# Browsing by Subject "Structures"

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Item Open Access A Study in Laterally Restrained Buckled Beams for the use in a Vertical Isolation System(2021) McManus, Michael AllenLinear vibration isolation systems, used to reduce the transmissibility of vertical vibration, requires a vertical static displacement that increases with the square of the natural period of the isolation system. The static displacement of a vertical isolation system with a one second natural period is 0.25 m. The nonlinear stiffness of buckled beams loaded in the transverse direction can be designed to reduce the vertical static displacement requirement of vertical systems. This study presents an analysis of large displacement mechanics of slender beams that buckle against a constraint, and extracts the transverse constraint force via the Lagrange multiplier enforcing the constraint. The constraint prescribes a maximum allowable lateral displacement along the length of the beam and a specified longitudinal displacement at the mid span of the beam. No small curvature assumption is involved. Lateral and longitudinal displacements are parameterized in terms of Fourier coefficients. Coefficient values for constrained equilibria are found by minimizing the bending strain energy such that lateral and longitudinal constraints are satisfied. Because the full expression for curvature is used, this is a nonlinear constrained optimization problem.

Edge and mid-point horizontal constraint positions are varied to gain a better understanding of the constraint forces at each position. This modeling approach is then used to design a system of post-buckled leaf springs in order to meet vibration isolation requirements without over-stressing the springs. This process is discussed in detail along with the process and challenges associated with the physical model. Theoretical predictions are compared to laboratory scale measurements. Experimental results from the physical model are compared to the theoretical and numerical simulation results. The potential for rocking responses of the vertical isolation system are quantified via the modeling of the nonlinear dynamics of a platform supported by a system of springs and carrying a mass concentrated above the platform.

Item Open Access An Aeroelastic Evaluation of the Flexible Thermal Protection System for an Inflatable Aerodynamic Decelerator(2015) Goldman, Benjamin DouglasThe purpose of this dissertation is to study the aeroelastic stability of a proposed flexible thermal protection system (FTPS) for the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A flat, square FTPS coupon exhibits violent oscillations during experimental aerothermal testing in NASA's 8 Foot High Temperature Tunnel, leading to catastrophic failure. The behavior of the structural response suggested that aeroelastic flutter may be the primary instability mechanism, prompting further experimental investigation and theoretical model development. Using Von Karman's plate theory for the panel-like structure and piston theory aerodynamics, a set of aeroelastic models were developed and limit cycle oscillations (LCOs) were calculated at the tunnel flow conditions. Similarities in frequency content of the theoretical and experimental responses indicated that the observed FTPS oscillations were likely aeroelastic in nature, specifically LCO/flutter.

While the coupon models can be used for comparison with tunnel tests, they cannot predict accurately the aeroelastic behavior of the FTPS in atmospheric flight. This is because the geometry of the flight vehicle is no longer a flat plate, but rather (approximately) a conical shell. In the second phase of this work, linearized Donnell conical shell theory and piston theory aerodynamics are used to calculate natural modes of vibration and flutter dynamic pressures for various structural models composed of one or more conical shells resting on several circumferential elastic supports. When the flight vehicle is approximated as a single conical 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, as "hump-mode" flutter is possible. Aeroelastic models that consider the individual FTPS layers as separate shells exhibit asymmetric flutter at high dynamic pressures relative to the single shell models. Parameter studies also examine the effects of tension, shear modulus reduction, and elastic support stiffness.

Limitations of a linear structural model and piston theory aerodynamics prompted a more elaborate evaluation of the flight configuration. Using nonlinear Donnell conical shell theory for the FTPS structure, the pressure buckling and aeroelastic limit cycle oscillations were studied for a single elastically-supported conical shell. While piston theory was used initially, a time-dependent correction factor was derived using transform methods and potential flow theory to calculate more accurately the low Mach number supersonic flow. Three conical shell geometries were considered: a 3-meter diameter 70 degree shell, a 3.7-meter 70 degree shell, and a 6-meter diameter 70 degree shell. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD vehicle. Though agreement between theoretical and experimental strains was poor, circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With piston theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with piston theory alone.

In the final phase of this work, the existing linear and nonlinear FTPS shell models were coupled with NASA's FUN3D Reynolds Averaged Navier Stokes CFD code, allowing for the most physically realistic flight predictions. For the linear shell structural model, the elastically-supported shell natural modes were mapped to a CFD grid of a 6-meter HIAD vehicle, and a linear structural dynamics solver internal to the CFD code was used to compute the aeroelastic response. Aerodynamic parameters for a proposed HIAD re-entry trajectory were obtained, and aeroelastic solutions were calculated at three points in the trajectory: Mach 1, Mach 2, and Mach 11 (peak dynamic pressure). No flutter was found at any of these conditions using the linear method, though oscillations (of uncertain origin) on the order of the shell thickness may be possible in the transonic regime. For the nonlinear shell structural model, a set of assumed sinusoidal modes were mapped to the CFD grid, and the linear structural dynamics equations were replaced by a nonlinear ODE solver for the conical shell equations. Successful calculation and restart of the nonlinear dynamic aeroelastic solutions was demonstrated. Preliminary results indicated that dynamic instabilities may be possible at Mach 1 and 2, with a completely stable solution at Mach 11, though further study is needed. A major benefit of this implementation is that the coefficients and mode shapes for the nonlinear conical shell may be replaced with those of other types of structures, greatly expanding the aeroelastic capabilities of FUN3D.