Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties

Nonlinear vibration analysis is performed using a C-0 assumed strain interpolated finite element plate model based on Reddy's third order theory. An earlier model is modified to include the effect of transverse shear variation along the plate thickness and Von-Karman nonlinear strain terms. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. The numerical results are validated with the available literature. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also r

Note: Dynamic point spread function for single and multiphoton fluorescence microscopy

We propose and demonstrate a dynamic point spread function (PSF) for single and multiphoton fluorescence microscopy. The goal is to generate a PSF whose shape and size can be maneuvered from highly localized to elongated one, thereby allowing shallow-to-depth excitation capability during active imaging. The PSF is obtained by utilizing specially designed spatial filter and dynamically altering the filter parameters. We predict potential applications in nanobioimaging and fluorescence microscopy.

On the use of a coordinate transformation for analysis of axisymmetric vibration of polar orthotropic annular plates

Estimates of natural frequencies corresponding to axisymmetric modes of flexural vibration of polar orthotropic annular plates have been obtained for various combinations of clamped, simply supported and free edge conditions. A coordinate transformation in the radial direction has been used to obtain effective solutions by the classical Rayleigh-Ritz method. The analysis with this transformation has been found to be advantageous in computations, particularly for large hole sizes, over direct analysis. Numerical results have been obtained for various values of hole sizes and rigidity ratio. The eigenvalue parameter has been found to vary more or less linearly with the rigidity ratio. A comparison with the results for isotropic plates has brought out some interesting features.

A new ELISA plate based microtiter well assay for mycobacterial topoisomerase I for the direct screening of enzyme inhibitory monoclonal antibody supernatants

Antigen specific monoclonal antibodies present in crude hybridoma supernatants are normally screened by ELISA on plates coated with the relevant antigen. Screening for inhibitory monoclonals to enzymes would require the evaluation of purified antibodies or antibody containing supernatants for their inhibition of enzyme activity in a separate assay. However, screening for inhibitory antibodies against DNA transacting enzymes such as topoisomerase I (topo I) cannot be done using hybridoma supernatants due to the presence of nucleases in tissue culture media containing foetal calf serum which degrade the DNA substrates upon addition. We have developed a simple and rapid screening procedure for the identification of clones that secrete inhibitory antibodies against mycobacterial topo I using 96 well ELISA microtiter plates. The principle of the method is the selective capture of monoclonal antibodies from crude hybridoma supernatants by topo I that is tethered to the plate through the use of plate-bound polyclonal anti-topo I antibodies. This step allows the nucleases present in the medium to be washed off leaving the inhibitor bound to the tethered enzyme. The inhibitory activity of the captured antibody is assessed by performing an in situ DNA relaxation assay by the addition of supercoiled DNA substrate directly to the microtiter well followed by the analysis of the reaction products by agarose gel electrophoresis. The validity of this method was confirmed by purification of the identified inhibitory antibody and its evaluation in a DNA relaxation assay. Elimination of all enzyme-inhibitory constituents of the culture medium from the well in which the inhibitory antibody is bound to the tethered enzyme may make this method broadly applicable to enzymes such as DNA gyrases, restriction enzymes and other DNA transaction enzymes. Further, the method is simple and avoids the need of prior antibody purification for testing its inhibitory activity. (C) 2010 Elsevier B.V. All rights reserved.

Multiple imaging with an aberration optimized hololens array

The imaging performance of hololenses formed with four different geometries were studied through an analysis of their third-order aberration coefficients. It is found that the geometry proposed by Brandt (1969) gives the least residual aberration with minimum variation of this aberration with the reconstruction angle. When the ideal position of one of the construction beams is changed in order to generate a hololens array, the residual aberration is found to increase sharply, which in turn affects the image resolution among the multiplied images in the output. A hololens array was generated using Brandt's geometry with the help of a one-dimensional sinusoidal grating. The results of multiple imaging with the hololens array are presented. The image resolution is reasonably high and can be further improved by reducing the f-number of the hololenses.

Analysis of clearance fit pin joints

The analysis of clearance fit joints falls within the realm of mixed boundary problems with moving boundaries. In this paper, this problem is solved by a simple continuum method of analysis applying an inverse technique; the region of contact is specified and the corresponding causative load is evaluated. Illustrations are given for a rigid clearance fit pin in a large elastic plate with smooth zero-shear interface between pin and plate, under biaxial plate stress at infinity and due to load transfer through pin.

Stability Analysis of Composite Skew Plates Using a Dynamic Method

Stability analysis is carried out considering free lateral vibrations of simply supported composite skew plates that are subjected to both direct and shear in-plane forces. An oblique stress component representation is used, consistent with the skew-geometry of the plate. A double series, expressed in Chebyshev polynomials, is used here as the assumed deflection surface and Ritz method of solution is employed. Numerical results for different combinations of side ratios, skew angle, and in-plane loadings that act individually or in combination are obtained. In this method, the in-plane load parameter is varied until the fundamental frequency goes to zero. The value of the in-plane load then corresponds to a critical buckling load. Plots of frequency parameter versus in-plane loading are given for a few typical cases. Details of crossings and quasi degeneracies of these curves are presented.

Elastic analysis of pin joints

The advent of large and fast digital computers and development of numerical techniques suited to these have made it possible to review the analysis of important fundamental and practical problems and phenomena of engineering which have remained intractable for a long time. The understanding of the load transfer between pin and plate is one such. Inspite of continuous attack on these problems for over half a century, classical solutions have remained limited in their approach and value to the understanding of the phenomena and the generation of design data. On the other hand, the finite element methods that have grown simultaneously with the recent development of computers have been helpful in analysing specific problems and answering specific questions, but are yet to be harnessed to assist in obtaining with economy a clearer understanding of the phenomena of partial separation and contact, friction and slip, and fretting and fatigue in pin joints. Against this background, it is useful to explore the application of the classical simple differential equation methods with the aid of computer power to open up this very important area. In this paper we describe some of the recent and current work at the Indian Institute of Science in this last direction.

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.

Mixed Convection Induced in a Gas Flowing Past a Hot Horizontal Flat Plate

A boundary layer analysis of mixed convective motion over a hot horizontal flat plate is performed under the conditions of steady flow and low speed. Use of the Howarth-Dorodnytsyn transformation makes it possible to dispense with the usual Boussinesq approximation, and variable gas properties are accounted for via the assumption that dynamic viscosity and thermal conductivity are proportional to the absolute temperature. The formulation presented enables the entire mixed convection regime to be described by a single set of equations. Finite difference solutions when the Prandtl number is 0.72 are obtained over the entire range of the mixed convection parameter ξ from 0 (free convection) to 1 (forced convection) and heating parameter ▵ values from 2 to 12. The effects of both ξ and ▵on the velocity profiles, the temperature profiles, and the variation of skin friction and heat transfer functions are clearly illustrated in tables and graphs.

Stress and strength analysis of pin joints in laminated anisotropic plates

Mechanical joints in composites can be tailored to achieve improved performance and better life by appropriately selecting the laminate parameters. In order to gain the best advantage of this possibility of tailoring the laminate, it is necessary to understand the influence of laminate parameters on the behaviour of joints in composites. Most of the earlier studies in this direction were based on simplified assumptions regarding load transfer at the pin-plate interface and such studies were only carried out on orthotropic and quasi-isotropic laminates. In the present study, a more rigorous analysis is carried out to study pin joints in laminates with anisotropic properties. Two types of laminates with (0/ + ?4/90)s and (0/ ± ?2/90)s layups made out of graphite epoxy T300/5208 material system are considered. The analysis mainly concentrates on clearance fit in which the pin is of smaller diameter compared to the hole. The main aspect of the analysis of pin joints is the changing contact between the pin and the plate with increasing load levels. The analysis is carried out by an iterative finite element technique and a computationally efficient routine is developed for this purpose. Numerical studies indicate that the location and magnitude of the peak stresses along the hole boundary are functions of fibre angle and the overall anisotropic properties. It is also shown that the conventional assumption of cosine distribution for the contact pressure between pin and the plate in the analysis lead to underestimation of bearing failure load and overestimation of shear and tensile failure loads in typical (0/905)s cross-ply laminates.

New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

Experimental analysis of thermo-physical processes in acoustically levitated heated droplets

An experimental setup using radiative heating has been used to understand the thermo-physical phenomena and chemical transformations inside acoustically levitated cerium nitrate precursor droplets. In this transformation process, through infrared thermography and high speed imaging, events such as vaporization, precipitation and chemical reaction have been recorded at high temporal resolution, leading to nanoceria formation with a porous morphology. The cerium nitrate droplet undergoes phase and shape changes throughout the vaporization process. Four distinct stages were delineated during the entire vaporization process namely pure evaporation, evaporation with precipitate formation, chemical reaction with phase change and formation of final porous precipitate. The composition was examined using scanning and transmission electron microscopy that revealed nanostructures and confirmed highly porous morphology with trapped gas pockets. Transmission electron microscopy (TEM) and high speed imaging of the final precipitate revealed the presence of trapped gases in the form of bubbles. TEM also showed the presence of nanoceria crystalline structures at 70 degrees C. The current study also looked into the effect of different heating powers on the process. At higher power, each phase is sustained for smaller duration and higher maximum temperature. In addition, the porosity of the final precipitate increased with power. A non-dimensional time scale is proposed to correlate the effect of laser intensity and vaporization rate of the solvent (water). The effect of acoustic levitation was also studied. Due to acoustic streaming, the solute selectively gets transported to the bottom portion of the droplet due to strong circulation, providing it rigidity and allows it become bowl shaped. (C) 2010 Elsevier Ltd. All rights reserved.

Analysis of continuum using boundary compatibility conditions of integrated force method

Static and vibration problems of an indeterminate continuum are traditionally analyzed by the stiffness method. The force method is more or less non-existent for such problems. This situation is primarily due to the incomplete state of development of the compatibility conditions which are essential for the analysis of indeterminate structures by the flexibility method. The understanding of the Compatibility Conditions (CC) has been substantially augmented. Based on the understanding of CC, a novel formulation termed the Integrated Force Method (IFM) has been established. In this paper IFM has been extended for the static and vibration analyses of a continuum. The IFM analysis is illustrated taking three examples: 1. (1) rectangular plate in flexure 2. (2) analysis of a cantilevered dam 3. (3) free vibration analysis of a beam. From the examples solved it is observed that the force response of an indeterminate continuum with mixed boundary conditions can be generated by IFM without any reference to displacements in the field or on the boundary. Displacements if required can be calculated by back substitution.

Ricin-membrane interaction: membrane penetration depth by fluorescence quenching and resonance energy transfer

The entry of the plant toxin ricin and its A- and B-subunits in model membranes in the presence as well as absence of monosialoganglioside (GM(1)) has been studied. Dioleoylphosphatidylcholine and 5-, 10-, and 12-doxyl- or 9,10-dibromophosphatidylcholines serve as quenchers of intrinsic tryptophan fluorescence of the proteins. The parallax method of Chattopadhyay and London [(1987) Biochemistry 26, 39-45] has been employed to measure the average membrane penetration depth of tryptophans of ricin and its B-chain and the actual depth of the sole Trp 211 in the A-chain. The results indicate that both of the chains as well as intact ricin penetrate the membrane deeply and the C-terminal end of the A-chain is well inside the bilayer, especially at pH 4.5. An extrinsic probe N-(iodoacetyl)-N'-(5-sulfo-1-naphthyl) ethylenediamine (I-AEDANS) has been attached to Cys 259 of the A-chain, and the kinetics of penetration has been followed by monitoring the increase in AEDANS fluorescence at 480 nm. The insertion follows first-order kinetics, and the rate constant is higher at a lower pH. The energy transfer distance analysis between Trp 211 and AEDANS points out that the conformation of the A-chain changes as it inserts into the membrane. CD studies indicate that the helicity of the proteins increases after penetration, which implies that some of the unordered structure in the native protein is converted to the ordered form during this process. Hydrophobic forces seem to be responsible for stabilizing a particular protein conformation inside the membrane.