Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The beam mode

Using asymptotics, the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell vibrating in the beam mode (viz. circumferential wave order n = 1) are studied. Initially, the uncoupled wavenumbers of the acoustic fluid and the cylindrical shell structure are discussed. Simple closed form expressions for the structural wavenumbers (longitudinal, torsional and bending) are derived using asymptotic methods for low- and high-frequencies. It is found that at low frequencies the cylinder in the beam mode behaves like a Timoshenko beam. Next, the coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter mu due to the coupling. An asymptotic expansion involving mu is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (as modifications to the uncoupled wavenumbers) separately for low- and high-frequency ranges and further, within each frequency range, for large and small values of mu. Only the flexural wavenumber, the first rigid duct acoustic cut-on wavenumber and the first pressure-release acoustic cut-on wavenumber are considered. The general trend found is that for small mu, the coupled wavenumbers are close to the in vacuo structural wavenumber and the wavenumbers of the rigid-acoustic duct. With increasing mu, the perturbations increase, until the coupled wavenumbers are better identified as perturbations to the pressure-release wavenumbers. The systematic derivation for the separate cases of small and large mu gives more insight into the physics and helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. This method of asymptotics is simple to implement using a symbolic computation package (like Maple). (C) 2008 Elsevier Ltd. All rights reserved.

Measurement of shock stand-off distance on a 120 degrees blunt cone model at hypersonic Mach number in Argon

The flow around a 120 degrees blunt cone model with a base radius of 60mm has been visualised at Mach 14.8 and 9.1 using argon as the test gas, at the newly established high speed schlieren facility in the IISc hypersonic shock tunnel HST2. The experimental shock stand off distance around the blunt cone is compared with that obtained using a commercial CFD package. The computed values of shock stand off distance of the blunt cone is found to agree reasonably well with the experimental data.

Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

Dynamics and control of buckling type devices using SMA wire integrated beam

An analysis and design study using Shape Memory Alloy (SMA) wire integrated beam and its buckling shape control are reported. The dynamical system performance is analyzed with a mathematical set-up involving nonlocal and rate sensitive kinetics of phase transformation in the SMA wire. A standard phenomenological constitutive model reported by Brinson (1993) is modified by considering certain consistency conditions in the material property tensors and by eliminating spurious singularity. Considering the inhomogeneity effects, a finite element model of the SMA wire is developed. Simulations are carried out to study the buckling shape control of a beam integrated with SMA wire.

Finnish Dosimetric Practice for Epithermal Neutron Beam Dosimetry in Boron Neutron Capture Therapy

Boron neutron capture therapy (BNCT) is a form of chemically targeted radiotherapy that utilises the high neutron capture cross-section of boron-10 isotope to achieve a preferential dose increase in the tumour. The BNCT dosimetry poses a special challenge as the radiation dose absorbed by the irradiated tissues consists of several dose different components. Dosimetry is important as the effect of the radiation on the tissue is correlated with the radiation dose. Consistent and reliable radiation dose delivery and dosimetry are thus basic requirements for radiotherapy. The international recommendations for are not directly applicable to BNCT dosimetry. The existing dosimetry guidance for BNCT provides recommendations but also calls for investigating for complementary methods for comparison and improved accuracy. In this thesis the quality assurance and stability measurements of the neutron beam monitors used in dose delivery are presented. The beam monitors were found not to be affected by the presence of a phantom in the beam and that the effect of the reactor core power distribution was less than 1%. The weekly stability test with activation detectors has been generally reproducible within the recommended tolerance value of 2%. An established toolkit for epithermal neutron beams for determination of the dose components is presented and applied in an international dosimetric intercomparison. The measured quantities (neutron flux, fast neutron and photon dose) by the groups in the intercomparison were generally in agreement within the stated uncertainties. However, the uncertainties were large, ranging from 3-30% (1 standard deviation), emphasising the importance of dosimetric intercomparisons if clinical data is to be compared between different centers. Measurements with the Exradin type 2M ionisation chamber have been repeated in the epithermal neutron beam in the same measurement configuration over the course of 10 years. The presented results exclude severe sensitivity changes to thermal neutrons that have been reported for this type of chamber. Microdosimetry and polymer gel dosimetry as complementary methods for epithermal neutron beam dosimetry are studied. For microdosimetry the comparison of results with ionisation chambers and computer simulation showed that the photon dose measured with microdosimetry was lower than with the two other methods. The disagreement was within the uncertainties. For neutron dose the simulation and microdosimetry results agreed within 10% while the ionisation chamber technique gave 10-30% lower neutron dose rates than the two other methods. The response of the BANG-3 gel was found to be linear for both photon and epithermal neutron beam irradiation. The dose distribution normalised to dose maximum measured by MAGIC polymer gel was found to agree well with the simulated result near the dose maximum while the spatial difference between measured and simulated 30% isodose line was more than 1 cm. In both the BANG-3 and MAGIC gel studies, the interpretation of the results was complicated by the presence of high-LET radiation.

Accuracy of absorbed dose in external photon beam radiotherapy : what level is sufficient and how to approach it?

Radiation therapy (RT) plays currently significant role in curative treatments of several cancers. External beam RT is carried out mostly by using megavoltage beams of linear accelerators. Tumor eradication and normal tissue complications correlate to dose absorbed in tissues. Normally this dependence is steep and it is crucial that actual dose within patient accurately correspond to the planned dose. All factors in a RT procedure contain uncertainties requiring strict quality assurance. From hospital physicist´s point of a view, technical quality control (QC), dose calculations and methods for verification of correct treatment location are the most important subjects. Most important factor in technical QC is the verification that radiation production of an accelerator, called output, is within narrow acceptable limits. The output measurements are carried out according to a locally chosen dosimetric QC program defining measurement time interval and action levels. Dose calculation algorithms need to be configured for the accelerators by using measured beam data. The uncertainty of such data sets limits for best achievable calculation accuracy. All these dosimetric measurements require good experience, are workful, take up resources needed for treatments and are prone to several random and systematic sources of errors. Appropriate verification of treatment location is more important in intensity modulated radiation therapy (IMRT) than in conventional RT. This is due to steep dose gradients produced within or close to healthy tissues locating only a few millimetres from the targeted volume. The thesis was concentrated in investigation of the quality of dosimetric measurements, the efficacy of dosimetric QC programs, the verification of measured beam data and the effect of positional errors on the dose received by the major salivary glands in head and neck IMRT. A method was developed for the estimation of the effect of the use of different dosimetric QC programs on the overall uncertainty of dose. Data were provided to facilitate the choice of a sufficient QC program. The method takes into account local output stability and reproducibility of the dosimetric QC measurements. A method based on the model fitting of the results of the QC measurements was proposed for the estimation of both of these factors. The reduction of random measurement errors and optimization of QC procedure were also investigated. A method and suggestions were presented for these purposes. The accuracy of beam data was evaluated in Finnish RT centres. Sufficient accuracy level was estimated for the beam data. A method based on the use of reference beam data was developed for the QC of beam data. Dosimetric and geometric accuracy requirements were evaluated for head and neck IMRT when function of the major salivary glands is intended to be spared. These criteria are based on the dose response obtained for the glands. Random measurement errors could be reduced enabling lowering of action levels and prolongation of measurement time interval from 1 month to even 6 months simultaneously maintaining dose accuracy. The combined effect of the proposed methods, suggestions and criteria was found to facilitate the avoidance of maximal dose errors of up to even about 8 %. In addition, their use may make the strictest recommended overall dose accuracy level of 3 % (1SD) achievable.

Terahertz wave characteristics of a single-walled carbon nanotube containing a fluid flow using the nonlocal Timoshenko beam model

This paper presents the effect of nonlocal scaling parameter on the terahertz wave propagation in fluid filled single walled carbon nanotubes (SWCNTs). The SWCNT is modeled as a Timoshenko beam,including rotary inertia and transverse shear deformation by considering the nonlocal scale effects. A uniform fluid velocity of 1000 m/s is assumed. The analysis shows that, for a fluid filled SWCNT, the wavenumbers of flexural and shear waves will increase and the corresponding wave speeds will decrease as compared to an empty SWCNT. The nonlocal scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or wave speed tends to zero). The frequency at which this phenomenon occurs is called the ``escape frequency''. The effect of fluid density on the terahertz wave propagation in SWCNT is also studied and the analysis shows that as the fluid becomes denser, the wave speeds will decrease. The escape frequency decreases with increase in nonlocal scaling parameter, for both wave modes. We also show that the effect of fluid density and velocity are negligible on the escape frequencies of flexural and shear wave modes. (C) 2010 Elsevier B.V. All rights reserved.

Strength design of composite beam using gradient and particle swarm optimization

This work addresses the optimum design of a composite box-beam structure subject to strength constraints. Such box-beams are used as the main load carrying members of helicopter rotor blades. A computationally efficient analytical model for box-beam is used. Optimal ply orientation angles are sought which maximize the failure margins with respect to the applied loading. The Tsai-Wu-Hahn failure criterion is used to calculate the reserve factor for each wall and ply and the minimum reserve factor is maximized. Ply angles are used as design variables and various cases of initial starting design and loadings are investigated. Both gradient-based and particle swarm optimization (PSO) methods are used. It is found that the optimization approach leads to the design of a box-beam with greatly improved reserve factors which can be useful for helicopter rotor structures. While the PSO yields globally best designs, the gradient-based method can also be used with appropriate starting designs to obtain useful designs efficiently. (C) 2006 Elsevier Ltd. All rights reserved.

Second order cone programming approaches for handling missing and uncertain data

We propose a novel second order cone programming formulation for designing robust classifiers which can handle uncertainty in observations. Similar formulations are also derived for designing regression functions which are robust to uncertainties in the regression setting. The proposed formulations are independent of the underlying distribution, requiring only the existence of second order moments. These formulations are then specialized to the case of missing values in observations for both classification and regression problems. Experiments show that the proposed formulations outperform imputation.

Growth and characterization of germanium nanowires by electron beam evaporation

Germanium nanowires were grown on Au coated Si substrates at 380 degrees C in a high vacuum (5 x 10(-5) Torr) by e-beam evaporation of Germanium (Ge). The morphology observation by a field emission scanning electron microscope (FESEM) shows that the grown nanowires are randomly oriented with an average length and diameter of 600 nm and 120 nm respectively for a deposition time of 60 min. The nanowire growth ratewas measured to be similar to 10 nm/min. Transmission electron microscope (TEM) studies revealed that the Ge nanowires were single crystalline in nature and further energy dispersive X-ray analysis(EDAX) has shown that the tip of the grown nanowires was capped with Au nanoparticles, this shows that the growth of the Ge nanowires occurs by the vapour liquid solid (VLS) mechanism. HRTEM studies on the grown Ge nanowire show that they are single crystalline in nature and the growth direction was identified to be along [110]. (C) 2010 Elsevier B.V. All rights reserved.

Effect of insertion of buffer-strip on the response of carbon-epoxy system in short beam tests

dThe work looks at the response to three-point loading of carbon-epoxy (CF-EP) composites with inserted buffer strip (BS) material. Short beam Shear tests were performed to study the load-deflection response as well as fracture features through macroscopy on the CF-EP system containing the interleaved PTFE-coated fabric material. Significant differences were noticed in the response of the CF-EP system to the bending process consequent to the architectural modification. It was inferred that introduction of small amounts of less adherent layers of material at specific locations causes a decrement in the load carrying capability. Further the number and the ease with which interface separation occurs is found to depend on the extent to which the inserted layer is present in either single or multiple layer positions.