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Report presents theoretical analysis of vibrations of simply supported beam, bending stiffness varying about steady value, sinusoidally with position along length. Problem of practical importance because related to vibrations of twisted-pair electric-power transmission lines. Twists promote nonuniform shedding of vortexes and prevents resonant accumulation of vibrational energy from wind.
A theoretical and experimental study is made to investigate the effect on plate vibrations of varying the stiffness of corner elastic point supports. An experiment is conducted in which the bending stiffness of horizontal beams is used to support a square plate at its four corners. The stiffness of these supports can be varied over such a range that the plate fundamental frequency is lowered to 40% of the rigid support frequency. The variation with support stiffness of the frequencies of the first eight plate modes is measured and is compared with results from a theoretical model in which a Rayleigh-Ritz analysis is used which approximates the plate mode shapes as products of free-free beam modes. The elastic point supports are modeled both as massless translational springs and springs with tip masses, which are included to better represent the experimental supports.
The objective of the study was to develop a more accurate model for the prediction of the compressive behavior of filament-wound composite cylindrical shells. Results from a closed-form analytical model and a three-dimensional finite element model show that the extensional and bending stiffness of the laminate is significantly reduced in tow cross-over regions and that bending-extension coupling is increased in comparison with classical lamination theory. The material properties predicted by a micromechanics analysis are included in a global finite element model of a filament-wound circular cylindrical shell which also incorporates variations in the laminate stacking thickness. Results from the global shell analysis are compared with experimental data.
Several studies have indicated that selective reinforcement offers the potential to significantly improve the performance of metallic structures for aerospace applications. Applying high-strength, high-stiffness fibers to the high-stress regions of aluminum-based structures can increase the structural load-carrying capability and inhibit fatigue crack initiation and growth. This paper discusses an investigation into potential methods for applying reinforcing fibers onto the surface of aluminum and aluminum-lithium plate. Commercially-available alumina-fiber reinforced aluminum alloy tapes were used as the reinforcing material. Vacuum hot pressing was used to bond the reinforcing tape to aluminum alloy 2219 and aluminum-lithium alloy 2195 base plates. Static and cyclic three-point bend testing and metallurgical analysis were used to evaluate the enhancement of mechanical performance and the integrity of the bond between the tape and the base plate. The tests demonstrated an increase in specific bending stiffness. In addition, no issues with debonding of the reinforcing tape from the base plate during bend testing were observed. The increase in specific stiffness indicates that selectively-reinforced structures could be designed with the same performance capabilities as a conventional unreinforced structure but with lower mass.
A lattice type structural panel concept which exploits the unidirectional character of filamentary advanced composite materials was described. This lattice has potential for applications where stiff lightweight structures are needed such as large area panels for space satellites. Formulae are presented to calculate the panel weight and plate bending stiffness. This analysis indicates that structures with significantly lighter weight than conventional minimum gauge sandwich construction can be fabricated. A suggested fabrication procedure is also presented along with photographs of some typical panels.
Efficient structures for geosynchronous spacecraft solar arrays were investigated. The STACBEAM (stacking triangular articulated compact beam) concept was selected. The primary component, the solar array blanket, is stored in a folded configuration and is deployed by controlled linear extension. Blanket stiffness is attained by axially tensioning the blanket and by providing periodic lateral ribs and standoffs which attach the blanket to the beam at several places along its length. The STACBEAM deploys sequentially (one bay at a time) using a deployer of sufficient rigidity so that beam stiffness is not degraded during deployment. The beam does not rotate during deployment, thus making blanket beam attachment possible in the packaged condition. In addition to high bending stiffness, the STACBEAM possesses high torsional rigidity due to nonflexible diagonals. The concept is adaptable to various size and loading requirements by changing member diameter and baylength, thus affecting the ratio of packaged and deployed length.
An experimental investigation of the flap-lag stability of a hingeless rotor in hovering flight is presented and discussed. The rotor blade and hub configuration were selected such that the hub and blade had comparable levels of bending stiffness. Experimental measurements of the lag damping were made for various values of rotor rotational speed and blade pitch angle. Specifically at a blade pitch angle of 8 deg at three-quarters radius, the lag damping was determined over a range of rotational speeds from 200 RPM to 320 RPM and also over a range of blade pitch angles from 0 deg to 8 deg.
Further measurements of buffeting, using wing-root strain gauges, were made in the NASA Langley 0.3 m Cryogenic Wind Tunnel to refine techniques which will be used in larger cryogenic facilities such as the United States National Transonic Facility (NTF) and European Transonic Wind Tunnel (ETW). The questions addressed included the relative importance of variations in frequency parameter and Reynolds number, the choice of model material (considering both stiffness and damping) and the effects of static aeroelastic distortion. The main series of tests was made on half models of slender 65 deg delta wings with a sharp leading edge. The three delta wings had the same planform but widely different bending stiffness and frequencies (obtained by varying both the material and the thickness of the wings). It was known that the flow on this configuration would be insensitive to variations in Reynold number. Additional tests were made on one unswept half-wing of aspect ratio 1.5 with an NPL 9510 aerofoil section, known to be sensitive to variations in Reynolds number at transonic speeds. For brevity the test Mach numbers were restricted to M = 0.21 and 0.35 for the delta wings and to M = 0.30 for the unswept wing.
Measurements of wing buffeting, using root strain gages, were made in the NASA Langley 0.3 m cryogenic wind tunnel to refine techniques which will be used in larger cryogenic facilities such as the United States National Transonic Facility (NTF) and the European Transonic Wind Tunnel (ETW). The questions addressed included the relative importance variations in frequency parameter and Reynolds number, the choice of model material (considering both stiffness and damping) and the effects of static aeroelastic distortion. The main series of tests was made on three half models of slender 65 deg delta wings with a sharp leading edge. The three delta wings had the same planform but widely differing bending stiffnesses and frequencies (obtained by varying both the material and the thickness of the wings). It was known that the steady flow on this configuration would be insensitive to variations in Reynolds number. On this wing at vortex breakdown the spectrum of the unsteady excitation is unusual, having a sharp peak at particular frequency parameter. Additional tests were made on one unswept half-wing of aspect ratio 1.5 with an NPL 9510 aerofoil section, known to be sensitive to variations in Reynolds number at transonic speeds. The test Mach numbers were M = 0.21 and 0.35 for the delta wings and to M = 0.30 for the unswept wing. On this wing the unsteady excitation spectrum is fairly flat (as on most wings). Hence correct representation of the frequency parameter is not particularly important.
The concept of stiffness tailoring for improved shear buckling resistance of rectangular composite plates is investigated analytically. The tailoring involves only the redistribution of the given material with given orientations to create beneficial stiffening patterns across the planform of the plate. The resulting local nonuniformities in thickness and membrane and bending stiffness combine to change the buckling response of the plate. The weight and average membrane shear stiffness are essentially unaffected by the tailoring. Practical limitations on the degree to which the tailoring may be carried out are shown to govern most designs. Improvements in the shear buckling load on the order of 50 percent are shown possible with monolithic tailoring. Tailored sandwich concepts, in which a light-weight core material is added to keep both plate surfaces flat, can produce improvements well over 100 percent in specific buckling loads compared with uniform composite plates.
Accurate non-invasive mechanical measurement of long bones is made difficult by the masking effect of surrounding soft tissues. Mechanical Response Tissue Analysis (MRTA) offers a method for separating the effects of the soft tissue and bone; however, a direct validation has been lacking. A theoretical analysis of wave propagation through the compressed tissue revealed a strong mass effect dependent on the relative accelerations of the probe and bone. The previous mathematical model of the bone and overlying tissue system was reconfigured to incorporate the theoretical finding. This newer model (six-parameter) was used to interpret results using MRTA to determine bone cross-sectional bending stiffness, EI(sub MRTA). The relationship between EI(MRTA) and theoretical EI values for padded aluminum rods was R(exp 2) = 0.999. A biological validation followed using monkey tibias. Each bone was tested in vivo with the MRTA instrument. Postmortem, the same tibias were excised and tested to failure in three-point bending to determine EI(sub 3-PT) and maximum load. Diaphyseal Bone Mineral Density (BMD) measurements were also made. The relationship between E(sub 3-PT) and in vivo EI(sub MRTA) using the six-parameter model is strong (R(exp 2) = 0.947) and better than that using the older model (R(exp 2) = 0.645). EI(MRTA) and BMD are also highly correlated (R(exp 2) = 0.853). MRTA measurements in vivo and BMD ex vivo are both good predictors of scaled maximum strength (R(exp 2) = 0.915 and R(exp 2) = 0.894, respectively). This is the first biological validation of a non-invasive mechanical measurement of bone by comparison to actual values. The MRTA technique has potential clinical value for assessing long-bone mechanical properties.
Accurate non-invasive mechanical measurement of long bones is made difficult by the masking effect of surrounding soft tissues. Mechanical response tissue analysis (MRTA) offers a method for separating the effects of the soft tissue and bone; however, a direct validation has been lacking. A theoretical analysis of wave propagation through the compressed tissue revealed a strong mass effect dependent on the relative accelerations of the probe and bone. The previous mathematical model of the bone and overlying tissue system was reconfigured to incorporate the theoretical finding. This newer model (six-parameter) was used to interpret results using MRTA to determine bone cross-sectional bending stiffness, EI(sub MRTA). The relationship between EI(sub MRTA) and theoretical EI values for padded aluminum rods was R(sup 2) = 0.999. A biological validation followed using monkey tibias. Each bone was tested in vivo with the MRTA instrument. Postmortem, the same tibias were excised and tested to failure in three-point bending to determine EI(sub 3-PT) and maximum load. Diaphyseal bone mineral density (BMD) measurements were also made. The relationship between EI(sub 3-PT) and in vivo EI(sub MRTA) using the six-parameter model is strong (R(sup 2) = 0.947) and better than that using the older model (R(sup 2) = 0.645). EI(sub MRTA) and BMD are also highly correlated (R(sup 2) = 0.853). MRTA measurements in vivo and BMD ex vivo are both good predictors of scaled maximum strength (R(sup 2) = 0.915 and R(sup 2) = 0.894, respectively). This is the first biological validation of a non- invasive mechanical measurement of bone by comparison to actual values. The MRTA technique has potential clinical value for assessing long-bone mechanical properties.
Test results from an international round robin are presented. The single cantilever beam (SCB) test was used to characterize face sheet/core disbonding in sandwich components in an effort to help standardization. Each of the seven participating laboratories performed a set of five baseline tests using the same protocol, however, using their own specific equipment. In addition, each laboratory performed two sets of tests with altered tests conditions which included using a test fixture with a translating carriage and performing the tests with different loading and unloading speeds. The orientation of the disbond front with respect to the honeycomb core cells was varied and the effect on the fracture toughness was also studied. Additional factors that could influence test results were investigated, such as the use of a saw cut starter disbond as an alternative to Teflon® release film, and the effects of using a face sheet doubler to increase the bending stiffness. For each set of tests, summary results such as load/displacements plots, observed disbond growth location and calculated energy release rates are reported and a comparison of results between labs is presented. Critical strain energy release rate measurements from SCB tests are also compared with measurements made from an alternative test, namely the double cantilever beam with uneven bending moments (DCB-UBM) test, which has been studied extensively at the Technical University of Denmark and proposed as a mixed-mode test standard. A set of recommendations are made with respect to improving the SCB test and a path to standardization is presented.
A theoretical and experimental study is made to investigate the effect on plate vibrations of varying the stiffness of corner elastic point supports. A theoretical model is developed using a Rayleigh-Ritz analysis which approximates the plate mode shapes as products of free-free beam modes. The elastic point supports are modelled both as massless translational springs, and springs with tip masses. The tip masses are included to better represent the experimental supports. An experiment is constructed using the bending stiffness of horizontal beams to support a square plate at its four corners. The stiffness of these supports can be varied over such a range that the plate fundamental frequency is lowered to 40% of the rigid support frequency. The variation with support stiffness of the frequencies of the first eight plate modes is measured, and compared with the theoretical results. The plate mode shapes for rigid supports are analyzed using holographic interferometry. There is excellent agreement between the theoretical and experimental results, except for high plate modes where the theoretical model is demonstrated to be inadequate.
A test program which determines the extensional, bending and torsional stiffness of various titanium multiwall sandwich configurations is described. It is shown that unlike honeycomb core, the dimpled core is a significant contributor to the stiffness and strength of the sandwich. the extensional stiffness test shows irregularities which are attributed to foil thickness variations and to the difficulty to determine linear values from nonlinear tests.
The buckling response of thin-walled cylindrical structures have long been shown to be sensitive to various imperfections. That is, imperfections related to load introduction, boundary conditions, material property variation, and geometric deviations can all contribute to experimentally obtained buckling loads being lower than the buckling loads predicted for perfect representations of the same thin-walled cylindrical structure. To account for the influence of geometry-based imperfections of a thin-walled cylindrical structure on buckling response, a design factor (also known as a buckling knockdown factor) is used during the design phase. Guidelines for buckling knockdown factors are readily available in NASA SP-8007, Buckling of Thin Walled Circular Cylinders, which was updated in 2020. Prior to this recent update, NASA SP-8007 had not been updated since 1969, and since that time, computational analysis, experimental testing, and manufacturing methods have significantly improved. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF, NESC Assessment 07-010-E) had the goal of developing buckling design recommendations for select classes of metallic and composite launch-vehicle structures [3]. Specifically, the test and analysis results from the fourth SBKF composite test article SBKF-P3-CYL-CTA8.2B, which is referred to as CTA8.2B, are described in this paper. This test was the fourth in a series of four tests on sandwich composite cylinders that will be used to experimentally validate analysis methods, which in turn can be used to develop new analysis-based shell buckling design guidelines for typical sandwich composite launch vehicle cylindrical structures. Publications describing previous test validation with analysis are available in Refs. CTA8.2B was designed to occupy one corner of the design space with approximately equal bending stiffnesses in the axial and transverse directions and have a larger ratio of radius to effective shell thickness. Each test article had a unique design and was designed to occupy a specific region of the design space. CTA8.2B was an 8-foot diameter honeycomb-core sandwich cylinder that was fabricated and tested at the NASA Marshall Space Flight Center (MSFC). The primary objectives of this test were to interrogate the structural capability of a composite test article, and to verify the test article design and analysis approach for cylinders subjected to axial compression and combined axial and bending loads. First, descriptions of the test article design and test are given in Section 2.0, and modeling and analysis methods used in support of the test article design and testing activities are described briefly in Section 3.0. Then, select test results are presented and compared to predicted results in Section 4.0, and concluding remarks are presented in Section 5.0. Finally, drawings of CTA8.2B and references used to support the test and analysis are provided in the Appendix.
A sandwich construction consists of a low-density core material with high strength face sheets bounded to the top and bottom surfaces. The construction has been widely used in the aerospace and marine industries due to its outstanding characteristics such as noise absorption, weight minimization, heat insulation, and better bending stiffness. In sandwich structures used in high-performance aircraft, the face sheets are often made of fiber-reinforced composite materials and the core is made of honeycomb. The structures may also have variable thickness so as to satisfy aerodynamic requirements. In the stress analysis, the constant-thickness face sheets are usually considered as membrane and the core is assumed to be inextensible but deformable in the thickness direction. The static behavior of variable-thickness, isotropic and homogeneous sandwich beams was successfully studied by employing a constant-thickness theory but allowing stiffnesses to vary in accordance with local thickness variations. It has been recently found in a refined theory that the analyses based on the constant thickness theory locally can lead to significant errors in structural responses if the sandwich beam is thickness-tapered and the cores are deformable in transverse shear. The errors arise mainly from two factors: (1) the transverse shear components of the membrane forces in the face sheets alter the transverse shears carried by the core; and (2) the face-sheet membrane strains arise from transverse shear deformation of the core. In practice the variable thickness may not only exist in core but also in face sheets. The thickness-variations may even be a type of step function. In this case the transverse shear stress in the face sheets and bending stress in the core should be taken into account in the refined theory mentioned. In the present study, energy principles are employed in deriving governing equations for general bending of anisotropic sandwich beams with variable thickness in both face sheets and cores. Solutions to these equations are based on a finite difference scheme. As an example in application, a simply supported thickness-tapered sandwich beam subject to a concentrated load at its center is considered. Let W' be the maximum deflection of the beam in which face sheets are considered as membrane, while W'' is that based on using the modified refined theory. It is found that W' is always larger than W'', however, the magnitude of (W'- W'') appears to be insensitive to the change of the taper of the beam.
Engineered non-stochastic cellular materials show promising characteristics on the laboratory scale,with nearly ideal specific stiffness and strength scaling at ultralight mass density. These propertiessuggest performance benefits in any application with combined stiffness and mass constraints, suchas air vehicles. We investigate here the application of re-configurable cellular composite materialsand structures to lighter than air vehicles. We describe the properties and applicability of these materials,provide an example analysis of governing loading conditions associated with airships, showan example optimization method for navigating the design space, and describe how recent advancesin cellular material manufacturing and reconfiguration enable system performance benefits includingnew concepts of operation. Lastly, we propose lighter than air vehicles that are assembled andmaintained in-flight, eliminating structural compromises associated with transitional flight modesand ground handling.Engineered non-stochastic cellular material properties suggest performance benefits in lighter than air vehicles due tostiffness and mass constraints that are intrinsic to the airship design problem. Recent advances in cellular materialmanufacturing and reconfiguration enable system performance benefits including new concepts of operation, such aslighter than air vehicles that are assembled and maintained in-flight, eliminating structural compromises associatedwith transitional flight modes and ground handling. Existing engineered cellular materials display properties allowinglarge large scale airships design as monocoque cellular solids. Inevitable improvements in cellular material propertiesand manufacturing will improve feasibility even further. Given the suggestion that the two most significant technologygaps exist across all current airship projects are manufacturing and assembly processes and ground handling [7],a strategy that encompasses construction and maintenance in flight could provide critical rephrasing of the systemdesign problem through these new concepts of operation. Refactoring of traditional manufacturing, operation, andservice process constraints could extend to other domains in aerospace systems and manufacturing in general.In future work, the complexity of the design task would benefit from a form of optimization in order to find themost suitable geometry for a chosen application. For example, the Sequential Least SQuares Programming (SLSQP)function from within the SciPy Minimize library is a multiobjective constrained optimization method that has beenapplied to fixed wing aircraft design. [17] In this situation it would allow for several objective functions such as drag,bending stiffness, buoyancy and cost of transport to be incorporated into a composite objective function.