An analytical study of the non-linear vibrations of cylindrical shells

The primary resonance response of simply supported circular cylindrical shells is investigated using the perturbation method. Donnell's non-linear shallow-shell theory is used to derive the governing partial differential equations of motion. The Galerkin technique is then employed to transform the equations of motion into a set of temporal ordinary differential equations. Considering only the primary resonance case, the method of multiple scales is used to study the periodic solutions and their stability. The necessary and sufficient conditions for appearance of the so-called companion mode are also discussed. To this end, a range of the possible multi-mode solution is obtained for response and excitation amplitudes and also excitation frequency as a function of damping, geometry and material properties of the shell. Parametric studies are performed to illustrate the effect of different values of thickness, length and material composition on the possibility of the companion mode participation in primary resonance response.     

Synthesis and characterization of [Cu(Phca2en)(PPh3)X] (X=Cl, Br, I, NCS, N3) complexes: crystal structures of [Cu(Phca2en)(PPh3)Br] and [Cu(Phca2en)(PPh3)I]

New mixed-ligand copper(I) complexes, [Cu(Phca₂en)(PPh₃)X], [Phca₂en = N,N′-bis(β-phenylci-nnamaldehyde)-1,2-diiminoethane and X=Cl (1), Br (2), I (3), NCS (4), N₃ (5)] have been synthesized and characterized by various techniques. ¹H and ¹³C-NMR and IR spectral data of these copper(I) complexes are compared with the free ligand to elucidate some structural features. The structures of [Cu(Phca₂en)(PPh₃)Br] (2) and [Cu(Phca₂en)(PPh₃)I] (3) have been determined from single-crystal data showing that the coordination geometry around copper atom is a distorted tetrahedron. Furthermore, these Cu(I) complexes exhibit supramolecular motifs of the type multiple phenyl embraces resulting from attractive interactions between phenyl rings of PPh₃ moieties. The presence of the C–H…Cu weak intramolecular hydrogen bonds, due to the trapping of C–H bonds in the vicinity of the metal atoms, is also reported.     

Evidence of Long-Range 13C-31P Couplings: A 13C NMR Investigation of Some Aryl Esters of Phosphor-Amidochloridic Acid and the Related Compounds

Abstract

In ¹³ NMR study organophosphorus compounds, sign and magnitude of ¹³ C-³¹ P spin-spin couplings has been of great interest to elucidate stereochemistry and electronic state of phosphorus central atom. However, a discussion about the mechanisms of carbon-phosphorus couplings is still complicated specially in the case of long-range couplings that also are not frequently observed. In this study, ¹³ C NMR chemical shifts and coupling constants have been determined for a series of aryl esters of phosphoramidochloridic acid with the general formula: R₂NP(O)(OAr)Cl, in which R = methyl and/or benzyl, Ar = p-tolyl. p-nitrophenyl, and phenyl. Besides usual W-couplings that could be found in these systems, we detected long-range couplings through five and six bonds. It has been shown that, these couplings are highly dependent on substituents on phosphorus nuclei. The data for some related compounds have been also obtained for a comparison.     

Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the galilean space

In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G₃. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G₃.     

Lentivirus-mediated transgene delivery to the hippocampus reveals sub-field specific differences in expression

Background  

In the adult hippocampus, the granule cell layer of the dentate gyrus is a heterogeneous structure formed by neurons of different ages, morphologies and electrophysiological properties. Retroviral vectors have been extensively used to transduce cells of the granule cell layer and study their inherent properties in an intact brain environment. In addition, lentivirus-based vectors have been used to deliver transgenes to replicative and non-replicative cells as well, such as post mitotic neurons of the CNS. However, only few studies have been dedicated to address the applicability of these widespread used vectors to hippocampal cells in vivo. Therefore, the aim of this study was to extensively characterize the cell types that are effectively transduced in vivo by VSVg-pseudotyped lentivirus-based vectors in the hippocampus dentate gyrus.     

Dynamic stability of functionally graded cantilever cylindrical shells under distributed axial follower forces

In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the critical circumferential mode number and the minimum flutter load is investigated. As expected, the flutter load increases as the follower force changes from the so-called Beck's load into the so-called Leipholz's and Hauger's loadings. The increased flutter load was calculated for homogeneous shell with different mechanical properties, and it was found that the difference in elasticity moduli bears the most significant effect on the flutter load increase in short, thick shells. Also, for an FGM shell, the increase in the flutter load was calculated directly, and it was found that it can be derived from the simple power law when the corresponding increase for the two base phases are known.     

The nature of the supramolecular association of 1,2,5-chalcogenadiazoles

Organochalcogen-nitrogen heterocycles such as the 1,2,5-chalcogenadiazoles have a distinct tendency to establish intermolecular links in the solid state through secondary bonding interactions E...N (E = S, Se, Te). The association of these molecules was examined in detail using relativistic density functional theory. Although there is an important electrostatic component, the interaction between these molecules is dominated by contributions arising from orbital mixing, which can be interpreted as the donation of a nitrogen lone pair into the chalcogen-centered antibonding orbitals. Because of its more polar character and lower-lying antibonding orbitals, the tellurium derivatives possess the strongest association energies; these are so large that the binding strength is comparable to that of some hydrogen bonds. In the absence of steric constraints, telluradiazoles associate in a coplanar fashion forming ribbon polymers. However, bulky susbstituents could be used to direct the formation of either helical chains or discrete dimers. In addition to its strength, the coplanar dimer is characterized by being rigid, yet no activation barrier is expected for the association/dissociation process. These attributes strongly indicate that tellurium-nitrogen heterocycles have great potential as building blocks in supramolecular architecture.