ON THE FREE VIBRATION OF STIFFENED SHALLOW SHELLS

A finite element analysis for free vibration behaviour of doubly curved stiffened shallow shells is presented. The stiffened shell element is obtained by the appropriate combinations of the eight-/nine-node doubly curved isoparametric thin shallow shell element with the three-node curved isoparametric beam element. The shell types examined are the elliptic and hyperbolic paraboloids, the hypar and the conoidal shells. The accuracy of the formulation is established by comparing some of the authors' results of specific problems with those available in the literature. Numerical results of additional stiffened shells are also presented to study the effects of various parameters of shells and stiffeners such as orientation (i.e., along x -/y -/both x and y directions), type (concentric, eccentric at top and eccentric at bottom) and number of stiffeners, stiffener depth to shell thickness ratio, and aspect ratio, shallowness and boundary conditions of shells on free vibration characteristics.     

Novel experimentally observed phenomena in soft matter

Soft materials such as colloidal suspensions, polymer solutions and liquid crystals are constituted by mesoscopic entities held together by weak forces. Their mechanical moduli are several orders of magnitude lower than those of atomic solids. The application of small to moderate stresses to these materials results in the disruption of their microstructures. The resulting flow is non-Newtonian and is characterized by features such as shear rate-dependent viscosities and non-zero normal stresses. This article begins with an introduction to some unusual flow properties displayed by soft matter. Experiments that report a spectrum of novel phenomena exhibited by these materials, such as turbulent drag reduction, elastic turbulence, the formation of shear bands and the existence of rheological chaos, flow-induced birefringence and the unusual rheology of soft glassy materials, are reviewed. The focus then shifts to observations of the liquid-like response of granular media that have been subjected to external forces. The article concludes with examples of the patterns that emerge when certain soft materials are vibrated, or when they are displaced with Newtonian fluids of lower viscosities.     

Existence of solution of the pullback equation involving volume forms

Let Ω ⊂ ℝ ⁿ be a smooth, bounded domain. We study the existence and regularity of diffeomorphisms of Ω satisfying the volume form equation

Exciplex parameters: key factors in the dielectric behaviour of magnetodynamics

Photoinduced electron transfer reactions in solution produce two primary geminate radical ion pairs: contact ion pair or exciplex and solvent-separated ion pair. The magnetodynamics of radical ion pairs involves suppression of the spin-evolution between singlet and triplet states of a fraction of solvent-separated ion pairs, the partners of which undergo prior diffusion to attain the distance where exchange interaction is negligible, in the presence of an external low magnetic field of the order of the hyperfine interactions present in the system. This results in an increase in geminate recombination of the singlet solvent-separated ion pairs and enhancement in exciplex luminescence since the precursor radical ion pair is singlet. Although seemingly magnetodynamics is a diffusion-controlled phenomenon that should depend mainly on the dielectric constant of the medium (keeping viscosity almost constant), it is not true for all the exciplex systems since the nature of the magnetic field effect versus medium dielectric curves differ from each other in peak positions, peak heights and onset points. To investigate this differential nature, magnetic field effects among exciplex systems consisting of different derivatives of carbazole as electron donors are compared with a universal acceptor, 1,4-dicyano-benzene, with the pyrene—N,N-dimethylaniline exciplex system as reference. It was found that, apart from the solvent dielectric, the exciplex energy and the bulk effect of the steric constraints present on either donor or acceptor site, regulating the optimum inter-radical distance in the initially formed radical ion pair, are the key factors in controlling the magnetodynamic behaviour.