Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers

The active structural component of a capacitive micromachined ultrasonic transducer (CMUT) is the top plate which vibrates under the influence of a time-varying electrostatic force thereby producing ultrasound waves of the desired frequency in the surrounding medium. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electrostatics-structure coupling aspect in the design of these devices. This paper presents an approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear. Traditionally, finite element simulations using some commercial software such as ANSYS are employed to determine the structural deflections caused by electrostatic forces. Since the structural deformation alters the electrostatic field, a coupled-field simulation is required wherein the electrostatic mesh is continuously updated to coincide with the deflection of the structure. Such simulations are extremely time consuming, in addition to being nontransparent and somewhat hard to implement. We employ the classical thin-plate theory which is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. We solve the thin-plate electrostatic-elastic equation using the Galerkin-weighted residual technique, under the assumption that the deflections are small in comparison to the thickness of the plate. The evaluation of the electrostatic force between the two plates is simplified due to the fact that the electrostatic gap is much smaller than the lateral dimensions of the device. The results obtained are compared to those found from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations.

Nucleophilic additions to 4-substituted snoutanones: getting a measure of long range electrostatic and orbital control of pi-face selectivity

Pentacyclic ketones 10a-e (snoutan-9-ones) undergo nucleophilic additions with the same facial preference as the corresponding norsnoutanones 9a-e, but with markedly reduced selectivity, revealing the involvement of electrostatic effects in the former and implying the importance of hyperconjugative orbital interactions in determining pi-face selectivity in the latter systems.

Estimation of gear tooth deflection by the finite element method

The finite element method (FEM) is used to determine for pitch-point, mid-point and tip loading, the deflection curve of a Image 1 diamentral pitch (DP) standard spur gear tooth corresponding to number of teeth of 14, 21, 26 and 34. In all these cases the deflection of the gear tooth at the point of loading obtained by FEM is in good agreement with the experimental value. The contraflexure in the deflection curve at the point of loading observed experimentally in the cases of pitch-point and mid-point loading, is predicted correctly by the FEM analysis.

Deflection analysis of hybrid laminated composite plates

In this paper an attempt is made to obtain deflections of hybrid, laminated, rectangular and skew composite plates. Analysis is performed by employing the Galerkin technique. Numerical results have been obtained for two types of layups employing Kevlar/epoxy and Boron/epoxy laminae. It is observed that for a given aspect ratio the rigidity of the skew plate increases with an increase in the skew angle. Further, for a specified deflection, the hybrid laminates turn out to be lighter.

Studies involving electrostatic potential of valinomycin

The electrostatic potential of valinomycin in various conformations as obtained by the crystal structures (uncomplexed, complexed) and theoretical considerations have been evaluated and compared. The potential energy profiles along the æ axis of the bracelet-like structures show a systematic variation from the uncomplexed to the complexed structure. This type of conformational change and the potential variation are probably associated with different states of ion transport, like the capture and release of ions by the ionophore. Also, the asymmetry of the molecule due to D-HyIV on one side and L-Lac on the other side is reflected in the potential values along the Z-axis, the magnitude of which, is considerable in the uncomplexed structure. The evaluation of the potential at the ab-initio level on smaller fragments indicate that the order of liganding capacity of oxygen is amide ether ester. Also, the inductive effects due to alkyl substitution is negligible as evidenced by the potential studies on the substituted amides and esters.

Load-Deflection Behavior of Restrained R/C Skew Slabs

A method is presented for determining the complete load-deflection behavior of reinforced concrete skew slabs restrained at the edges and subjected to uniformly-distributed loading. The analysis is considered in three stages. In the first stage the load-deflection behavior up to the cracking load is considered. The behavior between the cracking load and the yield line load is considered in the second stage. The load-deflection behavior beyond the yield line load, taking into account the effect of the membrane action, is considered in the third stage. Details of an experimental program of casting and testing 12 reinforced concrete skew slabs restrained at the edges are presented to verify the results of the analysis.

Effect of static deflection on natural frequency of non-linear spring mass system by direct linearization method

An exact expression for the frequency of a non-linear cubic spring mass system is obtained considering the effect of static deflection. An alternative expression for the approximate frequency is also obtained by the direct linearization procedure; it is shown that this is very accurate as compared with the exact method. This approximate frequency equation is used to explain a “dual behaviour” of the frequency amplitude curves.

Non-disruptive and null-deflection mass flow measurement by a pressure compensation technique

Accurate mass flow measurement is very important in various monitoring and control applications. This paper proposes a novel method of fluid flow measurement by compensating the pressure drop across the ends of measuring unit using a compensating pump. The pressure drop due to the flow is balanced by a feedback control loop. This is a null-deflection type of measurement. As the insertion of such a measuring unit does not affect the functioning of the systems, this is also a non-disruptive flow measurement method. The implementation and design of such a unit are discussed. The system is modeled and simulated using the bond graph technique and it is experimentally validated. (C) 2009 Elsevier Ltd. All rights reserved.

Molecular structure-activity relationship study of some non-steroidal antiinflammatory agents using electrostatic potential mapping

A series of 6,11-dihydro-11-oxodibenz[b,e]oxepin-2-acetic acids (DOAA) which are known to be anti-inflammatory agents were studied. The geometries of some of the molecules obtained from X-ray crystallography were used in the calculations as such while the geometries of their derivatives were obtained by local, partial geometry optimization around the Sites of substitution employing the AMI method, keeping the remaining parts of the geometries the same as those in the parent molecules. Molecular electrostatic potential (MEP) mapping was performed for the molecules using optimized hybridization displacement charges (HDC) combined with Lowdin charges, as this charge distribution has been shown earlier to yield near ab initio quality results. A good correlation has been found between the MEP values near the oxygen atoms of the hydroxyl groups of the carboxy groups of the molecules and their anti-inflammatory activities. The result is broadly in agreement with the model proposed earlier by other authors regarding the structure-activity relationship for other similar molecules.

Prediction of Specimen Strain from Extensometer Deflection Measurements in a Direct Stress Fatigue Test Specimen under Static Tensile Loading

The displacement between the ridges situated outside the filleted test section of an axially loaded unnotched specimen is computed from the axial load and shape of the specimen and compared with extensometer deflection data obtained from experiments. The effect of prestrain on the extensometer deflection versus specimen strain curve has been studied experimentally and analytically. An analytical study shows that an increase in the slope of the stress-strain curve in the inelastic region increases the slope of the corresponding computed extensometer deflection versus specimen strain curve. A mathematical model has been developed which uses a modified length ¯ℓef in place of the actual length of the uniform diameter test section of the specimen. This model predicts the extensometer deflection within 5% of the corresponding experimental value. This method has been successfully used by the authors to evolve an iterative procedure for predicting the cyclic specimen strain in axial fatigue tests on unnotched specimens.

Interactions of tris buffer with nucleotides: the crystal structure of tris(hydroxymethyl)methylammonium adenosine 5'-diphosphate dihydrate

The crystal and molecular structures of the Tris salt of adenosine 5'-diphosphate were determined from X-ray diffraction data. The crystals are monoclinic, space P21, and Z = 2 with a=9.198 (2) A, b=6.894 (1) A, c=18.440 (4) A, and beta = 92.55 (2) degrees. Intensity data were collected on an automated diffractometer. The structure was solved by the heavy-atom technique and refined by least squares to R = 0.047. The ADP molecule adopts a folded conformation. The conformation about the glycosidic bond is anti. The conformation of the ribose ring is close to a perfect C(2')-endo-C-(3')-exo puckering. The conformation about C(4')-C(5') is gauche-gauche, similar to other nucleotide structures. The pyrophosphate chain displays a nearly eclipsed geometry when viewed down the P-P vector, unlike the staggered conformation observed in crystal structures of other pyrophosphates. The less favorable eclipsed conformation probably results from the observed association of Tris molecules with the polar diphosphate chain through electrostatic interactions and hydrogen bonds. Such interactions may play an important role in Tris-buffered aqueous solutions of nucleotides and metal ions.

Electrostatic Field Analysis of Electrooptic Devices

We describe a Finite Difference Method for the determination of the electrostatic field in a multilayered electrooptic device. The Laplace equation is solved, assuming a suitable closed area, by taking into account the different permittivities of the various layers. The effect of a higher permittivity in the guiding layer has been explicitly considered. As a practical example, we calculate the phase shift of a guided optical wave within an electrooptic modulator. A review of the various methods in use for the field analysis is given. Some criteria for the selection of the appropriate method are also mentioned.

A simple computational model for predicting .pi.-facial selectivity in reductions of sterically unbiased ketones. Relative importance of electrostatic and orbital interactions

Various factore controlling the preferred facial selectivity in the reductions of a number of sterically unbiased ketones have been evaluated using a semiempirical MO procedure. MNDO optimized geometries do not reveal any significant ground-state distortions which can be correlated with the observed face selectivities. Electrostatic effecta due to an approaching reagent were modeled by placing a test negative charge at a fixed distance from the carbonyl carbon on each of the two faces. A second series of calculations was carried out using the hydride ion as a test nucleophile. The latter calculations effectively include orbital interactions involving the u and u* orbitals of the newly formed bond in the reaction. The computed energy differences with the charge model are generally much larger compared to those with the hydride ion. However, both models lead to predictions which are qualitatively consistent with the experimentally determined facial preferences for most of the systems. Thus, electrostatic interactions between the nucleophile and the substrate seem to effectively determine the face selectivities in these molecules. However, there are a few exceptions in which orbital interactions are found to contribute significantly and occasionally reverse the preference dictated by electrostatic effecta. The remarkable succew of the hydride model calculations, in spite of retaining the unperturbed geometries of the substrates, points to the unimportance of torsional effeds and orbital distortions associated with the pyramidalized carbonyl unit in the transition state in most of the substrates considered. Additional experimental results are reported which provide useful calibration for the present computational approach.

Prediction of load-deflection behaviour using fracture energy GF: A comparative study of two fracture models for concrete

Load-deflection curves for a notched beam under three-point load are determined using the Fictitious Crack Model (FCM) and Blunt Crack Model (BCM). Two values of fracture energy GF are used in this analysis: (i) GF obtained from the size effect law and (ii) GF obtained independently of the size effect. The predicted load-deflection diagrams are compared with the experimental ones obtained for the beams tested by Jenq and Shah. In addition, the values of maximum load (Pmax) obtained by the analyses are compared with the experimental ones for beams tested by Jenq and Shah and by Bažant and Pfeiffer. The results indicate that the descending portion of the load-deflection curve is very sensitive to the GF value used.