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

Rotorcraft aeroelastic stability

Theoretical and experimental developments in the aeroelastic and aeromechanical stability of helicopters and tilt-rotor aircraft are addressed. Included are the underlying nonlinear structural mechanics of slender rotating beams, necessary for accurate modeling of elastic cantilever rotor blades, and the development of dynamic inflow, an unsteady aerodynamic theory for low-frequency aeroelastic stability applications. Analytical treatment of isolated rotor stability in hover and forward flight, coupled rotor-fuselage stability in hover and forward flight, and analysis of tilt-rotor dynamic stability are considered. Results of parametric investigations of system behavior are presented, and correlation between theoretical results and experimental data from small and large scale wind tunnel and flight testing are discussed

Survey of Army/NASA rotorcraft aeroelastic stability research

Theoretical and experimental developments in the aeroelastic and aeromechanical stability of helicopters and tilt-rotor aircraft are addressed. Included are the underlying nonlinear structural mechanics of slender rotating beams, necessary for accurate modeling of elastic cantilever rotor blades, and the development of dynamic inflow, an unsteady aerodynamic theory for low frequency aeroelastic stability applications. Analytical treatment of isolated rotor stability in hover and forward flight, coupled rotor-fuselage stability are considered. Results of parametric investigations of system behavior are presented, and correlations between theoretical results and experimental data from small- and large-scale wind tunnel and flight testing are discussed

General Rotorcraft Aeromechanical Stability Program (GRASP): Theory manual

The general rotorcraft aeromechanical stability program (GRASP) was developed to calculate aeroelastic stability for rotorcraft in hovering flight, vertical flight, and ground contact conditions. GRASP is described in terms of its capabilities and its philosophy of modeling. The equations of motion that govern the physical system are described, as well as the analytical approximations used to derive them. The equations include the kinematical equation, the element equations, and the constraint equations. In addition, the solution procedures used by GRASP are described. GRASP is capable of treating the nonlinear static and linearized dynamic behavior of structures represented by arbitrary collections of rigid-body and beam elements. These elements may be connected in an arbitrary fashion, and are permitted to have large relative motions. The main limitation of this analysis is that periodic coefficient effects are not treated, restricting rotorcraft flight conditions to hover, axial flight, and ground contact. Instead of following the methods employed in other rotorcraft programs. GRASP is designed to be a hybrid of the finite-element method and the multibody methods used in spacecraft analysis. GRASP differs from traditional finite-element programs by allowing multiple levels of substructure in which the substructures can move and/or rotate relative to others with no small-angle approximations. This capability facilitates the modeling of rotorcraft structures, including the rotating/nonrotating interface and the details of the blade/root kinematics for various types. GRASP differs from traditional multibody programs by considering aeroelastic effects, including inflow dynamics (simple unsteady aerodynamics) and nonlinear aerodynamic coefficients

Laboratory measurements and theoretical calculations of O_2 A band electric quadrupole transitions

Frequency-stabilized cavity ring-down spectroscopy was utilized to measure electric quadrupole transitions within the ^(16)O_2 A band, b^1Σ^+_g ← X^3Σ^-_g(0,0). We report quantitative measurements (relative uncertainties in intensity measurements from 4.4% to 11%) of nine ultraweak transitions in the ^NO, ^PO, ^RS, and ^TS branches with line intensities ranging from 3×10^(−30) to 2×10^(−29) cm molec.^(−1). A thorough discussion of relevant noise sources and uncertainties in this experiment and other cw-cavity ring-down spectrometers is given. For short-term averaging (t<100 s), we estimate a noise-equivalent absorption of 2.5×10^(−10) cm^(−1) Hz^(−1/2). The detection limit was reduced further by co-adding up to 100 spectra to yield a minimum detectable absorption coefficient equal to 1.8×10^(−11) cm^(−1), corresponding to a line intensity of ~2.5×10^(−31) cm molec.^(−1). We discuss calculations of electric quadrupole line positions based on a simultaneous fit of the ground and upper electronic state energies which have uncertainties <3 MHz, and we present calculations of electric quadrupole matrix elements and line intensities. The electric quadrupole line intensity calculations and measurements agreed on average to 5%, which is comparable to our average experimental uncertainty. The calculated electric quadrupole band intensity was 1.8(1)×10^(−27) cm molec.−1 which is equal to only ~8×10^(−6) of the magnetic dipole band intensity

Functional Approach to Stochastic Inflation

We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point approximation scalar field probability distributions of various type are derived and the statistics of the inflationary-history-dependent functionals is developed.Comment: 20 pages, Preprint BROWN-HET-960, uses phyzz

Computation of microdosimetric distributions for small sites

Object of this study is the computation of microdosimetric functions for sites which are too small to permit experimental determination of the distributions by Rossi-counters. The calculations are performed on simulated tracks generated by Monte-Carlo techniques. The first part of the article deals with the computational procedure. The second part presents numerical results for protons of energies 0.5, 5, 20 MeV and for site diameters of 5, 10, 100 nm

Braneworld inflation from an effective field theory after WMAP three-year data

In light of the results from the WMAP three-year sky survey, we study an inflationary model based on a single-field polynomial potential, with up to quartic terms in the inflaton field. Our analysis is performed in the context of the Randall-Sundrum II braneworld theory, and we consider both the high-energy and low-energy (i.e. the standard cosmology case) limits of the theory. We examine the parameter space of the model, which leads to both large-field and small-field inflationary type solutions. We conclude that small field inflation, for a potential with a negative mass square term, is in general favored by current bounds on the tensor-to-scalar perturbation ratio rs.Comment: 11 pages, 5 figures; references updated and a few comments added; final version to appear in Phys. Rev.