Special Finite Elements for High Frequency Elastodynamic Problems: First Numerical Experiments

2009 ◽  
Author(s):  
O. Laghrouche ◽  
P. Bettess ◽  
D. Le Houédec
Keyword(s):  
Finite Elements ◽  
High Frequency ◽  
Numerical Experiments

scholarly journals High Frequency Magnetoimpedance of FeNi/Cu/FeNi Sensitive Elements with Different Geometries

2009 ◽  
Vol 152-153 ◽  
pp. 373-376 ◽  
Author(s):  
Stanislav O. Volchkov ◽  
Andrey V. Svalov ◽  
G.V. Kurlyandskaya
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
External Magnetic Field ◽  
Finite Elements ◽  
Magnetic Anisotropy ◽  
Constant Magnetic Field ◽  
High Frequency ◽  
Complex Impedance ◽  
Rf Sputtering ◽  
Frequency Range

In this work magnetoimpedance (MI) behaviour was studied experimentally for Fe19Ni81(175 nm)/Cu(350 nm)/Fe19Ni81(175 nm) sensitive elements deposited by rf-sputtering. A constant magnetic field was applied in plane of the sandwiches during deposition perpendicular to the Cu-lead in order to induce a magnetic anisotropy. Sandwiches with different width (w) of FeNi parts were obtained. The complex impedance was measured as a function of the external magnetic field for a frequency range of 1 MHz to 700 MHz for MI elements with different geometries. Some of MI experimental data are comparatively analysed with finite elements numerical calculations data. The obtained results can be useful for optimization of the design of miniaturized MI detectors.

Fundamental Understanding of Wave Propagation in a Beam Using PZT Actuators and Sensors

2013 ◽  
Author(s):  
Vishnu Prasad Venugopal ◽  
Gang Wang
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Finite Elements ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Beam Structure ◽  
Frequency Wave ◽  
Coupled Equations ◽  
High Frequency Wave ◽  
Spectral Finite Element

Embedded smart actuators/sensors, such as piezoelectric types, have been used to conduct wave transmission and reception, pulse-echo, pitch-catch, and phased array functions in order to achieve in-situ nondestructive evaluation for different structures. By comparing to baseline signatures, the damage location, amount, and type can be determined. Typically, this methodology does not require analytical structural models and interrogation algorithm is carefully designed with little wave propagation knowledge of the structure. However, the wave excitation frequency, waveform, and other signal characteristics must be comprehensively considered to effectively conduct diagnosis of incipient forms of damage. Accurate prediction of high frequency wave response requires a prohibitively large number of conventional finite elements in the structural model. A new high fidelity approach is needed to capture high frequency wave propagations in a structure. In this paper, a spectral finite element method (SFEM) is proposed to characterize wave propagations in a beam structure under piezoelectric material (i.e., PZT) actuation/sensing. Mathematical models are developed to account for both Uni-morph and bi-morph configurations, in which PZT layers are modeled as either an actuator or a sensor. The Timoshenko beam theory is adopted to accommodate high frequency wave propagations, i.e., 20–200 KHz. The PZT layer is modeled as a Timoshenko beam as well. Corresponding displacement compatibility conditions are applied at interfaces. Finally, a set of fully coupled governing equations and associated boundary conditions are obtained when applying the Hamilton’s principle. These electro-mechanical coupled equations are solved in the frequency domain. Then, analytical solutions are used to formulate the spectral finite element model. Very few spectral finite elements are required to accurately capture the wave propagation in the beam because the shape functions are duplicated from exact solutions. Both symmetric and antisymmetric mode of lamb waves can be generated using bimorph or uni-morph actuation. Comprehensive simulations are conducted to determine the beam wave propagation responses. It is shown that the PZT sensor can pick up the reflected waves from beam boundaries and damages. Parametric studies are conducted as well to determine the optimal actuation frequency and sensor sensitivity. Such information helps us to fundamentally understand wave propagations in a beam structure under PZT actuation and sensing. Our SFEM predictions are validated by the results in the literature.

Application of the Complex Envelope Vectorization to a Boundary Element Formulation

2008 ◽  
Author(s):  
Oliviero Giannini ◽  
Aldo Sestieri
Keyword(s):  
Finite Elements ◽  
External Field ◽  
Boundary Element ◽  
High Frequency ◽  
Computational Cost ◽  
Field Variable ◽  
Element Formulation ◽  
Complex Envelope ◽  
Reduced Dimensions ◽  
Core Solution

The complex envelope vectorization (CEV) is a recent method that has been successfully applied to structural and internal acoustic problems. Unlike other methods proposed in the last two decades to solve high frequency problems, CEV is not an energy method, although it shares with all the other techniques a variable transformation of the field variable. By such transformation involving a Hilbert transform, CEV allows the representation of a fast oscillating signal through a set of low oscillating signals. Thanks to such transformation it is possible to solve a high frequency dynamic problem at a computational cost that is lower than that required by finite elements. In fact, by using finite elements, a high frequency problem usually implies large matrices. On the contrary the CEV formulation is obtained by solving a set of linear problems of highly reduced dimensions. Although it was proved that CEV is in general a successful procedure, it was shown that it is particularly appropriate when the modes of the system have a negligible role on the solution. Moreover, the numerical advantage of the CEV formulation is much more pronounced when full matrices are used. Thus, for the first time it is applied to a boundary element formulation (BEM). Both external and internal acoustic fields of increasing complexity are considered: the internal and external field generated by a pulsating sphere; the external field of a forced box, where the velocity field is determined by finite elements; a set of 4 plates that form an open cavity. The results are compared with those obtained by a BEM procedure (SYSNOISE), highlighting the good quality of the proposed approach. An estimate of the computational advantage is also provided. Finally it is worthwhile to point out that the reduction of the BE matrices allows for an in-core solution even for large problems.

Optimal Strategy for Limit Order Book Submissions in High Frequency Trading

2016 ◽  
Vol 6 (2) ◽  
pp. 222-234
Author(s):  
Na Song ◽  
Yue Xie ◽  
Wai-Ki Ching ◽  
Tak-Kuen Siu ◽  
Cedric Ka-Fai Yiu
Keyword(s):  
High Frequency ◽  
Numerical Experiments ◽  
Numerical Procedure ◽  
Limit Order Book ◽  
Dynamic Programming Principle ◽  
Inventory Level ◽  
Order Book ◽  
Utility Maximisation ◽  
Poisson Arrivals ◽  
Finite Time Horizon

AbstractAn optimal selection problem for bid and ask quotes subject to a stock inventory constraint is investigated, formulated as a constrained utility maximisation problem over a finite time horizon. The arrivals of buy and sell orders are governed by Poisson processes, and a diffusion approximation is employed on assuming the Poisson arrivals intensity is sufficiently large. Using the dynamic programming principle, we adopt an efficient numerical procedure to solve this constrained utility maximisation problem based on a successive approximation algorithm, and conduct numerical experiments to analyse the impacts of the inventory constraint on a dealer's terminal profit and stock inventory level. It is found that the stock inventory constraint significantly affects the terminal stock inventory level.

A review of the central role of nonlinear interactions in wind—wave evolution

1993 ◽  
Vol 342 (1666) ◽  
pp. 505-524 ◽  
Keyword(s):  
Surface Waves ◽  
Nonlinear Wave ◽  
High Frequency ◽  
Numerical Experiments ◽  
Wind Wave ◽  
Nonlinear Interactions ◽  
Wave Interactions ◽  
Detailed Review ◽  
Local Perturbations

Nonlinear wave-wave interactions play a central role in the development of wind-generated surface waves. A detailed review of com putational techniques which have been proposed for their evaluation is provided. Numerical experiments are used to determine the manner in which the nonlinear terms control spectral development with fetch, the directional spread of the spectrum and the high-frequency spectral tail. In addition, the nonlinear terms have a shape-stabilizing role, continually smoothing local perturbations in the spectrum and forcing it back to a ‘preferred’ shape.

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