The general solution to the classical problem of the finite Euler-Bernoulli beam

Summary An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler-Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

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Zusammenfassung Eine analytische Lösung wird angegeben für das Problem der freien und erzwungenen Schwingungen eines endlichen Euler-Bernoulli-Balkens bei beliebigen (teilweise fixierten) Randbedingungen. Die Einflüsse einer linearen Reibungsdämpfung, der Winkler-Einbettung, einer konstanten axialen Spannung, der konzentrierten Massen, sowie von beliebigen Anregungsfunktionen werden in der Lösung berücksichtigt. Es werden keine Einschränkungen bezüglich der Parameter des Problems angenommen, und die Lösung enthält alle früheren zitierten Lösungen als besondere Fälle.

     

Mechanical properties of magnetically oriented epoxy

The microstructure of an epoxy system oriented in high magnetic fields (15–25 T) has been observed to consist of highly oriented domains at the molecular level along the direction of the applied field. The changes in the microstructure have been characterized as a function of the magnetic‐field strength and have been investigated microscopically and with wide‐angle X‐ray diffraction. The mechanical properties of the epoxy have been examined in light of nanoindentation experiments at different load levels. The basic results of the experimental investigations for the effect of high magnetic fields on the structure and property of the epoxy are presented. Nanoindentation testing has revealed large differences in the nanomechanical behavior for thermomagnetically processed epoxy specimens. The differences can be ascribed to the microstructural changes (reorientation) of the polymer at the molecular level. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1586–1600, 2004     

cis-Selective synthesis of 2,5-disubstituted pyrrolidines

A concise approach to cis-2,5-disubstituted pyrrolidines is reported, which relies upon N-tert-butoxycarbonylmethyl substitution in a substrate derived from pyroglutamic acid. The method is especially noteworthy since a significant improvement in the conditions for a key Lawesson’s reaction have been established. Regioselective enolate generation and alkylation permits extension of the C-5 side chain.     

Dielectric studies of metal complexes of thiourea crystals for electro‐optic modulation

In the present study three crystals of thiourea family viz. Zinc Thiourea Chloride (ZTC), Zinc Thiourea Sulfate (ZTS) and Bisthiourea Cadmium Chloride (BTCC) were grown from aqueous solution by slow evaporation technique. The grown crystals were studied by powder XRD, FT‐IR and UV‐visible. The dielectric study of grown crystals was carried out in X‐band using transmission line wave guide method. It was found that the BTCC has lowest dielectric constant among three metal complexes of thiourea crystals (ZTC, ZTS and BTCC), therefore it can be used for high speed electro‐optic modulation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

2,5-Disubstituted pyrrolidines: versatile regioselective and diastereoselective synthesis by enamine reduction and subsequent alkylation

A direct and versatile route enabling the regio- and diastereoselective synthesis of 2,5-disubstituted pyrrolidines by reduction of enamines derived from pyroglutamic acid is reported.     

Modeling laser-assisted particle removal using molecular dynamics

Laser-assisted particle removal, a method of cleaning nano- to micro-scale particles from surfaces, was modeled using molecular dynamics. A two-dimensional molecular model consisting of substrate, particle, and adsorbed fluid was used. In order to obtain statistical accuracy of cleaning efficiencies, over 1200 particle-removal simulations were conducted. The effects of fluid thickness and substrate temperature were both considered, and good qualitative agreement with experimental results was obtained. The molecular dynamics approach is shown to be an effective way to study these systems. PACS 81.65.Cf; 79.20.Ds     

Single crystal growth,structural, optical,mechanical, dielectric and thermal studies of formic acid doped potassium dihydrogen phosphate crystal for NLO applications

Optically transparent formic acid (FA) doped potassium dihydrogen phosphate (KDP) crystal of dimension 21×15×9 mm³ has been grown by slow evaporation solution technique (SEST). The X‐ray diffraction (XRD) technique was used to confirm the cell parameters and the shifts in peak positions of identified reflecting planes. The incorporation of FA in KDP has been qualitatively analyzed by fourier transform infrared analysis. The UV‐visible absorption spectrum of crystals has been recorded in the range of 200 to 900 nm and the doped KDP crystal is found to have improved optical parameters than pure KDP. The color centered photoluminescence emission spectrum of grown crystal has been illustrated in visible region. The mechanical behavior of pure and doped KDP crystal has been investigated using the Vicker's microhardness analyzer and hardness parameters have been calculated. The effect of FA on thermal stability of KDP crystal was examined by means of thermogravimetric and differential thermal analysis. The temperature dependent dielectric behavior of crystals was studied.     

Synthesis of Arylnaphthoquinones and Their Reactions with o‐Substituted Primary Aromatic Amines

Cycloaddition reaction of 2‐aryl‐1,4‐benzoquinones 1a‐d with a number of different dienes, namely 2,3‐dimethylbutadiene; 1,4‐diphenylbutadiene and anthracene yield 2‐aryl‐6,7‐dimethyl‐1,4‐ naphthoquinones 3a,b ; 2,5,8‐triphenyl‐1,4‐naphthoquinone 4 and 2‐aryl‐1,4,9,10‐tetrahydro‐9,10‐o‐benzoanthracene‐1,4‐dione 5 , respectively were investigated. In addition, the cycloaddition reaction of 2‐aryl‐1,4‐benzoquinones 1d,e with 2,3‐dimethylbutadiene was also investigated to yield 2‐aryl‐5,8‐dihydro‐6,7‐dimethyl‐1,4‐naphthohydroquinones 2a,b . Cyclocondensation reactions of Diels‐Alder adducts 2b, 3b, 5a with ethylenediamine, o‐substituted primary aromatic amines gave quinoxaline, phenazine, phenoxazine and phenothiazine ocyclic derivatives 6–14.     

Growth and high frequency dielectric study of pure and thiourea doped KDP crystals

Non linear optical (NLO) materials have acquired new significance with the advent of a large number of devices utilizing solid‐state laser sources. Several NLO materials have been used for this kind of technological applications. The Potassium di‐hydrogen phosphate (KDP) one of NLO material having superior non linear optical properties has been exploited for variety of applications. In the present investigation we have grown KDP crystals from aqous solution with thiourea, an organic non linear optical material. We could enhance the SHG efficiency of thiourea doped KDP crystal. It was 1.99 times more that of pure KDP. We observed more enhancements in nonlinearity for low concentration of thiourea.The crystal structure and cell parameters of grown crystal were determined from Powder XRD.The incorporation of thiourea in the grown crystals was qualitatively analyzed from FT‐IR study. The absorption spectra of pure and thiourea doped KDP crystal reveal that thiourea doped KDP crystals would be a better nonlinear optical (NLO) material for second harmonic generation (SHG) than pure KDP. The thermal decomposition and weight loss of pure and thiourea doped KDP crystal was observed by thermogravimetric (TGA) analysis and Differential Scanning Calorimetry (DSC). The high frequency dielectric study of pure KDP crystal, thiourea doped KDP crystals and organic additive thiourea was carried out using X‐band at frequency 8GHZ and 12GHZ by transmission line wave guide method. We observed low dielectric constant of thiourea doped KDP crystal when it is doped with 2mole% of thiourea. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)