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Analytical method for determining axisymmetric longitudinal mode shapes and frequencies of incompressible and inviscid fluid in pressurized flexible oblate spheroidal propellant tank
Pressure distribution effects on shape of tension shell entry vehicles determined analytically and experimentally
Description of a casting technique for fabricating high-quality plastic structural models, and review of results regarding the use of such specimens to parametrically study the effect of base ring stiffness on the critical buckling pressure of a ring-stiffened conical shell. The fabrication technique involves machining a metal mold to the desired configuration and vacuum-drawing the plastic material into the mold. A room-temperature curing translucent thermoset epoxy was the casting material selected. A shell of revolution computer program which employs a nonlinear axisymmetric prebuckling strain field to obtain a bifurcation buckling solution was used to guide the selection of congifurations tested. The shell experimentally exhibited asymmetric collapse behavior, and the ultimate load was considerably higher than the analytical bifurcation prediction. The asymmetric buckling mode shape, however, initially appeared at a pressure near the analysis bifurcation solution.
The placement of thermal or force actuators to control slowly varying disturbances in the shape of large space structures is investigated analytically. Expressions are derived based on disturbances defined as the worst linear combination of a given set of functions and minimized numerically using the NEWSUMT optimization package. Results are presented in tables and graphs for a free-free beam with equidistant controls and polynomial-form (order 2-6) disturbances. Control placement is found to be of greater importance for force actuators, but is also of significance for thermal actuators.
A research effort was undertaken to develop personal computer based software for vibrational analysis. The software was developed to analytically determine the natural frequencies and mode shapes for the uncoupled lateral vibrations of the blade and counterweight assemblies used in a single bladed wind turbine. The uncoupled vibration analysis was performed in both the flapwise and chordwise directions for static rotor conditions. The effects of rotation on the uncoupled flapwise vibration of the blade and counterweight assemblies were evaluated for various rotor speeds up to 90 rpm. The theory, used in the vibration analysis codes, is based on a lumped mass formulation for the blade and counterweight assemblies. The codes are general so that other designs can be readily analyzed. The input for the codes is generally interactive to facilitate usage. The output of the codes is both tabular and graphical. Listings of the codes are provided. Predicted natural frequencies of the first several modes show reasonable agreement with experimental results. The analysis codes were originally developed on a DEC PDP 11/34 minicomputer and then downloaded and modified to run on an ITT XTRA personal computer. Studies conducted to evaluate the efficiency of running the programs on a personal computer as compared with the minicomputer indicated that, with the proper combination of hardware and software options, the efficiency of using a personal computer exceeds that of a minicomputer.
The method of matched asymptotic expansions is used to solve the transverse free vibration of a slightly curved, thin rectangular plate. Analytical results for natural frequencies and mode shapes are presented in the limit when the dimensionless bending rigidity, epsilon, is small compared with in-plane forces. Results for different boundary conditions are obtained when the initial deflection is: (1) a polynomial in both directions, and (2) the product of a polynomial and a trigonometric function, and arbitrary. For the arbitrary initial deflection case, the Fourier series technique is used to define the initial deflection. The results obtained show that the natural frequencies of vibration of slightly curved plates are coincident with those of perfectly flat, prestressed rectangular plates. However, the eigenmodes are very different from those of initially flat prestressed rectangular plates. The total deflection is found to be the sum of the initial deflection, the deflection resulting from the solution of the flat plate problem, and the deflection resulting from the static problem.
A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict the flutter speed, frequency, and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis.
A new analytical method is presented for generating component shape vectors, or Ritz vectors, for use in component synthesis. Based on the concept of a block-Krylov subspace, easily derived recurrence relations generate blocks of Ritz vectors for each component. The subspace spanned by the Ritz vectors is called a block-Krylov subspace. The synthesis uses the new Ritz vectors rather than component normal modes to reduce the order of large, finite-element component models. An advantage of the Ritz vectors is that they involve significantly less computation than component normal modes. Both 'free-interface' and 'fixed-interface' component models are derived. They yield block-Krylov formulations paralleling the concepts of free-interface and fixed-interface component modal synthesis. Additionally, block-Krylov reduced-order component models are shown to have special disturbability/observability properties. Consequently, the method is attractive in active structural control applications, such as large space structures. The new fixed-interface methodology is demonstrated by a numerical example. The accuracy is found to be comparable to that of fixed-interface component modal synthesis.
A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other.
Report presents study of some sources of error in analysis, by geometric theory of diffraction (GTD), of performance of high-gain, dual-shaped antenna reflector. Study probes into underlying analytic causes of singularity, with view toward devising and testing practical methods to avoid problems caused by singularity. Hybrid physical optics (PO) approach used to study near-field spillover or noise-temperature characteristics of high-gain relector antenna efficiently and accurately. Report illustrates this approach and underlying principles by presenting numerical results, for both offset and symmetrical reflector systems, computed by GTD, PO, and PO/GO methods.
An analytical investigation is conducted to determine the shape of a growing delamination and the distribution of the energy release rate along the delamination front in a laminated composite double cantilever beam specimen. Distributions of the energy release rate for specimens with straight delamination fronts and delamination front contours for delaminations whose growth is governed by the fracture criterion that G = Gc at all points are predicted as a function of material properties and delamination length. The predicted delamination front contours are utilized to ascertain the effect of the changing shape of the delamination front on the value of the critical strain energy release rate as computed from double cantilever beam fracture toughness test data.
ESMOSS is a specialized software system for the construction of geometric descriptive and discrete analytical models of engine parts, components and substructures which can be transferred to finite element analysis programs such as NASTRAN. The software architecture of ESMOSS is designed in modular form with a central executive module through which the user controls and directs the development of the analytical model. Modules consist of a geometric shape generator, a library of discretization procedures, interfacing modules to join both geometric and discrete models, a deck generator to produce input for NASTRAN and a 'recipe' processor which generates geometric models from parametric definitions. ESMOSS can be executed both in interactive and batch modes. Interactive mode is considered to be the default mode and that mode will be assumed in the discussion in this document unless stated otherwise.
An experimental method has been developed to determine the water droplet impingement characteristics on two- and three-dimensional aircraft surfaces. The experimental water droplet impingement data are used to validate particle trajectory analysis codes that are used in aircraft icing analyses and engine inlet particle separator analyses. The aircraft surface is covered with thin strips of blotter paper in areas of interest. The surface is then exposed to an airstream that contains a dyed-water spray cloud. The water droplet impingement data are extracted from the dyed blotter paper strips by measuring the optical reflectance of each strip with an automated reflectometer. Experimental impingement efficiency data represented for a NLF (1)-0414 airfoil, a swept MS (1)-0317 airfoil, a Boeing 737-300 engine inlet model, two simulated ice shapes and a swept NACA 0012 wingtip. Analytical impingement efficiency data are also presented for the NLF (1)-0414 airfoil and the Boeing 737-300 engine inlet model.
An analytical procedure for the determination of the shape of a Leading-Edge Extension (LEE) which satisfies design criteria, including especially noninterference at the wing design point, has been developed for thick delta wings. The LEE device best satisfying all criteria is designed to be mounted on a wing along a dividing stream surface associated with an attached flow design lift coefficient (C L,d ) of greater than zero. This device is intended to improve the aerodynamic performance of transonic aircraft at C L greater than C L,d system emanating from the LEE leading edge. In order to quantify this process a twisted and cambered thick delta wing was chosen for the initial application of this design procedure. Appropriate computer codes representing potential and vortex flows were employed to determine the dividing stream surface at C L,d and an optimized LEE planform shape at C L greater than C L,d , respectively. To aid in the LEE selection, the aerodynamic effectiveness of 36 planforms was investigated at C L greater than C L,d . This study showed that reducing the span of the candidate LEEs has the most detrimental effect on overall aerodynamic efficiency, regardless of the shape or area. Furthermore, for a fixed area, constant-chord LEE candidates were relatively more efficient than those with sweep less than the wing. At C L,d , the presence of the LEE planform best satisfying the design criteria was found to have no effect on the wing alone aerodynamic performance.
How does experimental mechanics contribute to aircraft aeroelastic airworthiness? The aviation community is always improving analysis and testing techniques to realize quicker, cheaper, reliable solutions. A ground vibration test (GVT) is conducted to identify structural mode shapes, frequencies, and damping values to validate analytical models used for flutter analysis, which shows whether a structure has acceptable aeroelastic flutter margins for airworthiness. The FLL recently conducted a GVT of the Passive Aeroelastic Tailored (PAT) Wing using an experimental modal technique called Fixed Base Correction (FBC). The GVT objective was to obtain the PAT wing modal characteristics to compare test results with finite element model (FEM) results for the tow-steered wingbox.
Bisphenol A-based epoxies are much used in a wide range of composite and coating applications due to their excellent thermomechanical properties. However, their 3D printability remains a challenge with most reported materials suffering from high brittleness and low toughness. In this work, we have described especially modified epoxy resins that enable 3D printing with both fast and slow curing rates. These materials exhibit greatly enhanced toughness, tunable thermomechanical properties, and excellent shape memory behavior. Two different printing systems, including a two-part static mixing printhead and a single extrusion printhead, were developed for fast- and slow-curing epoxies, respectively. The rheology of inks in both systems has been modified into printable thixotropic fluids with the aid of silica nanoparticles and other additives. Epoxide-functionalized telechelic polybutadiene was added into the resins, which are then introduced inside the epoxy network after cross-linking. The addition of polybutadiene rubber significantly improves the toughness (over 135%), fracture strain (over 200%), and shape memory behavior. By adding different amounts of the rubber telechelic, thermomechanical properties, including modulus, elongation, and Tg of epoxy, can be well controlled in a wide range to satisfy different applications.
Ion mobility spectrometry (IMS) is a gas-phase analytical technique that separates ions with different sizes and shapes and is compatible with mass spectrometry (MS) to provide an additional separation dimension. The rapid nature of the IMS separation combined with the high sensitivity of MS-based detection and the ability to derive structural information on analytes in the form of the property collision cross section (CCS) makes IMS particularly well-suited for characterizing complex samples in -omics applications. In such applications, the quality of CCS from IMS measurements is critical to confident annotation of the detected components in the complex -omics samples. However, most IMS instrumentation in mainstream use requires calibration to calculate CCS from measured arrival times, with the most notable exception being drift tube IMS measurements using multifield methods. The strategy for calibrating CCS values, particularly selection of appropriate calibrants, has important implications for CCS accuracy, reproducibility, and transferability between laboratories. The conventional approach to CCS calibration involves explicitly defining calibrants ahead of data acquisition and crucially relies upon availability of reference CCS values. In this work, we present a novel reference-free approach to CCS calibration which leverages trends among putatively identified features and computational CCS prediction to conduct calibrations post-data acquisition and without relying on explicitly defined calibrants. We demonstrated the utility of this reference-free CCS calibration strategy for proteomics application using high-resolution structures for lossless ion manipulations (SLIM)-based IMS-MS. In conclusion, we first validated the accuracy of CCS values using a set of synthetic peptides and then demonstrated using a complex peptide sample from cell lysate.
Tunneling barriers are an essential component of electron sources, sensors, detectors, and vacuum nanoelectronics, and a pivotal factor in their performance, but the barriers themselves routinely depart from the analytic models used to model their behavior. Here, a new formalism is developed to analytically and accurately model emission through and over barriers associated with depletion layers, nanotip barriers, and MIM structures. The transmission probability for depletion layer and metal-insulator-metal (MIM) and metaloxide-semiconductor (MOS) barriers is accurately modeled as the electron energy exceeds the barrier height using approaches designed for rapid implementation demanded by simulation codes, and extensible to general barriers. The models supersede conventional thermal and field models in depletion and MIM/MOS barrier studies. Thermal-field methods are used to treat the transmission probability, and shape factor methods to treat the tunneling factor. Analytic formulae for current density are obtained. The methods ease device simulation and characterization of current-voltage relations for emerging technologically interesting barriers with better accuracy.