Dynamic analysis of space-related linear and non-linear structures

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized

Parametric studies of advanced turboprops

The effects of geometric variables (sweep and twist) on the structural performance of advanced turboprops are investigated. The investigation is limited to aerodynamically efficient turboprops using an acceptable design configuration as a baseline. The baseline configuration is modified using a seven by seven array of independently varying sweep and twist parameters while maintaining acceptable aerodynamic efficiency. The turboprop structural performance is evaluated in terms of critical speeds, tip displacements, and vibration frequencies where geometric nonlinearities are included. The results obtained are presented in such a manner as to highlight the effects of sweep and twist on the structural performance of aerodynamically efficient turboprop configurations

Grounding of Space Structures

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the \u27blanket\u27 of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as \u27grounding\u27, or false stiffening, of the stiffness matrix occurs during rigid body rotation. This paper examines the grounding phenomenon in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. A force imbalance inherent in the formulations examined is the likely cause of the grounding problem, suggesting the need for a directed force formulation

A New Preloaded Beam Geometric Stiffness Matrix with Full Rigid Body Capabilities

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the \u27blanket\u27 of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as \u27grounding, or false stiffening, of the stiffness matrix occurs during rigid body rotation. The authors have previously shown that the grounding phenomenon is caused by a lack of rigid body rotational capability, and is typical in beam geometric stiffness matrices formulated by others, including those which contain higher order effects. The cause of the problem was identified as the force imbalance inherent in the formulations. In this paper, the authors develop a beam geometric stiffness matrix for a directed force problem, and show that the resultant global stiffness matrix contains complete rigid body mode capabilities, and performs very well in the diagonalization methodology customarily used in dynamic analysis

Grounding of Space Structures

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the \u27blanket\u27 of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as \u27grounding\u27, or false stiffening, of the stiffness matrix occurs during rigid body rotation. This paper examines the grounding phenomenon in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. A force imbalance inherent in the formulations examined is the likely cause of the grounding problem, suggesting the need for a directed force formulation

Exponents of the localization lengths in the bipartite Anderson model with off-diagonal disorder

We investigate the scaling properties of the two-dimensional (2D) Anderson model of localization with purely off-diagonal disorder (random hopping). In particular, we show that for small energies the infinite-size localization lengths as computed from transfer-matrix methods together with finite-size scaling diverge with a power-law behavior. The corresponding exponents seem to depend on the strength and the type of disorder chosen.Comment: 6 pages, 8 EPS-figures, requires phbauth.cl

Unitary limit and quantum interference effect in disordered two-dimensional crystals with nearly half-filled bands

Based on the self-consistent $T$-matrix approximation, the quantum interference (QI) effect is studied with the diagrammatic technique in weakly-disordered two-dimensional crystals with nearly half-filled bands. In addition to the usual 0-mode cooperon and diffuson, there exist $\pi$-mode cooperon and diffuson in the unitary limit due to the particle-hole symmetry. The diffusive $\pi$-modes are gapped by the deviation from the exactly-nested Fermi surface. The conductivity diagrams with the gapped $\pi$-mode cooperon or diffuson are found to give rise to unconventional features of the QI effect. Besides the inelastic scattering, the thermal fluctuation is shown to be also an important dephasing mechanism in the QI processes related with the diffusive $\pi$-modes. In the proximity of the nesting case, a power-law anti-localization effect appears due to the $\pi$-mode diffuson. For large deviation from the nested Fermi surface, this anti-localization effect is suppressed, and the conductivity remains to have the usual logarithmic weak-localization correction contributed by the 0-mode cooperon. As a result, the dc conductivity in the unitary limit becomes a non-monotonic function of the temperature or the sample size, which is quite different from the prediction of the usual weak-localization theory.Comment: 21 pages, 4 figure