Zum Nachweis und zur Bestimmung des Titans

Ohne Zusammenfassung     

Significance of sample dimensions and other parameters for characterizing drawing process of polymer films

Summary Uniaxial drawing of polymer samples by tensile testing, machines usually is characterized by drawing temperature, velocity and ratio. These data in general do not succeed in describing the drawing process completely, therefore different and/or additional parameters are necessary for characterization of drawing process.Striplike specimens of polyamide 6 and polyethylene terephthalate films were cut and drawn to a constant draw ratio. Especially sample dimensions, drawing velocity, drawing temperature and ambient medium were varied. Local draw ratio, birefringence and yield stresses were investigated.

---

Zusammenfassung Die Herstellung uniaxial verstreckter Proben mit Hilfe einer Zugpriifmaschine wird üblicherweise durch Angabe von Verstrecktemperatur, relativer Verstreckgeschwindigkeit und Verstreckgrad beschrieben. Es wird gezeigt, dag diese Angaben i. a. nicht ausreichen, um den Verstreckvorgang zu beschreiben, dag hingegen andere und/oder zusätzliche Verstreckparameter eine vollständige Charakterisierung des Verstreckprozesses eher ermöglichen. Hierzu werden aus Polyamid- und Polyäthylenterephthalat-Folien geschnittene Polymerbänder unter Variation von Probendimensionen, absoluter Verstreckgeschwindigkeit, Verstrecktemperatur und Umgebungsmedium uniaxial auf den gleichen relativen Verstreckgrad gedehnt und auf ihre lokale Dehnung und ihre Doppelbrechung hin untersucht.

---

---

With 11 figures and 1 table     

Zur Struktur verstreckter Folien und Fäden sowie aus verdünnten Lösungen hergestellter Einkristalle aus Polyacrylnitril

Zusammenfassung Kolloid- und Kristallstruktur von verstreckten Folien und Fäden und aus verdünnten Lösungen hergestellten Einkristallen von Polyacrylnitril wurden mit Hilfe von Röntgenklein- und -weitwinkeluntersuchungen, Elektronenbeugung und Elektronenmikroskopie untersucht. Es kann gezeigt werden, da entgegen den bisher publizierten Ergebnissen bei dem verstreckten Polyacrylnitril eine periodische Abfolge von besser und schlechter geordneten Bereichen erzielt werden kann, die sich in dem Auftreten einer röntgenografisch erfaßbaren Langperiode äußert und, wie die vergleichenden Untersuchungen an Einkristallen zeigen, durch eine Zwei-Phasen-Struktur beschrieben werden kann. Innerhalb der besser geordneten Bereiche ordnen sich die Ketten, indem ein zwar stark gestörtes, aber dreidimensionales Gitter mit der orthorhombischen Elementarzellea=10,6 Å,b=11,6 Å,c=5,04 Å aufgebaut wird. Kristallisationsfähig sind nur die syndiotaktischen Kettensequenzen des Polyacrylnitrils.

---

Summary Colloidal and crystallographic structure of drawn films and solution grown single crystals of polyacrylonitrile were investigated by small and wide angle X-ray scattering, electron scattering and electron microscopical observations. In contrast to the published results it is shown that in the case of drawn polyacrylonitrile there exists a periodical arrangement of more and less ordered regions which manifests in the appearance of a so called long period and which — as shown by comparative investigations on single crystals — can be described by a two-phase-model. Within the ordered regions chains are arranged building up a strongly disturbed but three-dimensional crystal lattice. The orthorhombic unit cell has the dimensiona=10,6 Å,b=11,6 Å,c=5,04 Å. Only the syndiotactic chain sequences are able to crystallize.

---

---

Vorgetragen auf der Arbeitssitzung des Fachausschusses Physik der Hochpolymeren in der Frühjahrstagung Berlin 1971 vom 9. bis 13. März des Regionalverbandes Physikalische Gesellschaft zu Berlin.

---

Für die Hilfe bei den experimentellen Arbeiten danken die Verfasser FräuleinM. Collatz und den HerrenE. Vey undH. Gladbach.     

IMPROVEMENT OF THE SEMI-ANALYTICAL METHOD, FOR DETERMINING THE GEOMETRICALLY NON-LINEAR RESPONSE OF THIN STRAIGHT STRUCTURES. PART I: APPLICATION TO CLAMPED-CLAMPED AND SIMPLY SUPPORTED-CLAMPED BEAMS

In a previous series of papers (Benamar 1990 Ph.D. Thesis, University of Southampton; Benamaret al. 1991 Journal of Sound and Vibration149, 179-195;164, 399-424 [1-3]) a general model based on Hamilton's principle and spectral analysis has been developed for non-linear free vibrations occurring at large displacement amplitudes of fully clamped beams and rectangular homogeneous and composite plates. The results obtained with this model corresponding to the first non-linear mode shape of a clamped-clamped (CC) beam and to the first non-linear mode shape of a CC plate are in good agreement with those obtained in previous experimental studies (Benamaret al. 1991 Journal of Sound and Vibration 149, 179-195;164, 399-424 [2, 3]). More recently, this model has been re-derived (Azar et al. 1999 Journal of Sound and Vibration224, 377-395; submitted [4, 5]) using spectral analysis, Lagrange's equations and the harmonic balance method, and applied to obtain the non-linear steady state forced periodic response of simply supported (SS), CC, and simply supported-clamped (SSC) beams. The practical application of this approach to engineering problems necessitates the use of appropriate software in each case or use of published tables of data, obtained from numerical solution of the non-linear algebraic system, corresponding to each problem. The present work was an attempt to develop a more practical simple “multi-mode theory” based on the linearization of the non-linear algebraic equations, written on the modal basis, in the neighbourhood of each resonance. The purpose was to derive simple formulae, which are easy to use, for engineering purposes. In this paper, two models are proposed. The first is concerned with displacement amplitudes of vibrationW_max /H, obtained at the beam centre, up to about 0·7 times the beam thickness and the second may be used for higher amplitudes W_max/H up to about 1·5 times the beam thickness. This new approach has been successfully used in the free vibration case to the first, second and third non-linear modes shapes of CC beams and to the first non-linear mode shape of a CSS beam. It has also been applied to obtain the non-linear steady state periodic forced response of CC and CSS beams, excited harmonically with concentrated and distributed forces.     

Embedding Uq(sl(2)) and Sine Algebras in Generalized Clifford Algebras

We establish the connection between certain quantum algebras and generalizedClifford algebras (GCA). To be precise, we embed the quantum tori Lie algebraand U _q (sl(2)) in GCA.