems ◽  
Free Vibration Analysis ◽  
Computationally Efficient ◽  
Commercial Code ◽  
Wing Structures ◽  
Order Of Magnitude ◽  
The Cross ◽  
3D Elasticity ◽  
Reinforced Shell

This paper proposes advanced approaches to the free vibration analysis of reinforced-shell wing structures. These approaches exploit a hierarchical, one-dimensional (1D) formulation, which leads to accurate and computationally efficient finite element (FE) models. This formulation is based on the unified formulation (UF), which has been recently proposed by the first author and his coworkers. In the study presented in this paper, UF was used to model the displacement field above the cross-section of reinforced-shell wing structures. Taylor-like (TE) and Lagrange-like (LE) polynomial expansions were adopted above the cross-section. A classical 1D FE formulation along the wing's span was used to develop numerical applications. Particular attention was given to the component-wise (CW) models obtained by means of the LE formulation. According to the CW approach, each wing's component (i.e. spar caps, panels, webs, etc.) can be modeled by means of the same 1D formulation. It was shown that Msc/Patran® can be used as pre- and postprocessor for the CW models, whereas Msc/Nastran® DMAP alters can be used to solve the eigenvalue problems. A number of typical aeronautical structures were analyzed and CW results were compared to classical beam theories (Euler-Bernoulli and Timoshenko), refined models (TE) and classical solid/shell FE solutions from the commercial code Msc/Nastran®. The results highlight the enhanced capabilities of the proposed formulation. In fact, the CW approach is clearly the natural tool to analyze wing structures, since it leads to results that can only be obtained through 3D elasticity (solid) elements whose computational costs are at least one-order of magnitude higher than CW models.

Static and Dynamic Analysis of Aircraft Structures by Component-Wise Approach

2013 ◽  
Author(s):  
E. Carrera ◽  
A. Pagani ◽  
M. Petrolo
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Aircraft Structures ◽  
Static And Dynamic Analysis ◽  
Computational Costs ◽  
Commercial Code ◽  
Wing Structures ◽  
Order Of Magnitude ◽  
The Cross ◽  
Beam Theories

This paper proposes an advanced approach to the analysis of reinforced-shell aircraft structures. This approach, denoted as Component-Wise (CW), is developed by using the Carrera Unified Formulation (CUF). CUF is a hierarchical formulation allowing for the straightforward implementation of any-order one-dimensional (1D) beam theories. Lagrange-like polynomials are used to discretize the displacement field on the cross-section of each component of the structure. Depending on the geometrical and material characteristics of the component, the capabilities of the model can be enhanced and the computational costs can be kept low through smart discretization strategies. The global mathematical model of complex structures (e.g. wings or fuselages) is obtained by assembling each component model at the cross-section level. Next, a classical 1D finite element (FE) formulation is used to develop numerical applications. It is shown that MSC/PATRAN can be used as pre- and post-processor for the CW models, whereas MSC/NASTRAN DMAP alters can be used to solve both static and dynamic problems. A number of typical aeronautical structures are analyzed and CW results are compared to classical beam theories (Euler-Bernoulli and Timoshenko), refined models and classical solid/shell FE solutions from the commercial code MSC/NASTRAN. The results highlight the enhanced capabilities of the proposed formulation. In fact, the CW approach is clearly the natural tool to analyze wing structures, since it leads to results that can be only obtained through three-dimensional elasticity (solid) elements whose computational costs are at least one-order of magnitude higher than CW models.

ISOSPIN DECOMPOSITION OF pp → NNππ CROSS SECTIONS — DO WE SEE A SIGN OF Δ(1600) EXCITATION IN THE nnπ+π+ CHANNEL?

2009 ◽  
Vol 24 (02n03) ◽  
pp. 450-453
Author(s):  
◽  
T. SKORODKO ◽  
M. BASHKANOV ◽  
D. BOGOSLOWSKY ◽  
H. CALÉN ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Pion Production ◽  
Significant Contribution ◽  
Differential Cross Sections ◽  
Pp Collisions ◽  
Theoretical Predictions ◽  
Order Of Magnitude ◽  
The Cross

The two-pion production in pp-collisions has been investigated in exclusive measurements from threshold up to Tp = 1.36 GeV . Total and differential cross sections have been obtained for the channels pnπ+π0, ppπ+π-, ppπ0π0 and also nnπ+π+. For intermediate incident energies Tp > 1 GeV , i.e. in the region, which is beyond the Roper excitation but at the onset of ΔΔ excitation the total ppπ0π0 cross section falls behind theoretical predictions by as much as an order of magnitude near 1.2 GeV, whereas the nnπ+π+ cross section is a factor of five larger than predicted. A model-unconstrained isospin decompostion of the cross section points to a significant contribution of an isospin 3/2 resonance other than the Δ(1232). As a possible candidate the Δ(1600) is discussed.

New Results on Double Charmonium Production in e+e- Annihilation at $\sqrt{s} \approx 10.6~{\rm GeV}$ with the Belle Detector

2005 ◽  
Vol 20 (16) ◽  
pp. 3617-3620
Author(s):  
◽  
T. Ziegler
Keyword(s):  
Cross Section ◽  
Strong Evidence ◽  
Previous Analysis ◽  
Charmonium State ◽  
Data Set ◽  
Charmonium Production ◽  
Belle Detector ◽  
Theoretical Predictions ◽  
Order Of Magnitude ◽  
The Cross

Extending a previous analysis1 the double charmonium production [Formula: see text] and [Formula: see text] has been investigated with a data set of 155 fb-1 with the Belle detector. Theoretical predictions for the cross section are one order of magnitude lower than the measured value and this discrepancy is still not understood. In a very recent update with a dataset of 285 fb-1 strong evidence for a new charmonium state at a mass of 3.940 GeV was found.

scholarly journals Sudakov Form Factors in Leptoproduction of Vector Mesons

1997 ◽  
Vol 12 (35) ◽  
pp. 2717-2723
Author(s):  
I. M. Dremin
Keyword(s):  
Cross Section ◽  
Form Factors ◽  
Model Parameters ◽  
Vector Mesons ◽  
Large Size ◽  
Color Dipole ◽  
Order Of Magnitude ◽  
The Cross ◽  
Qcd Inspired Model

It is shown that Sudakov form factors for a color dipole in a QCD-inspired model of leptoproduction of vector mesons reduce the value of the cross-section of the process by an order of magnitude. They suppress the large size quark–antiquark pairs and unequal sharing of energy among the components of the dipole. Some freedom in the choice of the model parameters is also discussed.

Vibration Analysis of Composite Beams With End Effects via the Formal Asymptotic Method

2009 ◽  
Author(s):  
Jun-Sik Kim ◽  
K. W. Wang
Keyword(s):  
Finite Element ◽  
Asymptotic Expansion ◽  
Cross Section ◽  
Asymptotic Method ◽  
Vibration Analysis ◽  
Eigenvalue Problems ◽  
Free Vibration Analysis ◽  
Expansion Method ◽  
Composite Beams ◽  
Asymptotic Expansion Method

Free vibration analysis of composite beams is carried out by using a finite element-based formal asymptotic expansion method. The formulation begins with three-dimensional equilibrium equations in which cross-sectional coordinates are scaled by the characteristic length of the beam. Microscopic 2D and macroscopic 1D equations obtained via the asymptotic expansion method are discretized by applying a conventional finite element method. Boundary conditions associated with macroscopic 1D equations are also considered in order to investigate the end effect. We then describe how to form and solve the eigenvalue problems derived from the asymptotic method beyond the classical approximation. The results obtained are compared to those of 3D FEM and those available in literature for composite beams with solid cross-section and thin-walled cross-section.

UPS of a-Si:H: What is the energy of the Er 4f states?

2000 ◽  
Vol 609 ◽  
Author(s):  
Leandro R. Tessler ◽  
Cínthia Piamonteze ◽  
Ana Carola Iniguez ◽  
Abner de Siervo ◽  
Richard Landers ◽  
...  
Keyword(s):  
Binding Energy ◽  
Excitation Energy ◽  
Cross Section ◽  
Energy Gap ◽  
Valence States ◽  
Erbium Doped ◽  
Order Of Magnitude ◽  
Synchrotron Light ◽  
The Cross ◽  
Er Doped

ABSTRACTOne very important problem concerning erbium-doped silicon is the electronic structure of the Er3+ impurities. In particular, it is still not clear if the 4f levels can be treated as frozen core levels or their overlap with s and p states of their neighbors must be considered explicitly. For crystalline Si, the 4f levels have been supposed to be anywhere between 20 eV below the valence band and within the energy gap. In this paper we report on the first ultraviolet photoemission spectroscopy (UPS) measurements on Er-doped a-Si:H. Samples of a-Si:H<Er> with different Er contents (up to 1 at. % Er) were prepared by co-sputtering from a Si target partially covered with metallic Er platelets. In order to enhance the Er states relative to the Si and H states, the excitation energy was tuned between 40 and 140 eV with a synchrotron light source. At 140 eV excitation energy the cross-section of the Er 4f and 5p states is more than an order of magnitude higher than the cross section of the Si 3s or 3p states. As the Er concentration increases, a shoulder and then a peak appears at 10.0±0.5 eV binding energy. The intensity and width of this peak is well correlated with the Er concentration, and with the Er 5p and 5p½ levels at 26 and 32 eV binding energy, respectively. We attribute the peak at 10.0±0.5 eV binding energy to the Er 4f level. These are the only occupied states that can be related to the presence of Er, indicating that these levels are not valence states and consequently can be treated as frozen core levels.

Monte-Carlo simulation of hydrogen-atom recombination

1973 ◽  
Vol 333 (1595) ◽  
pp. 419-434 ◽  
Keyword(s):  
Hydrogen Atom ◽  
Cross Section ◽  
Rate Constant ◽  
Relative Velocity ◽  
Classical Trajectory ◽  
Hydrogen Atoms ◽  
Order Of Magnitude ◽  
The Cross ◽  
The Right ◽  
Right Order

Classical trajectory calculations have been used to calculate the cross-section (and hence the rate constant) for the recombination of hydrogen atoms on a third hydrogen atom, in the temperature range 500–6000 K. The model involves the stabilization of a quasi-bound molecule in an encounter with the third atom. The results indicate that the cross-section for direct stabilization is small and insensitive to the relative velocity, whereas the cross-section for exchange stabilization is large at low velocities and decreases rapidly as the relative velocity is increased. The calculated rate constant, although of the right order of magnitude at 500 K, does not exhibit the anomalous features previously observed experimentally at higher temperatures.

scholarly journals Δ-Isobar contribution to the pion production in the reaction pp → {pp}sπ0

2019 ◽  
Vol 204 ◽  
pp. 01015
Author(s):  
Yuriy Uzikov
Keyword(s):  
Excitation Energy ◽  
Cross Section ◽  
Pion Production ◽  
Forward Direction ◽  
Dominant Contribution ◽  
Final State ◽  
Proton Pair ◽  
Order Of Magnitude ◽  
The Cross ◽  
The One

ANKE@COSY data on the cross section of the reaction pp → {pp}sπ0, where {pp}s is the proton pair in the 1S 0 state at small excitation energy Epp = 0 – 3 MeV, obtained at beam energies 0.5 - 2.0 GeV are analyzed within the one-pion exchange model. The model involves the subprocess π0 p → π0 p and accounts for the final state pp-interaction. A broad maximum observed in the cross section of the reaction pp → {pp}sπ0 at 0.5 - 1.4 GeV in the forward direction is explained by this model as a dominant contribution of the isospin $\cfrac{3}{2}$ in the π0 p-scattering. The second bump in data at 2 GeV is underpredicted within this model by one order of magnitude. An explicit excitation of the Δ(1232)-isobar using the box-diagram is also considered in the region of the first maximum.

scholarly journals A Minimal GBT Model for Distortional-Twist Elastic Analysis of Box-Girder Bridges

2021 ◽  
Vol 11 (6) ◽  
pp. 2501
Author(s):  
Francesca Pancella ◽  
Angelo Luongo
Keyword(s):  
Cross Section ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Form Solution ◽  
Box Girder Bridges ◽  
Torsional Mode ◽  
Box Girder ◽  
Girder Bridges ◽  
Order Of Magnitude ◽  
The Cross

A simple and efficient method is proposed for the analysis of twist of rectangular box-girder bridges, which undergo distortion of the cross section. The model is developed in the framework of the Generalized Beam Theory and oriented towards semi-analytical solutions. Accordingly, only two modes are accounted for: (i) the torsional mode, in which the box-girder behaves as a Vlasov beam under nonuniform torsion, and, (ii) a distortional mode, in which the cross section behaves as a planar frame experiencing skew-symmetric displacements. By following a variational approach, two coupled, fourth-order differential equations in the modulating amplitudes are obtained. The order of magnitude of the different terms is analyzed, and further reduced models are proposed. A sample system, taken from the literature, is considered, for which generalized displacement and stress fields are evaluated. Both a Fourier solution for the coupled problem and a closed-form solution for the uncoupled problem are carried out, and the results are compared. Finally, the model is validated against finite element analyses.

THE ELASTIC SCATTERING OF Co60 γ-RAYS

1962 ◽  
Vol 40 (5) ◽  
pp. 622-653 ◽  
Author(s):  
K. G. Standing ◽  
J. V. Jovanovich
Keyword(s):  
Form Factor ◽  
Elastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Thomson Scattering ◽  
Special Method ◽  
Knock Out ◽  
Order Of Magnitude ◽  
Γ Rays ◽  
The Cross

Cross sections have been measured for 90° elastic scattering of Co60 γ-rays (1.33 and 1.17 Mev) from aluminum, copper, and tin. They agree with theoretical predictions for Rayleigh and nuclear Thomson scattering. A continuum between the Compton and the elastically scattered γ-rays interfered with the measurements for heavier elements, since it increased rapidly with Z.The continuum was investigated by observing the γ-rays scattered through 60° by thin gold foils. It was found to be produced directly by the γ-rays themselves, not by the electrons they knock out of the target atoms. The experimental cross section was compared with that expected for incoherent scattering from the bound atomic electrons. It agrees within a factor of 2 with the cross section given by the form factor approximation, although it is more than an order of magnitude larger than a modification of the form factor, which is based on comparison with elastic scattering calculations.The spectrum of elastically scattered γ-rays from lead was examined by a special method in order to reduce the contribution of the inelastic continuum; two photomultipliers faced a single scintillator and pulses from one photomultiplier were counted only when they corresponded to the largest pulses from the other. The cross section between 12° and 150° was found to be much lower than that of most previous measurements. It agrees with the calculated cross section for Rayleigh and nuclear Thomson scattering within the possible errors in the calculations. Therefore the measurements yield no evidence for the presence of Delbrück scattering, the upper limit on its intensity now being set primarily by the uncertainties in the theory.

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