On quasi-degeneracies in plate vibration problems

In plotting the variation of frequencies with geometric parameters such as side ratio, skew angle, thickness taper, etc. in detailed studies of the vibration characteristics of plates, situations are encountered such as crossing of the frequency curves or the tendency of these curves to come close together and veer away from each other. These have been generally referred to as “frequency crossings” and “transitions” respectively. The latter may preferably be referred to as “quasi-degeneracies”. In the literature there appears to be some ambiguity in the analysis and interpretation of these features. In this paper, a clarification of some of these questions as regards rectangular and skew plates is presented by making use of concepts from physics dealing with molecular vibrations.

Exact analysis of simply supported rhombic plates under uniform pressure

The simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method

A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.

Vertical uplift resistance of circular plate anchors in clays under undrained condition

The vertical uplift resistance of circular plate anchors, embedded horizontally in a clayey stratum whose cohesion increases linearly with depth, has been obtained under undrained (phi = 0) condition. The axi-symmetric static limit analysis formulation in combination with finite elements proposed recently by the authors has been employed. The variation of the uplift factor (F,) with changes in the embedment ratio (H/B) has been computed for several rates of increases of soil cohesion with depth. It is noted that in all the cases, the magnitude of F-c increases continuously with depth up to a certain value of H-cr/B beyond which the uplift factor becomes essentially constant. The proposed static limit analysis formulation is seen to provide acceptable results even for the two other simple chosen axi-symmetric problems.

Distance dependence of fluorescence resonance energy transfer

Deviations from the usual R (-6) dependence of the rate of fluorescence resonance energy transfer (FRET) on the distance between the donor and the acceptor have been a common scenario in the recent times. In this paper, we present a critical analysis of the distance dependence of FRET, and try to illustrate the non R (-6) type behaviour of the rate for the case of transfer from a localized electronic excitation on the donor, a dye molecule to three different energy acceptors with delocalized electronic excitations namely, graphene,two-dimensional semiconducting sheet and the case of such a semiconducting sheet rolled to obtain a nanotube. We use simple analytic models to understand the distance dependence in each case.

Modeling and analysis of a tunable piezoelectric structure for transverse shear wave generation

An analytical investigation of the transverse shear wave mode tuning with a resonator mass (packing mass) on a Lead Zirconium Titanate (PZT) crystal bonded together with a host plate and its equivalent electric circuit parameters are presented. The energy transfer into the structure for this type of wave modes are much higher in this new design. The novelty of the approach here is the tuning of a single wave mode in the thickness direction using a resonator mass. First, a one-dimensional constitutive model assuming the strain induced only in the thickness direction is considered. As the input voltage is applied to the PZT crystal in the thickness direction, the transverse normal stress distribution induced into the plate is assumed to have parabolic distribution, which is presumed as a function of the geometries of the PZT crystal, packing mass, substrate and the wave penetration depth of the generated wave. For the PZT crystal, the harmonic wave guide solution is assumed for the mechanical displacement and electric fields, while for the packing mass, the former is solved using the boundary conditions. The electromechanical characteristics in terms of the stress transfer, mechanical impedance, electrical displacement, velocity and electric field are analyzed. The analytical solutions for the aforementioned entities are presented on the basis of varying the thickness of the PZT crystal and the packing mass. The results show that for a 25% increase in the thickness of the PZT crystal, there is ~38% decrease in the first resonant frequency, while for the same change in the thickness of the packing mass, the decrease in the resonant frequency is observed as ~35%. Most importantly the tuning of the generated wave can be accomplished with the packing mass at lower frequencies easily. To the end, an equivalent electric circuit, for tuning the transverse shear wave mode is analyzed.

Analysis of the binding of polymyxin B to endotoxic lipid A and core glycolipid using a fluorescent displacement probe

Dansylcadaverine, a cationic fluorescent probe binds to bacterial lipopolysaccharide and lipid A, and is displaced competitively by other compounds which possess affinity toward endotoxins. The binding parameters of dansylcadaverine for lipid A were determined by Scatchard analysis to be two apparently equivalent sites with apparent dissociation constants (Kd) ranging between 16 μM to 26 μM, while that obtained for core glycolipid from Salmonella minnesota Re595 yielded a Kd of 22 μM to 28 μM with three binding sites. The Kd of polymyxin B for lipid A was computed from dansylcadaverine displacement by the method of Horovitz and Levitzki (Horovitz, A., and Levitzki, A. (1987) Proc. Natl. Acad. Sci. USA 84, 6654–6658). The applicability of this method for analyzing fluorescence data was validated by comparing the Kds of melittin for lipid A obtained by direct Scatchard analysis, and by the Horovitz-Levitzki method. The displacement of dansylcadaverine from lipid A by polymyxin B was distinctly biphasic with Kds for polymyxin B-lipid A interactions corresponding to 0.4 μM and 1.5 μM, probably resulting as a consequence of lipid A being a mixture of mono- and di-phosphoryl species. This was not observed with core glycolipid, for which the Kd for polymyxin was estimated to range from 1.1 μM to 5.8 μM. The use of dansylcadaverine as a displacement probe offers a novel and convenient method of quantitating the interactions of a wide variety of substances with lipid A.

Unsteady mixed convection on the stagnation-point flow adjacent to a vertical plate with a magnetic field

An analysis is performed to study the unsteady combined forced and free convection flow (mixed convection flow) of a viscous incompressible electrically conducting fluid in the vicinity of an axisymmetric stagnation point adjacent to a heated vertical surface. The unsteadiness in the flow and temperature fields is due to the free stream velocity, which varies arbitrarily with time. Both constant wall temperature and constant heat flux conditions are considered in this analysis. By using suitable transformations, the Navier-Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (eta, tau). These transformations also uncouple the momentum and energy equations resulting in a primary axisymmetric flow, in an energy equation dependent on the primary flow and in a buoyancy-induced secondary flow dependent on both primary flow and energy. The resulting system of partial differential equations has been solved numerically by using both implicit finite-difference scheme and differential-difference method. An interesting result is that for a decelerating free stream velocity, flow reversal occurs in the primary flow after certain instant of time and the magnetic field delays or prevents the flow reversal. The surface heat transfer and the surface shear stress in the primary flow increase with the magnetic field, but the surface shear stress in the buoyancy-induced secondary flow decreases. Further the heat transfer increases with the Prandtl number, but the surface shear stress in the secondary flow decreases.

Analysis of the impact of a uracil DNA glycosylase attenuated in AP-DNA binding in maintenance of the genomic integrity in Escherichia coli

Uracil DNA glycosylase (Ung)initiates the uracil excision repair pathway. We have earlier characterized the Y66W and Y66H mutants of Ung and shown that they are compromised by similar to 7- and similar to 170-fold, respectively in their uracil excision activities. In this study, fluorescence anisotropy measurements show that compared with the wild-type, the Y66W protein is moderately compromised and attenuated in binding to AP-DNA. Allelic exchange of ung in Escherichia coli with ung::kan, ungY66H:amp or ungY66W:amp alleles showed similar to 5-, similar to 3.0- and similar to 2.0-fold, respectively increase in mutation frequencies. Analysis of mutations in the rifampicin resistance determining region of rpoB revealed that the Y66W allele resulted in an increase in A to G (or T to C) mutations. However, the increase in A to G mutations was mitigated upon expression of wild-type Ung from a plasmid borne gene. Biochemical and computational analyses showed that the Y66W mutant maintains strict specificity for uracil excision from DNA. Interestingly, a strain deficient in AP-endonucleases also showed an increase in A to G mutations. We discuss these findings in the context of a proposal that the residency of DNA glycosylase(s) onto the AP-sites they generate shields them until recruitment of AP-endonucleases for further repair.

Thermodynamic analysis of three state denaturation of Peanut Agglutinin

Peanut Agglutinin (PNA) is a homotetrameric protein with a very unusual open quaternary structure. During denaturation, it first dissociates into a molten globule like state, which subsequently undergoes complete denaturation. Urea denaturation of PNA at neutral pH has been studied by intrinsic fluorescence spectroscopy and has been fitted to a three state model, A(4) double left right arrow 4I double left right arrow 4U, to get all the relevant thermodynamic parameters. Urea denaturation leads to continuous red shift of wavelength maxima. The molten globule like state is formed in a short range of urea concentration. Refolding of the denatured PNA has been attempted by intrinsic fluorescence study. Refolding by instantaneous dilution shows the occurrence of the formation of an intermediate at a relatively rapid rate, within few seconds. The transition from PNA tetramer to molten globule like state is found to have a Delta G value of similar to 33 kcal/mole while it is similar to 8 kcal/mole for the transition from molten globule like state to a completely denatured state. This in turn indicates that the tetramerization in PNA contributes significantly to the stability of the oligomer.

Fracture analysis of stiffened panels under combined tensile, bending, and shear loads

The objective is to present the formulation of numerically integrated modified virtual crack closure integral technique for concentrically and eccentrically stiffened panels for computation of strain-energy release rate and stress intensity factor based on linear elastic fracture mechanics principles. Fracture analysis of cracked stiffened panels under combined tensile, bending, and shear loads has been conducted by employing the stiffened plate/shell finite element model, MQL9S2. This model can be used to analyze plates with arbitrarily located concentric/eccentric stiffeners, without increasing the total number of degrees of freedom, of the plate element. Parametric studies on fracture analysis of stiffened plates under combined tensile and moment loads have been conducted. Based on the results of parametric,studies, polynomial curve fitting has been carried out to get best-fit equations corresponding to each of the stiffener positions. These equations can be used for computation of stress intensity factor for cracked stiffened plates subjected to tensile and moment loads for a given plate size, stiffener configuration, and stiffener position without conducting finite element analysis.

Determination of the orthotropic plate parameters of stiffened plates and grillages in free vibration

It is well known that the analysis of vibration of orthogonally stiffened rectangular plates and grillages may be simplified by replacing the actual structure by an orthotropic plate. This needs a suitable determination of the four elastic rigidity constants Dx, Dy, Dxy, D1 and the mass {Mathematical expression} of the orthotropic plate. A method is developed here for determining these parameters in terms of the sectional properties of the original plate-stiffener combination or the system of interconnected beams. Results of experimental work conducted on aluminium plates agree well with the results of the theory developed here.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

An exact analysis of free vibrations of simply-supported viscoelastic plates

In this paper an exact three-dimensional analysis for free vibrations of a class of simply-supported viscoelastic rectangular plates is given. The characteristic equation defining the eigenvalues is of closed form. Some numerical results are presented for standard linear solids. Results from thin plate and Mindlin theories are also given for the purpose of comparison.

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.