A joint vector and scalar potential formulation for driven high frequency problems using hybrid edge and nodal finite elements

1996 ◽  
Vol 44 (1) ◽  
pp. 15-23 ◽  
Author(s):  
R. Dyczij-Edlinger ◽  
O. Biro
Keyword(s):  
Finite Elements ◽  
High Frequency ◽  
Scalar Potential ◽  
Potential Formulation

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.

Dual Approach for Electromechanical Coupling in MEMS

2009 ◽  
Author(s):  
Ve´ronique Rochus ◽  
Jean-Claude Golinval ◽  
Christophe Geuzaine
Keyword(s):  
Electromechanical Coupling ◽  
Virtual Work ◽  
Scalar Potential ◽  
Test Cases ◽  
Electrostatic Problem ◽  
Dual Approach ◽  
Virtual Work Principle ◽  
Potential Formulation ◽  
Primal And Dual ◽  
Analytic Derivation

In this paper we present an approach for the computation of coupled electromechanical problems in micro-electromechanical systems based on a vector potential formulation of the electrostatic problem. This formulation is the dual of the scalar potential approach commonly used in the literature. We present an analytic derivation of the force computed using this dual method based on the virtual work principle, and compare the primal and dual approaches on the finite element solution of simple two-dimensional test-cases.

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.

scholarly journals Scalar Potential Formulation and Inverse Problem Applied to Thin Magnetic Sheets

2008 ◽  
Vol 44 (6) ◽  
pp. 1054-1057 ◽  
Author(s):  
Y. Vuillermet ◽  
O. Chadebec ◽  
J.-L. Coulomb ◽  
L.-L. Rouve ◽  
G. Cauffet ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Scalar Potential ◽  
Potential Formulation
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