Oddvar O. Bendiksen

Design and development of NIRSPEC: a near-infrared echelle spectrograph for the Keck II telescope

The design and development of NIRSPEC, a near-IR echelle spectrograph for the Keck II 10-meter telescope is described. This instrument is a large, facility-class vacuum-cryogenic spectrometer with a resolving power of R equals 25,000 for a 0.4 inch slit. It employs diamond-machined metal optics and state-of-the-art IR array detectors for high throughput, together with powerful user-friendly software for ease of use.

Mode localization phenomena in large space structures

The possibility of localization or confinement of vibratory modes in large space structures is investigated theoretically and numerically. These structures belong to a class of periodic structures that have recently been shown to be sensitive to periodicity-b reaking disorder or imperfections . When localization occurs, the modal amplitude of a global mode becomes confined to a local region of the structure, with serious implications for the control problem. The results of this study indicate that mode localization is most likely to occur in structures consisting of a large number of weakly coupled substructures. Certain large space structures with high modal densities fall in this category, and it is therefore important to include the effect of structural imperfections and disorder when designing control systems for shape or directional control of such structures. [ / ] K, Kh , Kw,Ku [K] [k] [M] [ m ] m n N p qi qt t u, v, w uf 8fj e 6

LOCALIZATION OF VIBRATIONS IN LARGE SPACE REFLECTORS

A study is presented of the mode localization phenomenon in a generic class of large space reflectors. The study is based on a Rayleigh-Ritz formulation using the first five cantilevered beam bending modes and a finite-element formulation using Bernoulli-Euler beam elements. Coupling between the structures is provided by massless axial members. Numerical results indicate that mode localization does, in fact, occur in engineering structures of this type. Localization is characterized by the amplitude of a global mode becoming confined to a local region of the structure. For the 18-rib reflector studied, the first rib bending mode did not localize, but the second and third modes did. Localization is found to become more severe with increasing mode number. Increasing the number of ribs to 48 resulted in significant distortion in some of the first rib bending modes and severe localization of the second and third bending modes. The phenomenon of wave confinement in finite structures is also demonstrated using a single-degree-of-freedom per substructure model. Nomenclature

Coupled Bending-Torsion Flutter in Cascades

A method is presented for determining the aeroelastic stability boundaries of a cascade with aerodynamic, inertial, and structural coupling between the bending and torsional degrees of freedom. A computer program has been written to systematically investigate the effect of this coupling on cascade stability over a wide range of design parameters. Results presented illustrate that the bending-torsion interaction has a pronounced effect on the cascade flutter boundary, despite no appreciable tendency toward frequency coalescence as flutter is approached. The analysis also indicates that bending flutter is possible even in the absence of finite mean lift.

Mode localization in multispan beams

The finite element method is used to study localization as a function of Timoshenko beam effects; beam end conditions; span length, mass, and stiffness imperfection; viscous damping; axial force; transverse support and rotational coupling stiffness; and modeling resolution. Three configurations are studied, starting with two separate 2-span models and culminating in a 10-span configuration that resembles lattice-type large space structures

Transonic panel flutter

FEM is here used to ascertain the stability and aeroelastic response of thin, 2D panels subjected to Mach 0.8-2.5 flows. In the absence of shocks, it is found that the Euler equations used to represent the unsteady flowfield dynamics predict response behaviors resembling those obtained via potential flow methods. Where shocks do play a significant role in the overall motion of the panel, divergence and limit cycle flutter are observed. In the Mach 1.4-1.5 range, flutter involved the higher modes of the panel, tending toward possible chaotic motion.

Unsteady transonic two-dimensional Euler solutions using finite elements

A finite element solution of the unsteady Euler equations is presented, and demonstrated for two-dimensional airfoil configurations oscillating in transonic flows. Computations are performed by spatially discretizing the conservation equations using the Galerkin weighted residual method and then employing a multistage RungeKutta scheme to march forward in time. Triangular finite elements are employed in an unstructured O-mesh computational grid surrounding the airfoil. Grid points are fixed in space at the far-field boundary and are constrained to move with the airfoil surface to form the near-field boundary. A mesh deformation scheme has been developed to efficiently move interior points in a smooth fashion as the airfoil undergoes rigid-body pitch and plunge motion. Both steady and unsteady results are presented, and a comparison is made with solutions obtained using finite volume techniques. The effects of using either a lumped or consistent mass matrix were studied and are presented. Results show the finite element method provides an accurate solution for unsteady transonic flows about isolated airfoils. HE accurate determination of the unsteady flowfield surrounding an oscillating airfoil or wing in transonic flow is of paramount importance in the prediction of the flutter characteristics of the body. Transonic flutter remains an active research topic because of the continued interest by both the military and commercial sectors to operate in these flight regimes with vehicles that are ever lighter and, as a result, more flexible. Typically, analysis of fluid-structure interaction in flight vehicles involves describing the vehicle structure using finite elements, whereas finite difference methods are used to model the surrounding fluid. Coupling of the two dissimilar models then presents problems because of the disparity between the two solution techniques. Additional complexities arise because of phase mismatching between the fluid pressures and the displacements of the structure. It seems a natural progression to use finite element methods to describe the behavior of both the fluid and structure, thus bringing more commonality into the analysis of the two media. Early research efforts concentrated on using the transonic small-disturbance equation or the nonlinear full potential equation as the model for the gas dynamic behavior in transonic flows. Unfortunately, this idealization leads to errors when strong shocks are present because of their inability to account for the production of entropy and vorticity. To properly account for these effects within the framework of the conservation laws, the Euler equations must be used. These equations, although they neglect fluid viscosity, have become the standard when unsteady transonic solutions are desired. The absence of a viscosity representation is an important limitation of the present formulation and must be considered

Nonlinear Flutter Calculations Using Finite Elements in a Direct Eulerian-Lagrangian Formulation

A fully nonlinear aeroelastic formulation of the direct Eulerian-Lagrangian computational scheme is presented in which both structural and aerodynamic nonlinearities are treated without approximations. The method is direct in the sense that the calculations are done at the finite element level, both in the fluid and structural domains, and the fluid-structure system is time-marched as a single dynamic system using a multistage Runge-Kutta scheme. The exact nonlinear boundary condition at the fluid-structure boundary is satisfied based on the actual deformation of the wing. The generalized forces associated with the in-plane and out-of-plane degrees of freedom are calculated in local Lagrangian element coordinate systems that fully account for large rigid-body translations and rotations. Finite rotation relations are used to update the nodal deformation vectors at the end of each time step. Numerical results are presented for several nonlinear static and dynamic examples for which published results are available. Results of aeroelastic calculations using the new nonlinear model demonstrate the importance of including the nonlinear stiffening arising from the in-plane strains when calculating limit-cycle-oscillation amplitudes of wings of low-to-moderate aspect ratios and the limitations of the von Karman nonlinear plate model in these cases.

Numerical study of vibration localization in disordered cyclic structures

A study of mode localization in disordered cyclic structures that have multi-degree-of-freedom substructures in presented. Particular emphasis is placed on the transition of the natural modes from being extended throughout the structure to being localized on a single substructure. A localization length scale is proposed as a measure of the spatial extent of a mode for the purpose of discussing the results of numerical experiments and comparing the localization of different modes. Different modes in the same mode group were found to have significantly different degrees of localization, and similar modes in different mode groups were found to be related to each other via a scaling parameter. Results also indicate that the particular set of random disorder introduced into the finite structure can have a significant effect on the degree of localization.

Development of Generalized Aeroservoelastic Reduced Order Models

Design of modern control laws motivates the creation of state-space models from aeroservoelastic models. Conventional methods for generating state-space models either result in a large number of states, or reduce models into inconsistent forms. In this development, a method is created that generates consistent state-space models. Specifically, the terms of the state-space matrices have a similar basis across a range of flight conditions. This enables meaningful interpolation of the state-space models away from the analyzed data points. Models that are generated in this method and applied across a range of flight conditions are referred to as generalized reduced-order models. With this method, reducedorder models (ROMs) can be generated that characterize a vehicle throughout its operation, and control laws can be simulated across a range of flight conditions.