On the nonlinear deformation geometry of Euler-Bernoulli beams

Nonlinear expressions are developed to relate the orientation of the deformed beam cross section, torsion, local components of bending curvature, angular velocity, and virtual rotation to deformation variables. The deformed beam kinematic quantities are proven to be equivalent to those derived from various rotation sequences by identifying appropriate changes of variable based on fundamental uniqueness properties of the deformed beam geometry. The torsion variable used is shown to be mathematically analogous to an axial deflection variable commonly used in the literature. Rigorous applicability of Hamilton's principle to systems described by a class of quasi-coordinates that includes these variables is formally established

Hingeless helicopter rotor with improved stability

Improved stability was provided in a hingeless helicopter rotor by inclining the principal elastic flexural axes and coupling pitching of the rotor blade with the lead-lag bending of the blade. The primary elastic flex axes were inclined by constructing the blade of materials that display non-uniform stiffness, and the specification described various cross section distributions and the resulting inclined flex axes. Arrangements for varying the pitch of the rotor blade in a predetermined relationship with lead-lag bending of the blade, i.e., bending of the blade in a plane parallel to its plane of rotation were constructed

New design of hingeless helicopter rotor improves stability

Cantilever blades are attached directly to rotor hub, thereby substantially reducing cost and complexity and increasing reliability of helicopter rotor. Combination of structural flap-lag coupling and pitch-lag coupling provides damping of 6 to 10%, depending on magnitude of coupling parameters

Two-stage fan. 3: Data and performance with rotor tip casing treatment, uniform and distorted inlet flows

A two stage fan with a 1st-stage rotor design tip speed of 1450 ft/sec, a design pressure ratio of 2.8, and corrected flow of 184.2 lbm/sec was tested with axial skewed slots in the casings over the tips of both rotors. The variable stagger stators were set in the nominal positions. Casing treatment improved stall margin by nine percentage points at 70 percent speed but decreased stall margin, efficiency, and flow by small amounts at design speed. Treatment improved first stage performance at low speed only and decreased second stage performance at all operating conditions. Casing treatment did not affect the stall line with tip radially distorted flow but improved stall margin with circumferentially distorted flow. Casing treatment increased the attenuation for both types of inlet flow distortion

Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade

Structure and clumping in the fast wind of NGC6543

Far-UV spectroscopy from the FUSE satellite is analysed to uniquely probe spatial structure and clumping in the fast wind of the central star of the H-rich planetary nebula NGC6543 (HD164963). Time-series data of the unsaturated PV 1118, 1128 resonance line P Cygni profiles provide a very sensitive diagnostic of variable wind conditions in the outflow. We report on the discovery of episodic and recurrent optical depth enhancements in the PV absorption troughs, with some evidence for a 0.17-day modulation time-scale. SEI line-synthesis modelling is used to derive physical properties, including the optical depth evolution of individual `events'. The characteristics of these features are essentially identical to the `discrete absorption components' (DACs) commonly seen in the UV lines of massive OB stars. We have also employed the unified model atmosphere code CMFGEN to explore spectroscopic signatures of clumping, and report in particular on the clear sensitivity of the PV lines to the clump volume filling factor. The results presented here have implications for the downward revision of mass-loss rates in PN central stars. We conclude that the temporal structures seen in the PV lines of NGC6543 likely have a physical origin that is similar to that operating in massive, luminous stars, and may be related to near-surface perturbations caused by stellar pulsation and/or magnetic fields.Comment: 11 pages, 11 figures. Accepted for publication in MNRA

Dewey Hodges’s Research in Structural Dynamics, Aeroelasticity, and Composites: A Personal Perspective

The contributions of Dewey Hodges within the specialized areas of structural dynamics, aeroelasticity, and composites are highlighted in this paper. Dewey Hodges has published 215 journal papers and 170 conference papers covering a wide range of topics in aerospace structures. His research and academic career span nearly five decades and it is difficult, if not impossible, to give a detailed commentary on his colossal achievement in the confines of a single paper. It is widely acknowledged that Dewey Hodges’s research record is no less than incredible. He has not only given an exceptional account of himself but has also demonstrated his extraordinary versatility in research. The author of this paper has known him both personally and professionally for nearly three decades and, with great humility, he acknowledges the enormous benefit he has received from his association with him. Given the huge volume of work Dewey Hodges has produced and the enormity of the task of commenting on it, the author has understandably been highly selective in choosing which contributions to discuss

Principles of Control for Decoherence-Free Subsystems

Decoherence-Free Subsystems (DFS) are a powerful means of protecting quantum information against noise with known symmetry properties. Although Hamiltonians theoretically exist that can implement a universal set of logic gates on DFS encoded qubits without ever leaving the protected subsystem, the natural Hamiltonians that are available in specific implementations do not necessarily have this property. Here we describe some of the principles that can be used in such cases to operate on encoded qubits without losing the protection offered by the DFS. In particular, we show how dynamical decoupling can be used to control decoherence during the unavoidable excursions outside of the DFS. By means of cumulant expansions, we show how the fidelity of quantum gates implemented by this method on a simple two-physical-qubit DFS depends on the correlation time of the noise responsible for decoherence. We further show by means of numerical simulations how our previously introduced "strongly modulating pulses" for NMR quantum information processing can permit high-fidelity operations on multiple DFS encoded qubits in practice, provided that the rate at which the system can be modulated is fast compared to the correlation time of the noise. The principles thereby illustrated are expected to be broadly applicable to many implementations of quantum information processors based on DFS encoded qubits.Comment: 12 pages, 7 figure

Environment Assisted Metrology with Spin Qubit

We investigate the sensitivity of a recently proposed method for precision measurement [Phys. Rev. Lett. 106, 140502 (2011)], focusing on an implementation based on solid-state spin systems. The scheme amplifies a quantum sensor response to weak external fields by exploiting its coupling to spin impurities in the environment. We analyze the limits to the sensitivity due to decoherence and propose dynamical decoupling schemes to increase the spin coherence time. The sensitivity is also limited by the environment spin polarization; therefore we discuss strategies to polarize the environment spins and present a method to extend the scheme to the case of zero polarization. The coherence time and polarization determine a figure of merit for the environment's ability to enhance the sensitivity compared to echo-based sensing schemes. This figure of merit can be used to engineer optimized samples for high-sensitivity nanoscale magnetic sensing, such as diamond nanocrystals with controlled impurity density.Comment: 9 pages, 6 figure