One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges

In this paper the dynamics of axisymmetric, slender, viscous liquid bridges having volume close to the cylindrical one, and subjected to a small gravitational field parallel to the axis of the liquid bridge, is considered within the context of one-dimensional theories. Although the dynamics of liquid bridges has been treated through a numerical analysis in the inviscid case, numerical methods become inappropriate to study configurations close to the static stability limit because the evolution time, and thence the computing time, increases excessively. To avoid this difficulty, the problem of the evolution of these liquid bridges has been attacked through a nonlinear analysis based on the singular perturbation method and, whenever possible, the results obtained are compared with the numerical ones.

Long-term dynamics of fast rotating tethers around planetary satellites

We derive a semi-analytic formulation that enables the study of the long-term dynamics of fast-rotating inert tethers around planetary satellites. These equations take into account the coupling between the translational and rotational motion, which has a non-negligible impact on the dynamics, as the orbital motion of the tether center of mass strongly depends on the tether plane of rotation and its spin rate, and vice-versa. We use these governing equations to explore the effects of this coupling on the dynamics, the lifetime of frozen orbits and the precession of the plane of rotation of the tether.

Nonlinear seismic behaviour of concrete arch bridges

Arch bridge structural solution has been known for centuries, in fact the simple nature of arch that require low tension and shear strength was an advantage as the simple materials like stone and brick were the only option back in ancient centuries. By the pass of time especially after industrial revolution, the new materials were adopted in construction of arch bridges to reach longer spans. Nowadays one long span arch bridge is made of steel, concrete or combination of these two as "CFST", as the result of using these high strength materials, very long spans can be achieved. The current record for longest arch belongs to Chaotianmen bridge over Yangtze river in China with 552 meters span made of steel and the longest reinforced concrete type is Wanxian bridge which also cross the Yangtze river through a 420 meters span. Today the designer is no longer limited by span length as long as arch bridge is the most applicable solution among other approaches, i.e. cable stayed and suspended bridges are more reasonable if very long span is desired. Like any super structure, the economical and architectural aspects in construction of a bridge is extremely important, in other words, as a narrower bridge has better appearance, it also require smaller volume of material which make the design more economical. Design of such bridge, beside the high strength materials, requires precise structural analysis approaches capable of integrating the combination of material behaviour and complex geometry of structure and various types of loads which may be applied to bridge during its service life. Depend on the design strategy, analysis may only evaluates the linear elastic behaviour of structure or consider the nonlinear properties as well. Although most of structures in the past were designed to act in their elastic range, the rapid increase in computational capacity allow us to consider different sources of nonlinearities in order to achieve a more realistic evaluations where the dynamic behaviour of bridge is important especially in seismic zones where large movements may occur or structure experience P - _ effect during the earthquake. The above mentioned type of analysis is computationally expensive and very time consuming. In recent years, several methods were proposed in order to resolve this problem. Discussion of recent developments on these methods and their application on long span concrete arch bridges is the main goal of this research. Accordingly available long span concrete arch bridges have been studied to gather the critical information about their geometrical aspects and properties of their materials. Based on concluded information, several concrete arch bridges were designed for further studies. The main span of these bridges range from 100 to 400 meters. The Structural analysis methods implemented in in this study are as following: Elastic Analysis: Direct Response History Analysis (DRHA): This method solves the direct equation of motion over time history of applied acceleration or imposed load in linear elastic range. Modal Response History Analysis (MRHA): Similar to DRHA, this method is also based on time history, but the equation of motion is simplified to single degree of freedom system and calculates the response of each mode independently. Performing this analysis require less time than DRHA. Modal Response Spectrum Analysis (MRSA): As it is obvious from its name, this method calculates the peak response of structure for each mode and combine them using modal combination rules based on the introduced spectra of ground motion. This method is expected to be fastest among Elastic analysis. Inelastic Analysis: Nonlinear Response History Analysis (NL-RHA): The most accurate strategy to address significant nonlinearities in structural dynamics is undoubtedly the nonlinear response history analysis which is similar to DRHA but extended to inelastic range by updating the stiffness matrix for every iteration. This onerous task, clearly increase the computational cost especially for unsymmetrical buildings that requires to be analyzed in a full 3D model for taking the torsional effects in to consideration. Modal Pushover Analysis (MPA): The Modal Pushover Analysis is basically the MRHA but extended to inelastic stage. After all, the MRHA cannot solve the system of dynamics because the resisting force fs(u; u_ ) is unknown for inelastic stage. The solution of MPA for this obstacle is using the previously recorded fs to evaluate system of dynamics. Extended Modal Pushover Analysis (EMPA): Expanded Modal pushover is a one of very recent proposed methods which evaluates response of structure under multi-directional excitation using the modal pushover analysis strategy. In one specific mode,the original pushover neglect the contribution of the directions different than characteristic one, this is reasonable in regular symmetric building but a structure with complex shape like long span arch bridges may go through strong modal coupling. This method intend to consider modal coupling while it take same time of computation as MPA. Coupled Nonlinear Static Pushover Analysis (CNSP): The EMPA includes the contribution of non-characteristic direction to the formal MPA procedure. However the static pushovers in EMPA are performed individually for every mode, accordingly the resulted values from different modes can be combined but this is only valid in elastic phase; as soon as any element in structure starts yielding the neutral axis of that section is no longer fixed for both response during the earthquake, meaning the longitudinal deflection unavoidably affect the transverse one or vice versa. To overcome this drawback, the CNSP suggests executing pushover analysis for governing modes of each direction at the same time. This strategy is estimated to be more accurate than MPA and EMPA, moreover the calculation time is reduced because only one pushover analysis is required. Regardless of the strategy, the accuracy of structural analysis is highly dependent on modelling and numerical integration approaches used in evaluation of each method. Therefore the widely used Finite Element Method is implemented in process of all analysis performed in this research. In order to address the study, chapter 2, starts with gathered information about constructed long span arch bridges, this chapter continuous with geometrical and material definition of new models. Chapter 3 provides the detailed information about structural analysis strategies; furthermore the step by step description of procedure of all methods is available in Appendix A. The document ends with the description of results and conclusion of chapter 4.

Estabilidad de puentes líquidos bajo el efecto de una rotación no axilsimétrica

El estudio de la influencia de perturbaciones de distinta naturaleza en configuraciones de puentes líquidos apoyados en dos discos coaxiales en rotación encuentra una importante motivación en el uso de dicha configuración en la fabricación de cristales semiconductores ultra-puros por la denominada técnica de zona flotante, en la que la rotación de los discos se utiliza para alcanzar temperaturas uniformes. El presente estudio muestra los resultados obtenidos mediante la aplicación de un método numérico en el análisis de la estabilidad de puentes líquidos en isorrotación sometidos al efecto de una fuerza axial uniforme (gravedad axial) y una excentricidad entre el eje de giro y el eje de los discos. Se analiza el efecto de la aplicación de estos factores tanto de forma conjunta como por separado. Aunque existen numerosos estudios previos sobre puentes líquidos sometidos a diversos efectos, el análisis del efecto combinado de la rotación con excentricidad y gravedad axial no ha sido realizado con anterioridad. Este estudio permite además entender los resultados del experimento a bordo de la misión TEXUS-23, en el que un puente líquido sujeto entre dos discos circulares y coaxiales es sometido al efecto de una rotación creciente en torno a un eje desplazado respecto al eje de los discos. Aunque en el experimento no se impone una fuerza axial controlada, la desestabilización y rotura del puente se produce de forma notablemente asimétrica, lo que no puede ser explicado con los estudios precedentes y sugiere una posible presencia de una aceleración axial residual. Se ha desarrollado por tanto un método de análisis de imágenes que permite comparar las formas obtenidas en el experimento con las calculadas numéricamente. En este estudio se muestran los detalles del procesado realizado en las imágenes de la misión TEXUS-23, y los resultados de su comparación con el análisis numérico, que permiten determinar el valor de la gravedad axial que mejor reproduce los resultados del experimento. Estos resultados ponen de manifiesto la importancia del conocimiento y la modelización de efectos cuya presencia (intencionada o no) afectan de forma visible a la estabilidad y la morfología de los puentes líquidos. ABSTRACT The study of the influence of various disturbances in configurations consisting of a liquid bridge supported by two co-axial disks in rotation has an important motivation in the use of this configuration in the fabrication of ultrapure semiconductor crystals via the so-called floating zone technique, in which the rotation of the disks is used to achieve a uniform temperature field. The present study shows the results obtained through the application of a numerical method in the analysis of the stability of liquid bridges in isorotation under the effect of a uniform axial force field (axial gravity) and an offset between the rotation axis and the axis of the supporting disks (eccentricity). The analysis studies the effect of both the combined and separate application of these factors. Although there are numerous studies on liquid bridges subject to various effects, the analysis of the combined effect of rotation with eccentricity and axial gravity has not been done before. Furthermore, this study allows us to understand the results from the experiment aboard the TEXUS-23 mission, in which a liquid bridge supported between two circular-shaped, co-axial disks is subject to the effect of an increasing rotation around an axis with an offset with respect to the axis of the disks. Although the experiment conditions do not include a controlled axial force field, the instability and breakage of the bridge occurs with a marked asymmetry, which cannot be explained by previous studies and suggests the possible presence of a residual axial gravity. Therefore, an image analysis method has been developed which allows to compare the shapes obtained in the experiment with those calculated with the numerical method. This study shows the details of the processing performed on the images from the TEXUS-23 mission and the results from their comparison with the numerical analysis, which allow to determine the axial gravity value which best recovers the experimental results. These results highlight the importance of the understanding and modelling of effects which, when present (intentionally or not), noticeably affect the stability and shape of the liquid bridges.