Application of an Itô-based approximation method to random vibration of a pinching hysteretic system

In this paper, an extension of the Cumulant-Neglect closure scheme is utilized for the random vibration analysis of a single degree of freedom system with a general pinching hysteresis restoring force. The hysteresis element used in the system model can simulate commonly observed forms of stiffness, strength and pinching degradations. The second order statistics of the system response to a stationary Gaussian white noise input are derived using an Itô-based approximation technique. The validity of these response statistics are then verified by comparing them to Monte Carlo simulation results. The numerical studies performed for different combinations of degradation parameters and excitation levels show that the response estimates obtained by this solution method are in good agreement with Monte Carlo simulation. These studies also indicate the applicability of this technique for response analysis of complicated forms of non-linearities.     

A consideration of curved interfaces in stress-assisted martensite formation

A purely mechanical, sharp interface model is developed to consider curved interfaces that have been observed between martensite phase variants. The approach is based on a theory of small strains as distinct from small displacement gradients. It admits a realistic characterization of each phase with standard elasticity tensors and allows for inhomogeneous states of strain within each phase including inhomogeneous, finite rotations. The model indicates that any signficant interface curvature must be due to material rotation because interfaces cannot be finitely curved with respect to the material lattice. It is also found that the interface driving traction is not influenced by local lattice rotations unless inertia affects the reaction.     

Water waves in a suspended container

Analysis and experiments are carried out on a horizontal rectangular wave tank which swings at the lower end of a pendulum. The walls of the tank generate waves which affect the motion of the pendulum. For small displacements of the tank, linearised shallow water equations are used to model the motion, and there exist time-periodic solutions for the system whose periods are governed by a transcendental relation. Numerical and analytic solutions of this relation show that the fundamental period is greater than both the period of the empty tank (moving like a simple pendulum) and the fundamental period of the standing wave which occurs when the tank is removed from its supports and held fixed. For a rectangular tank the theory compares well with some experimental measurements. Qualitative observations are also made of the effect of breaking waves on the tank motion: for a tank which has a mass small compared with its load the energy dissipated by breaking waves can rapidly reduce the amplitude of swing of the tank. Potential flow theory is used with linearised free-surface boundary conditions to find time periodic motions for a tank with a hyperbolic cross section.     

Hydrodynamically induced crystallization of polymers from solution

Summary This paper deals with a study on the melting behaviour of polyethylene crystals showing a fibrillar morphology. These crystals were prepared by hydrodynamically induced crystallization from xylene solutions. Use was made of several techniques, such as differential scanning calorimetry, polarizing microscopy and infrared dichroism. The experimental observations indicate that the melting process of the fibrous crystals can only partly be related to morphological structures. The infrared dichroism and persistent birefringence up to temperatures of 200 °C are due mainly to the molecular orientation in the melt. The shrinkage on melting was found to depend on the thickness of and fibre orientation in the sample, as well as on the molecular weight of the polyethylene. A maximum shrinkage value of 93% was measured on fibrillar crystals of Marlex (M _w =90 · 10³). Calorimetric studies on the fusion of fibrillar crystals of high molecular weight polyethylene (M _w =1.5 · 10⁶) revealed that extendedchain backbones melt at 150 °C and even at 180 °C. The melt of these crystal structures remains partly oriented, as could be inferred from the constant temperature position of the melting peak on repeated crystallizing and melting.The areas of the melting peaks at 150 °C and 180 °C were found to depend on the maximum temperature at which the samples were heated and, in addition, on the exposure time. From measurements of the area of the backbone crystallization peak as a function of time and heating temperature, an apparent activation energy of 100 kcal/mole was derived, which suggests that several chains are simultaneously involved in the relaxation of structural order of the backbone melt.The melting temperatures of the lamellar over-growth and backbones were found to increase with the crystallization temperature of the fibrillar crystals. The melting studies also suggest that extended-chain fibrillar crystals can be formed in xylene solutions at a low temperature (85 °C) if the stirrer speed is sufficiently high.

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Zusammenfassung Dieser Bericht befaßt sich mit einem Studium des Schmelzverhaltens von Polyäthylen-Kristallen, welche eine faserige Morphologie aufweisen. Diese Kristalle werden durch eine hydrodynamisch induzierte Kristallisation aus Xylollösungen hergestellt. Es werden verschiedene Techniken angewandt, z. B. differential scanning calorimetry, Polarisationsmikroskopie und Ultrarot-Dichroismus.Die experimentellen Beobachtungen zeigen, daß es nur teilweise eine Beziehung zwischen dem Schmelzvorgang der faserigen Kristalle und morphologischen Strukturen gibt. Der Ultrarot-Dichroismus und die anhaltende Doppelbrechung bis zu Temperaturen von 200 °C sind hauptsächlich auf die Molekularorientierung in der Schmelze zurückzuführen.Die Kontraktion beim Schmelzvorgang wird, wie sich herausstellt, bedingt durch die Dicke der Probe und die Orientierung der Fasern in der Probe, sowie durch das Molekulargewicht des Polyäthylens. Eine maximale Kontraktion von 93% wird bei faserigen Kristallen von Marlex gemessen (M _w =90 · 10³). Kalorimetrische Untersuchungen des Schmelzvorgangs faseriger Kristalle von Polyäthylen mit hohem Molekulargewicht (M _w =1,5 · 10⁶) ergeben, daß extended-chain-Faserkerne bei 150 °C und sogar bei 180 °C schmelzen.Die Schmelze dieser Kristallstrukturen bleibt teilweise orientiert, wie aus der konstanten Temperaturlage des Schmelzpeaks nach wiederholtem Kristallisieren und Schmelzen abgeleitet werden kann.Es stellt sich heraus, daß die Oberfläche der Schmelzpeaks bei 150 und 180 °C bedingt wird durch die maximale Temperatur, bei der die Proben erhitzt werden, und darüber hinaus durch die Erhitzungszeit. Anhand der gemessenen Oberfläche der Kristallisationspeaks der Faserkerne als Funktion von Zeit und Erhitzungstemperatur wird eine scheinbare Aktivierungsenergie von 100 kcal/Mol festgestellt; dies deutet darauf hin, daß mehrere Ketten gleichzeitig an der Relaxation der strukturellen Ordnung der Faserkernschmelze beteiligt sind. Es ergibt sich, daß die Schmelztemperaturen der Lamellarüberwachsung und Faserkerne mit der Kristallisationstemperatur der faserigen Kristalle zunehmen. Die Schmelzuntersuchungen deuten auch darauf hin, daß extended-chain-Faserkerne bei niedriger Temperatur (85 °C) in Xylollösungen gebildet werden können, wenn nur die Rührgeschwindigkeit ausreichend hoch ist.

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Paper presented at the Symposium at Leende of De Nederlandse Rheologische Vereniging on 21st and 22nd May 1970.     

Test-time extension behind reflected shock waves using CO2–He and C3H8–He driver mixtures

To study combustion chemistry at low temperatures in a shock tube, it is of great importance to increase experimental test times, and this can be done by tailoring the interface between the driver and driven gases. Using unconventional driver-gas tailoring with the assistance of tailoring curves, shock-tube test times were increased from 1 to 15 ms for reflected-shock temperatures below 1,000 K. Provided in this paper is the introduction of tailoring curves, produced from a one-dimensional perfect gas model for a wide range of driver gases and the production and demonstration of successful driver mixtures containing helium combined with either propane or carbon dioxide. The He/CO₂ and He/C₃H₈ driver mixtures provide a unique way to produce a tailored interface and, hence, longer test times, when facility modification is not an option. The tailoring curves can be used to guide future applications of this technique to other configurations. Nonreacting validation experiments using driver mixtures identified from the tailoring curves were performed over a range of reflected-shock temperatures from approximately 800 to 1,400 K, and some examples of ignition-time experiments that could not have otherwise been erformed are presented.