Analytical modeling and vibration analysis of internally cracked rectangular plates

This study proposes an analytical model for nonlinear vibrations in a cracked rectangular isotropic plate containing a single and two perpendicular internal cracks located at the center of the plate. The two cracks are in the form of continuous line with each parallel to one of the edges of the plate. The equation of motion for isotropic cracked plate, based on classical plate theory is modified to accommodate the effect of internal cracks using the Line Spring Model. Berger?s formulation for in-plane forces makes the model nonlinear. Galerkin?s method used with three different boundary conditions transforms the equation into time dependent modal functions. The natural frequencies of the cracked plate are calculated for various crack lengths in case of a single crack and for various crack length ratio for the two cracks. The effect of the location of the part through crack(s) along the thickness of the plate on natural frequencies is studied considering appropriate crack compliance coefficients. It is thus deduced that the natural frequencies are maximally affected when the crack(s) are internal crack(s) symmetric about the mid-plane of the plate and are minimally affected when the crack(s) are surface crack(s), for all the three boundary conditions considered. It is also shown that crack parallel to the longer side of the plate affect the vibration characteristics more as compared to crack parallel to the shorter side. Further the application of method of multiple scales gives the nonlinear amplitudes for different aspect ratios of the cracked plate. The analytical results obtained for surface crack(s) are also assessed with FEM results. The FEM formulation is carried out in ANSYS.     

Fluorescence Anisotropy Studies on Bodipy (Pyrromethene 546) Dye as a Novel Thermal Probe

Journal of Fluorescence - In the present work, fluorescence anisotropy studies of BODIPY (pyrromethene 546 or C14H17BF2N2) dye have been performed and found that it has a potential to be used as a...     

Spectrophotometric determination of ruthenium(III) and iridium(TV) with 8-hydroxyquinoIine N-oxide

The spectrophotometric characteristics and the stability constants of the yellow to brown 1:1 and 1:2 complexes of platinum metals with oxine N-oxide (existing as chloro mixed-ligand complexes) have been investigated. Oxine N-oxide can be used as a spectrophotometric reagent for ruthenium(III) and iridium(IV).     

Efficient Transition‐Metal‐Free Oxidation of Benzylic and Secondary Alcohols to the Carbonyl Compounds Using an N‐Bromosuccinimide/NH4Cl System

The oxidation of a variety of benzylic and secondary alcohols was achieved in excellent yields using an NBS/NH₄Cl system in aqueous acetonitrile (CH₃CN‐H₂O; 7/3 v/v) at 80°C under very mild conditions.     

Thermal decomposition of cesium hexanitratouranium(IV)

As cesium hexanitratouranium(IV), Cs₂U(NO₃)₆, has the same Cs:U stoichiometry as that of Cs₂UO₄, thermal decomposition of this nitrato complex in air and nitrogen was studied in detail as a possible alternate method of preparing pure Cs₂UO₄. The volatility of cesium nitrate, which is one of the intermediate products, changed this Cs:U ratio during thermal decomposition. Hence, only Cs₂U₂O₇ was obtained on heating the sample to 775 K or higher. A scheme for the thermal decomposition of Cs₂U(NO₃)₆ is given by combining the observed TG, XRD and IR data.     

Thermodynamic and lfer studies for the oxidation of anilines by the periodate ion

The various thermodynamic parameters for the periodate oxidation of six anilines, viz. aniline, p-chloroaniline, p-ethoxyaniline, o- and p-methoxyanilines and p-methylaniline have been reported and discussed. The validity of the isokinetic relationship and various linear free energy relationships (LFERs) have been tested and discussed. An attempt has been made to correlate these findings with the mechanism operative in these reactions.     

A minimal composite theory for stability of non-parallel compressible boundary-layer flow

A new minimal composite theory that extends the approach of Govindarajan and Narasimha [1] is proposed here for 2D non-parallel compressible boundary-layer stability subject to 3D disturbances. The mean profiles are obtained from Hortons analysis, which provides a good approximation for a large range of Prandtl numbers at non-zero pressure gradients. In the lowest order, all effects of order lower than O(R^-2/3) anywhere in the boundary-layer are included, R being the local boundary-layer Reynolds number; the resulting non-parallel formulation yields a set of four ordinary differential equations, as compared to the five coupled equations of classical parallel flow theory of Mack [2]. The largest effect on stability of flow non-parallelism is found to be due to the wall-normal advection of velocity and temperature disturbance quantities by the mean flow. The present theory shows that the bulk viscosity, invariably included in compressible stability theories, is irrelevant at the lowest order. In comparison with the full [O(R^-1)] non-parallel theory, the present theory is marginally better than the parallel flow theory. PACS 03.50.De, 04.20-q, 42.65-k     

Lower bounds for adaptive locally decodable codes

An error‐correcting code is said to be locally decodable if a randomized algorithm can recover any single bit of a message by reading only a small number of symbols of a possibly corrupted encoding of the message. Katz and Trevisan 12 showed that any such code C : {0, 1}ⁿ → Σ^m with a decoding algorithm that makes at most q probes must satisfy m = Ω((n/log |Σ|)^q/(q?1)). They assumed that the decoding algorithm is non‐adaptive, and left open the question of proving similar bounds for adaptive decoders. We show m = Ω((n/log |Σ|)^q/(q?1)) without assuming that the decoder is nonadaptive. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005