Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports.The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness. Nomenclature a n , b n , c n Modal coordinates for the three shell displacements, m D ef f Effective material bending stiffness, P a m 3 D y , D θ Shell Bending stiffness in the y and θ directions, respectively, P a m 3 D yθ Shell in-plane twisting stiffness, P a m 3 E Material Young's Modulus, P a E y , E θ Shell Young's Modulus in the y and θ directions, respectively, P a fFrequency, Hz f crit Critical frequency, at the flutter or divergence boundary, Hz G yθ Shear modulus, P a h Shell thickness, m k Circumferential wavenumber k crit Critical circumferential wavenumber, at the flutter or divergence boundary K s Spring stiffness for the circumferential elastic supports, P a K P Y R Pyrogel spring stiffness, P a/m m Shell mass per area, kg/m 2
We have measured photon emission cross sections from neutral fragments produced by collisions of 50-350 keV protons with H 2 O molecules. Balmer α−δ emissions from both the target and projectile were recorded. We also analyzed A 2 + − X 2 (0,0) and (1,0) emission from the excited OH fragment produced during target dissociation. Trends in the cross sections revealed two key properties of the collision process: (1) The Bethe theory accurately describes target emission from both H and OH fragments and (2) the ratio of any two Balmer emission cross sections for both the target and projectile can be approximated by simple functions of the respective optical oscillator strengths. Finally, we provide the Bethe fit parameters necessary to calculate the target emission cross sections at all nonrelativistic impact energies.
Nomenclature a, b = plate length, width a nm , a = deflection modal coordinate E = Young's modulus F = Airy stress function f nm = stress function modal coordinate h = plate thickness K Fd = dimensionless unidirectional (compressive) elastic foundation stiffness, ka 4 ∕D k Fd = unidirectional (compressive) elastic foundation stiffness, or linear foundation stiffness M = Mach number m = plate mass per area N x , N y , N xy = in-plane stress resultants q = flow dynamic pressure U ∞ = freestream velocity ν = Poisson's ratio w = deflection Δp = dynamic pressure λ = dimensionless dynamic pressure, 2qa 3 ∕D ω ma 4 ∕D p ξ, η = dimensionless plate length, width ϕ nm = mode shape ω = angular frequency ω = dimensionless frequency, ω ma 4 ∕D p
A combination of classical plate theory and a supersonic aerodynamic model is used to study the aeroelastic flutter behavior of a proposed thermal protection system (TPS) for the NASA HIAD. The analysis pertains to the rectangular configurations currently being tested in a NASA wind-tunnel facility, and may explain why oscillations of the articles could be observed. An analysis using a linear flat plate model indicated that flutter was possible well within the supersonic flow regime of the wind tunnel tests. A more complex nonlinear analysis of the TPS, taking into account any material curvature present due to the restraint system or substructure, indicated that significantly greater aerodynamic forcing is required for the onset of flutter. Chaotic and periodic limit cycle oscillations (LCOs) of the TPS are possible depending on how the curvature is imposed. When the pressure from the base substructure on the bottom of the TPS is used as the source of curvature, the flutter boundary increases rapidly and chaotic behavior is eliminated.
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