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Variable viscosity, variable stiffness dampers using polymeric materials near glass transition temperatures for shock and vibration attenuation in space environment
An investigation of the possible performance improvements of thin circular cylindrical shells through the use of the variable stiffness concept is presented. The variable stiffness concept implies that the stiffness parameters change spatially throughout the structure. This situation is achieved mainly through the use of curvilinear fibers within a fiber-reinforced composite laminate, though the possibility of thickness variations and discrete stiffening elements is also allowed. These three mechanisms are incorporated into the constitutive laws for thin shells through the use of Classical Lamination Theory. The existence of stiffness variation within the structure warrants a formulation of the static equilibrium equations from the most basic principles. The governing equations include sufficient detail to correctly model several types of nonlinearity, including the formation of a nonlinear shell boundary layer as well as the Brazier effect due to nonlinear bending of long cylinders. Stress analysis and initial buckling estimates are formulated for a general variable stiffness cylinder. Results and comparisons for several simplifications of these highly complex governing equations are presented so that the ensuing numerical solutions are considered reliable and efficient enough for in-depth optimization studies. Four distinct cases of loading and stiffness variation are chosen to investigate possible areas of improvement that the variable stiffness concept may offer over traditional constant stiffness and/or stiffened structures. The initial investigation deals with the simplest solution for cylindrical shells in which all quantities are constant around the circumference of the cylinder. This axisymmetric case includes a stiffness variation exclusively in the axial direction, and the only pertinent loading scenarios include constant loads of axial compression, pressure, and torsion. The results for these cases indicate that little improvement over traditional laminates exists through the use of curvilinear fibers, mainly due to the presence of a weak link area within the stiffness variation that limits the ultimate load that the structure can withstand. Rigorous optimization studies reveal that even though slight increases in the critical loads can be produced for designs with an arbitrary variation of the fiber orientation angle, the improvements are not significant when compared to traditional design techniques that utilize ring stiffeners and frames. The second problem that is studied involves arbitrary loading of a cylinder with a stiffness variation that changes only in the circumferential direction. The end effects of the cylinder are ignored, so that the problem takes the form of an analysis of a cross-section for a short cylinder segment. Various load cases including axial compression, pressure, torsion, bending, and transverse shear forces are investigated. It is found that the most significant improvements in load-carrying capability exist for cases which involve loads that also vary around the circumference of the shell, namely bending and shear forces. The stiffness variation of the optimal designs contribute to the increased performance in two ways: lowering the stresses in the critical areas through redistribution of the stresses; and providing a relatively stiff region that alters the buckling behavior of the structure. These results lead to an in-depth optimization study involving weight optimization of a fuselage structure subjected to typical design constraints. Comparisons of the curvilinear fiber format to traditional stiffened structures constructed of isotropic and composite materials are included. It is found that standard variable stiffness designs are quite comparable in terms of weight and load-carrying capability yet offer the added advantage of tailorability of distinct regions of the structure that experience drastically different loading conditions. The last two problems presented in this work involve the nonlinear phenomenon of long tubes under bending. Though this scenario is not as applicable to fuselage structures as the previous problems, the mechanisms that produce the nonlinear effect are ideally suited to be controlled by the variable stiffness concept. This is due to the fact that the dominating influence for long cylinders under bending is the ovalization of the cross-section, which is governed mainly by the stiffness parameters of the cylindrical shell. Possible improvement of the critical buckling moments for these structures is investigated using either a circumferential or axial stiffness variation. For the circumferential case involving infinite length cylinders, it is found that slight improvements can be observed by designing structures that resist the cross-sectional deformation yet do not detract from the buckling resistance at the critical location. The results also indicate that buckling behavior is extremely dependent on cylinder length. This effect is most easily seen in the solution of finite length cylinders under bending that contain an axial stiffness variation. For these structures, the only mechanism that exhibits improved response are those that effectively shorten the length of the cylinder, thus reducing the cross-sectional deformation due to the forced restraint at the ends. It was found that the use of curvilinear fibers was not able to achieve this effect in sufficient degree to resist the deformation, but that ring stiffeners produced the desired response admirably. Thus, it is shown that the variable stiffness concept is most effective at improving the bending response of long cylinders through the use of a circumferential stiffness variation.
Results of an analytical and experimental study to characterize the structural response of two compression-loaded variable stiffness composite panels are presented and discussed. These variable stiffness panels are advanced composite structures, in which tows are laid down along precise curvilinear paths within each ply and the fiber orientation angle varies continuously throughout each ply. The panels are manufactured from AS4/977-3 graphite-epoxy pre-preg material using an advanced tow placement system. Both variable stiffness panels have the same layup, but one panel has overlapping tow bands and the other panel has a constant-thickness laminate. A baseline cross-ply panel is also analyzed and tested for comparative purposes. Tests performed on the variable stiffness panels show a linear prebuckling load-deflection response, followed by a nonlinear response to failure at loads between 4 and 53 percent greater than the baseline panel failure load. The structural response of the variable stiffness panels is also evaluated using finite element analyses. Nonlinear analyses of the variable stiffness panels are performed which include mechanical and thermal prestresses. Results from analyses that include thermal prestress conditions correlate well with measured variable stiffness panel results. The predicted response of the baseline panel also correlates well with measured results.
The concept of exploiting wing flexibility to improve aerodynamic performance was investigated in the wind tunnel by employing multiple control surfaces and by varying wing structural stiffness via a Variable Stiffness Spar (VSS) mechanism. High design loads compromised the VSS effectiveness because the aerodynamic wind-tunnel model was much stiffer than desired in order to meet the strength requirements. Results from tests of the model include stiffness and modal data, model deformation data, aerodynamic loads, static control surface derivatives, and fuselage standoff pressure data. Effects of the VSS on the stiffness and modal characteristics, lift curve slope, and control surface effectiveness are discussed. The VSS had the most effect on the rolling moment generated by the leading-edge outboard flap at subsonic speeds. The effects of the VSS for the other control surfaces and speed regimes were less. The difficulties encountered and the ability of the VSS to alter the aeroelastic characteristics of the wing emphasize the need for the development of improved design and construction methods for static aeroelastic models. The data collected and presented is valuable in terms of understanding static aeroelastic wind-tunnel model development.
Results from structural analyses of three tow-placed AS4/977-3 composite panels with both geometric and material nonlinearities are presented. Two of the panels have variable stiffness layups where the fiber orientation angle varies as a continuous function of location on the panel planform. One variable stiffness panel has overlapping tow bands of varying thickness, while the other has a theoretically uniform thickness. The third panel has a conventional uniform-thickness [plus or minus 45](sub 5s) layup with straight fibers, providing a baseline for comparing the performance of the variable stiffness panels. Parametric finite element analyses including nonlinear material shear are first compared with material characterization test results for two orthotropic layups. This nonlinear material model is incorporated into structural analysis models of the variable stiffness and baseline panels with applied end shortenings. Measured geometric imperfections and mechanical prestresses, generated by forcing the variable stiffness panels from their cured anticlastic shapes into their flatter test configurations, are also modeled. Results of these structural analyses are then compared to the measured panel structural response. Good correlation is observed between the analysis results and displacement test data throughout deep postbuckling up to global failure, suggesting that nonlinear material behavior is an important component of the actual panel structural response.
In a torsion spring the spring action is a result of the relationships between the torque applied in twisting the spring, the angle through which the torsion spring twists, and the modulus of elasticity of the spring material in shear. Torsion springs employed industrially have been strips, rods, or bars, generally termed shafts, capabable of being flexed by twisting their axes. They rely on the variations in shearing forces to furnish an internal restoring torque. In the torsion springs herein the restoring torque is external and therefore independent of the shearing modulus of elasticity of the torsion spring shaft. Also provided herein is a variable stiffness torsion spring. This torsion spring can be so adjusted as to have a given spring constant. Such variable stiffness torsion springs are extremely useful in gimballed payloads such as sensors, telescopes, and electronic devices on such platforms as a space shuttle or a space station.
In a torsion spring the spring action is a result of the relationships between the torque applied in twisting the spring, the angle through which the torsion spring twists, and the modulus of elasticity of the spring material in shear. Torsion springs employed industrially have been strips, rods, or bars, generally termed shafts, capabable of being flexed by twisting their axes. They rely on the variations in shearing forces to furnish an internal restoring torque. In the torsion springs herein the restoring torque is external and therefore independent of the shearing modulus of elasticity of the torsion spring shaft. Also provided herein is a variable stiffness torsion spring. This torsion spring can be so adjusted as to have a given spring constant. Such variable stiffness torsion springs are extremely useful in gimballed payloads such as sensors, telescopes, and electronic devices on such platforms as a space shuttle or a space station.
A solution has been obtained to the plane elasticity problem for a symmetrically laminated composite panel with spatially varying fiber orientations. Since variation of the fiber angles along the length of a composite laminate results in stiffness properties that change as a function of location, the laminates are called variable stiffness panels. An analysis of the stiffness variation and its effect on the elastic response of the panel is presented here. A numerical solution has been obtained using an iterative collocation technique. Corresponding closed-form solutions are given for three different sets of boundary conditions. Two of the cases considered have exact solutions and thus serve to validate the numerical model.
Synthesis, mechanical testing, and modeling have been performed for carbon nanotube based materials. Tests using nanoindentation indicated a six-fold enhancement in the storage modulus when comparing the base material (no nanotubes) to the composite that contained 5.3 wt% of nanotubes. To understand how crosslinking the nanotubes may further alter the stiffness, a model of the system was constructed using nanotubes crosslinked with a variable stiffness tether (VST). The model predicted that for a composite with 5 wt% nanotubes at random orientations, crosslinked with the VST, the bulk Young's modulus was reduced by 30% compared to the noncrosslinked equivalent.
Commercial systems for precise placement of pre-preg composite tows are enabling technology that allows fabrication of advanced composite structures in which the tows may be precisely laid down along curvilinear paths within a given ply. For laminates with curvilinear tow paths, the fiber orientation angle varies continuously throughout the laminate, and is not required to be straight and parallel in each ply as in conventional composite laminates. Hence, the stiffness properties vary as a function of location in the laminate, and the associated composite structure is called a "variable stiffness" composite structure.
Damping mechanism, containing polymeric-like materials is applicable to a wide range of shock and vibration. The polymeric-like material changes from a relatively stiff material to a relatively soft, rubbery material in the region of their glass transition temperatures. The energy absorption characteristics and stiffness are controllable with temperature.
Shock and vibration damping device using temperature sensitive solid amorphous polymers
A new piezoceramic strut has been developed. This strut utilizes strain induced bending as a means of actuation. The significance of this design is that the displacement of the strut's motion arm is independent of the expansion of the piezoceramic material. Design criteria was developed using continuous and finite element modeling techniques. Experimental and analytical results were compared. Finally, a numerical analysis was conducted that demonstrated the benefits of the piezoceramic strut configuration.
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The constitutive properties of a cross-linked single-walled carbon nanotube material are predicted with a multi-scale model. The material is modeled as a transversely isotropic solid using concepts from equivalent-continuum modeling. The elastic constants are determined using molecular dynamics simulation. Some parameters of the molecular force field are determined specifically for the cross-linker from ab initio calculations. A demonstration of how the cross-linked nanotubes may affect the properties of a nanotube/polyimide composite is included using a micromechanical analysis.
Simple shock isolator synthesis with bilinear stiffness and variable damping
The buckling response of a symmetrically laminated composite panel with a spatially varying fiber orientation has been analyzed. Variation of the fiber orientation angle as a function of the position in the panel results in a composite laminate with stiffness properties that are functions of the panel coordinates. The laminates are therefore termed variable stiffness panels. The fiber orientation is assumed to vary only in one spatial direction, although the analysis can be extended to fiber orientations that vary in two spatial directions. The Ritz Method has been used to find the buckling loads and buckling modes for the variable stiffness panels for two different cases. In one of the cases the fiber orientation is assumed to change in the direction of the applied load. The other case is the one in which the fiber orientation varies in a direction perpendicular to the loading direction. Improvements in the buckling load of up to 80 percent over straight fiber configurations were found. Results for three different panel aspect ratios are presented.
Tailoring composite laminates to vary the fiber orientations within a fiber layer of a laminate to address non-uniform stress states and provide structural advantages such as the alteration of principal load paths has potential application to future low-cost, light-weight structures for commercial transport aircraft. Evaluation of this approach requires the determination of the effectiveness of stiffness tailoring through the use of curvilinear fiber paths in flat panels including the reduction of stress concentrations around the holes and the increase in load carrying capability. Panels were designed through the use of an optimization code using a genetic algorithm and fabricated using a tow-steering approach. Manufacturing limitations, such as the radius of curvature of tows the machine could support, avoidance of wrinkling of fibers and minimization of gaps between fibers were considered in the design process. Variable stiffness tow-steered panels constructed with curvilinear fiber paths were fabricated so that the design methodology could be verified through experimentation. Finite element analysis where each element s stacking sequence was accurately defined is used to verify the behavior predicted based on the design code. Experiments on variable stiffness flat panels with central circular holes were conducted with the panels loaded in axial compression or shear. Tape and tow-steered panels are used to demonstrate the buckling, post-buckling and failure behavior of elastically tailored panels. The experimental results presented establish the buckling performance improvements attainable by elastic tailoring of composite laminates.