Higher-order ferromagnetic resonances in out-of-plane saturated Co/Au magnetic multilayers

2020 ◽  
Vol 102 (9) ◽  
Author(s):  
L. Fallarino ◽  
S. Stienen ◽  
R. A. Gallardo ◽  
J. A. Arregi ◽  
V. Uhlíř ◽  
...  
Keyword(s):  
Magnetic Multilayers ◽  
Higher Order ◽  
Out Of Plane

X-ray Probes of Magnetic Multilayer Structure

2000 ◽  
Vol 615 ◽  
Author(s):  
B.K. Tanner ◽  
T.P.A. Hase ◽  
B.D. Fulthorpe ◽  
J. Clarke ◽  
G.M. Luo ◽  
...  
Keyword(s):  
Local Environment ◽  
Grazing Incidence ◽  
Magnetic Multilayers ◽  
Anomalous Scattering ◽  
Magnetic Multilayer ◽  
Compositional Gradient ◽  
X Ray ◽  
Buried Interfaces ◽  
Out Of Plane ◽  
Roughness Amplitude

ABSTRACTWe discuss the application of x-ray scattering and fluorescence to the problem of unravelling the relationship between the structural and magnetic properties of magnetic multilayers. Particular attention is paid to the use of grazing incidence diffuse scatter to determine the compositional gradient, out-of-plane roughness amplitude, in-plane correlation length and fractal parameter of buried interfaces. Anomalous scattering provides information on the local environment of specific atoms and grazing incidence fluorescence is a depth -sensitive probe of chemical composition. We present examples indicating the sensitivity limits and the reproducibility of the techniques, all from multiple layer structures of magnetic metals.

scholarly journals Influence of in-Plane Deformation in Higher Order Beam Theories

2018 ◽  
Vol 68 (3) ◽  
pp. 77-94 ◽  
Author(s):  
Evangelos Sapountzakis ◽  
Amalia Argyridi
Keyword(s):  
Degrees Of Freedom ◽  
Plane Deformation ◽  
Beam Theory ◽  
Higher Order ◽  
Essential Difference ◽  
Numerical Example ◽  
Out Of Plane ◽  
Geometric Constants ◽  
Beam Theories

AbstractComparing Euler-Bernoulli or Tismoshenko beam theory to higher order beam theories, an essential difference can be depicted: the additional degrees of freedom accounting for out-of plane (warping) and in-plane (distortional) phenomena leading to the appearance of respective higher order geometric constants. In this paper, after briefly overviewing literature of the major beam theories taking account warping and distortional deformation, the influence of distortion in the response of beams evaluated by higher order beam theories is examined via a numerical example of buckling drawn from the literature.

A Survey With Numerical Assessment of Classical and Refined Theories for the Analysis of Sandwich Plates

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
E. Carrera ◽  
S. Brischetto
Keyword(s):  
Higher Order ◽  
Benchmark Problems ◽  
Geometrical Parameters ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Numerical Assessment ◽  
Shell Analysis ◽  
Out Of Plane ◽  
The Face ◽  
Free Vibration Response

A large variety of plate theories are described and assessed in the present work to evaluate the bending and vibration of sandwich structures. A brief survey of available works is first given. Such a survey includes significant review papers and latest developments on sandwich structure modelings. The kinematics of classical, higher order, zigzag, layerwise, and mixed theories is described. An exhaustive numerical assessment of the whole theories is provided in the case of closed form solutions of simply supported panels made of orthotropic layers. Reference is made to the unified formulation that has recently been introduced by the first author for a plate/shell analysis. Attention has been given to displacements, stresses (both in-plane and out-of-plane components), and the free vibration response. Only simply supported orthotropic panels loaded by a transverse distribution of bisinusoidal pressure have been analyzed. Five benchmark problems are treated. The accuracy of the plate theories is established with respect to the length-to-thickness-ratio (LTR) geometrical parameters and to the face-to-core-stiffness-ratio (FCSR) mechanical parameters. Two main sources of error are outlined, which are related to LTR and FCSR, respectively. It has been concluded that higher order theories (HOTs) can be conveniently used to reduce the error due to LTR in thick plate cases. But HOTs are not effective in increasing the accuracy of the classical theory analysis whenever the error is caused by increasing FCSR values; layerwise analysis becomes mandatory in this case.

Exact Matching Condition at a Joint of Thin-Walled Box Beams Under Out-of-Plane Bending and Torsion

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Soomin Choi ◽  
Gang-Won Jang ◽  
Yoon Young Kim
Keyword(s):  
Beam Theory ◽  
Matching Condition ◽  
Higher Order ◽  
Transformation Matrix ◽  
Exact Matching ◽  
Box Beam ◽  
Out Of Plane ◽  
Box Beams ◽  
Thin Walled ◽  
Plane Bending

To take into account the flexibility resulting from sectional deformations of a thin-walled box beam, higher-order beam theories considering warping and distortional degrees of freedom (DOF) in addition to the Timoshenko kinematic degrees have been developed. The objective of this study is to derive the exact matching condition consistent with a 5-DOF higher-order beam theory at a joint of thin-walled box beams under out-of-plane bending and torsion. Here we use bending deflection, bending/shear rotation, torsional rotation, warping, and distortion as the kinematic variables. Because the theory involves warping and distortion that do not produce any force/moment resultant, the joint matching condition cannot be obtained just by using the typical three equilibrium conditions. This difficulty poses considerable challenges because all elements of the 5×5 transformation matrix relating the field variables of one beam to those in another beam should be determined. The main contributions of the investigation are to propose additional necessary conditions to determine the matrix and to derive it exactly. The validity of the derived joint matching transformation matrix is demonstrated by showing good agreement between the shell finite element results and those obtained by the present box beam analysis in various angle box beams.

Application of Higher-Order Compact Finite Difference Schemes to Out of Plane Vorticity Measurements

2003 ◽  
Author(s):  
Ali Etebari ◽  
Pavlos P. Vlachos
Keyword(s):  
Finite Difference ◽  
Flow Field ◽  
Random Error ◽  
Error Propagation ◽  
Higher Order ◽  
Finite Difference Schemes ◽  
Bias Error ◽  
Compact Schemes ◽  
Velocity Measurements ◽  
Out Of Plane

The accuracy of out-of-plane vorticity from in-plane experimental velocity measurements is investigated with particular application to Digital Particle Image Velocimetry (DPIV). Higher-order compact finite difference schemes are proposed as alternatives for the vorticity estimation. Simulations of known flow fields are used to quantify errors associated with the different methods of estimation. The effects of spatial sampling resolution with respect to the range of flow scales on the bias errors of the method accuracies are explored. In addition, estimation of the velocity measurement random error propagation into the vorticity measurement is presented. The higher-order compact schemes deliver improved accuracy compared with previously used methods, even when that domain is spatially undersampled or in the presence of strong velocity gradients. The compact schemes demonstrated less than 0.3% bias error throughout the core of the vortex, resolving flow structures as small as the Nyquist sampling frequency of the system, while the error in the conventional methods increased as the spatial sampling and the range of wave numbers present in the flow field was reduced. The bias error is an irrecoverable loss due to the truncation error of the method, and thus poses significant limitations to the system, whereas the random error propagation can be reduced for the higher-order schemes by applying a simple Gaussian smoothing to the flow field. Thus, the reduction in bias error is of greater importance to the accuracy of the system, particularly as modern global flow measurement technologies achieve higher spatial and temporal resolutions, as well as higher accuracies in velocity measurements. Overall, the compact schemes provide an improved approach for vorticity evaluation compared to conventional algorithms.

Analysis of Three-Dimensional Piezo-Electric Beams via a Unified Formulation

2013 ◽  
Vol 745 ◽  
pp. 101-118 ◽  
Author(s):  
Gaetano Giunta ◽  
Yao Koutsawa ◽  
Salim Belouettar
Keyword(s):  
Finite Elements ◽  
Cross Section ◽  
Electrical Potential ◽  
Three Dimensional ◽  
Higher Order ◽  
Computational Costs ◽  
Generic Term ◽  
Mass Matrices ◽  
Out Of Plane ◽  
Piezo Electric

A Unified Formulation for deriving several higher-order theories and related finite elements for beams is presented within this paper.Three-dimensional structures with piezo-electric layers are considered.Static and free vibration analyses are carried out.Models' main unknowns are the displacements and the electric potential.They are approximated above the beam cross-section via Lagrange's polynomials in a layer-wise sense.Finite elements stiffness and mass matrices are derived in a nucleal form using d'Alembert's Principle.This nucleal form is representative of the generic term in the approximating expansion of the displacements and electric potential over the cross-section.It is, therefore, invariant versus the theory expansion order and the element nodes' number.In such a manner, higher-order displacements-based theories that account for non-classical effectssuch as transverse shear deformations and cross-section in- and out-of-plane warping are straightforwardly formulated.Results are given in terms of displacements, electrical potential and stresses.Comparison with three-dimensional finite elements models are provided, showing thataccurate results can be obtained with reduced computational costs.

On higher order terms and out-of-plane singular mode

2011 ◽  
Vol 43 (6) ◽  
pp. 332-341 ◽  
Author(s):  
F. Berto ◽  
P. Lazzarin ◽  
A. Kotousov
Keyword(s):  
Higher Order ◽  
Higher Order Terms ◽  
Out Of Plane
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