Resonance finite element

One point, which is often disregarded when nsing AFM, is that accurate cantilever stiffness calibration is essential, in order to calculate accurate pull-off forces from measured displacements. Althongh many researchers take values quoted by cantilever manufacturers, which are usually calculated from approximate dimensions, more accurate methods include direct measurement with known springs [31], thermal resonant frequency curve fitting [32], temporary addition of known masses [33], and finite element analysis [34]. 

A. Scrinzi, N. Elander, A finite element implementation of exterior complex scaling for the accurate determination of resonance energies, 98 (5) (1993) 3866. 

The acoustic response of resonant viscoelastic fluid structures to a pressure wave may be simulated by a four-dimensional calculation, three dimensions in space and one in time. The Lagrangian, primitive finite element and Eulerian finite difference schemes form the basis for two models presented in this paper which are able to simulate a wide range of fluid structures containing inclusions of arbitrary spacing, shape and composition. 

Hagslatt, H., Jonsson, B., Nyden, M., and Soderman, O. Predictions of pulsed field gradient NMR echo-decays for molecules diffusing in various restrictive geometries. Simulations of diffusion propagators based on a finite element method, /. Magn. Reson., 161,138, 2003. 

The lowest level of abstraction, here called the geometry level, is the closest to physical reality, in which the physics is described by partial differential equations. This level is the domain of finite-element, boundary-element or related methods (e.g., [7-9]). Due to their high accuracy, these methods are well suited for calculating, for example, the distribution of stresses, distortions and natural resonant frequencies of MEMS structures. But they also entail considerable computational effort. Thus, these methods are used to solve detailed problems only when needed, whereas simulations of complete sensor systems and, in particular, transient analyses are carried out using methods at higher levels of abstraction. 

Finite element three-body studies of bound and resonant states in atoms and molecules. 

The development of a full angular momentum, three dimensional, smooth exterior complex dilated, finite element method for computing bound and resonant states in a wide class of quantum systems is described. Applications to the antiprotonic helium system, doubly excited states in the helium atom and to a model of a molecular van der Waals complex are discussed. 2001 by Academic Press. 

Finite Element Three-Body Studies of Bound and Resonant States... 

The role of resonances was in some sense verified by a study prototype three-body scattering reaction F + H2 — HF(v, J) + H problem[8]. Recent experimental as well as theoretical results indicate that resonances play a very important role in this reaction [9]. We have previously developed methods by which scattering cross sections can be computed from the properties associated with resonant states[19, 28, 29, 30]. Problems like the fluorine hydrogen collision encourage us to come back and combine these methods with our current 3-D finite element method in order to study the influence of intermediate resonant states FH2 (v, J, K) in... 

We present a new effective numerical method to compute resonances of simple but non-integrable quantum systems, based on a combination of complex coordinate rotations with the finite element and the discrete variable method. By using model potentials we were able to compute atomic data for alkali systems. As an example we show some results for the radial Stark and the Stark effect and compare our values with recent published ones. 

Table 3 Second and third resonance states, n = 2 m = 0, for the hydrogen Stark effect in dependence of the electric field strength. Comparison of our results obtained by discrete variable technique and finite element method with the results of C. Cerjan (1978)...

In addition to the interaction between the electromagnetic wave and the materials, the heating effect of applicators is also an important issue in microwave sintering. This is simply because applicators are necessary to build the cavity resonators. Various methods, such as finite-difference time domain (FDTD) [61-63], finite element method (FEM) [64], transmission line matrix (TLM) [65, 66], method of moments (MOM), have been used for such purposes. 

Fig. 1.3 Various cases of a plane wave incident upon infinite as well as finite arrays at 45° from normal in the H plane. Element length 21=1.5 cm, load impedance Zl = 0 and frequencies as indicated, (a) Element currents for an infinite x infinite array at 10 GHz as obtained by the PMM program (close to resonance), (b) Element currents for a finite x infinite array of 25 columns at 10 GHz (close to resonance), (c) Element currents for a finite x infinite array of 25 columns at 7.8 GHz ( 25% below resonance).

A few solutions exist for 3-D PZT bodies. Most well-known solutions for finite PZT plates were obtained from approximated two-dimensional (2-D) equations of extended Mindlin s solutions (Herrmann 1974). But, these solutions are not directly applicable to the analysis of AE sensors commercially available. In order to clarify the frequency response of AE sensor (function W(f) in eq. 3.5) and to optimize the design of PZT elements, resonance characteristics of PZT element were analyzed by using the finite element method (FEM) (Ohtsu Ono 1983). 

The second section deals with the analysis methods that are used in fuzzy finite element analysis. An overview of different approaches is presented first the transformation method, affine analysis, and global optimisation. The application to dynamic analysis is considered. The core of this section is the presentation of a consistent analysis approach to predict the effect of parameter uncertainties on different characteristics of dynamic behaviour of structures, resonance frequencies and dynamic response levels. A hybrid approach is developed, based on modal superposition and optimisation. 

M. Ganaba, L. C. Wellford and J. J. Lee, Finite element methods for boundary layer modeling with application to dissipative harbor resonance problem, Chapter 15 of Finite Elements in Fluid, Vol. 5 (John Wiley Sons, 1984), pp. 325 346. 

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