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Four processes for producing blades are examined. Two use filament winding techniques and two involve filling a mold or form to produce all or part of a blade. The processes are described and a comparison is made of costs, material properties, designs and free vibration characteristics. Conclusions are made regarding the feasibility of each process to produce low-cost, structurally adequate blades.
Status and recent applications of computerized symbolic manipulation to structural mechanics problems are summarized. The applications discussed include; (1) generation of characteristic arrays of finite elements; (2) evaluation of effective stiffness and mass coefficients of continuum models for repetitive lattice structures; and (3) application of Rayleigh-Ritz technique to free vibration analysis of laminated composite elliptic plates. The major advantages of using computerized symbolic manipulation in each of these applications are outlined. A number of problem areas which limit the realization of the full potential of computerized symbolic manipulation in structural mechanics are examined and some of the means of alleviating them are discussed.
Higher order correction terms for the stiffness and inertia matrices associated with a triangular plane stress-strain finite dynamic element are developed in detail. Numerical results are presented which indicate that the adoption of these matrices along with a suitable quadratic matrix eigenproblem solver effects a significant economy in the free vibration solution of structure when compared with the analysis based on the usual finite element procedure. Finally, a FORTRAN IV computer program listing of the various relevant matrices is given.
A simple procedure is presented for predicting the thermoelastic and free vibration responses of large repetitive beam-like trusses. The procedure is based on replacing the original lattice structure by an equivalent continuum beam model and obtaining closed-form (exact) solutions for the beam model. The equivalent beam model accounts for warping and shear deformation in the plane of the cross-section and is characterized by its thermoelastic strain and kinetic energies, from which the equations of motion and constitutive relations can be derived. The high accuracy of the results obtained by the proposed approach is demonstrated by means of numerical examples.
An unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, was developed to predict aerodynamic forces and moments associated with free vibration or flutter phenomena in the fan, compressor, or turbine stages of modern jet engines. Based on the assumption of small amplitude blade motions, the unsteady flow is governed by linear equations with variable coefficients which depend on the underlying steady low. These equations were approximated using difference expressions determined from an implicit least squares development and applicable on arbitrary grids. The resulting linear system of algebraic equations is block tridiagonal, which permits an efficient, direct (i.e., noniterative) solution. The solution procedure was extended to treat blades with rounded or blunt edges at incidence relative to the inlet flow.
A consistent approach is developed for the determination of trial functions for a class of shells of revolution. The trial functions satisfy the in-plane and out-of-plane boundary conditions at the shell ends and include the effects of tangential inertia. The resulting expressions converge rapidly for the problem of linear free vibration
After describing independent theoretical studies of the eigenfunctions of the X 2Pi and excited A 2Sigma(+), B 2Sigma(+), and C 2Sigma(+) states of OH, results are presented for the transition dipole moments connecting each excited state to the others and to the ground state. The radiative lifetimes derived from calculation of the bound-bound and bound-free vibrational band transition probabilities are compared with measured values, confirming recent measurements of the A 2Sigma(+) and C 2Sigma(+) states but not the lifetimes measured for the B 2Sigma(+) state.
Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.
Truss beams with members having viscous damping are modeled with a Timoshenko beam. Procedures for deriving the equivalent bending rigidity, transverse shear rigidity, and damping are presented. Explicit expressions for these equivalent beam properties are obtained for a specific truss beam. The beam model thus established is then used to investigate the effect of damping in free vibration. Finally, the beam is employed in the estimation of structural parameters in a simply-supported truss beam using a random search algorithm.
An experimental method of measuring material damping of a specimen in free fall has been developed. An initially simply-supported test specimen was simultaneously excited and lofted into free fall with a spring-mass launcher. The launcher could be tuned to produce varying initial stress amplitude levels in the specimens. Damping information was obtained from the transient response of the specimens while in free fall in a vacuum. A dynamic model of the launch process was developed which indicates the range of frequency and initial specimen stress amplitude over which tests can be performed. To verify the facility, material damping was measured in 2024-T3 aluminum, and (+ or - 45)2s AS1/3501-6 graphite/epoxy. Free-free frequencies ranged from 20-357 Hz in aluminum, and from 18-171 Hz in the (+ or - 45)2s specimens. Damping values in aluminum were found to be close to theoretical values and independent of stress levels below 130 MPa (18.7 Ksi). Damping ratios in the (+ or - 45)2s graphite/epoxy specimens were found to be largely independent of stress levels below 43.8 MPa (6.35 Ksi) and only slightly dependent on frequency. A small dependence of the frequency of free vibration on specimen stress amplitude was also noted.
A unified efficient formulation for the static and dynamic reanalysis of locally modified structures is presented. The reanalysis problem is to find the structural responses when some of the element properties are adjusted as a result of design modifications or when additional structures are appended to the original system. The reanalysis problem is formulated as a problem of much lower order than the original system. This is achieved by utilizing the linearity property of the structure using the pseudoload concept together with the solution of the original system. The modifications to the structure are treated as displacement-dependent pseudoloads of the system. By expressing the modified system response as linear combinations of the response of the original system and a term depending on the pseudoload, a reduced set of response equations can be obtained. In the static and sinusoidal steady state analysis, this leads to a set of linear algebraic equations. For a free vibration analysis, this results in a reduced eigenvalue problem. Using these reduced equations, a design problem can be solved; that is, the magnitude of a specified local modification for given dynamic response characteristics can be calculated. Several examples are presented to illustrate the general formulations.
A very low-power, low-interference Stirling cryocooler is being developed based on principles and techniques described in several previous publications over the last four years. It differs in several important details from those built previously. It uses a tapered displacer based upon an analytical optimization procedure. The displacer is driven by an auxiliary piston and cylinder (rather than by mechanical linkage) using some of the working fluid itself to provide the driving force. This provides smooth, vibration-free motion, and, more importantly, allows complete mechanical and spatial separation of the cryostat from the pressure-wave generator. Either of two different pressure-wave generators can be used. One is a non-contaminating, unlubricated ceramic piston and cylinder. The other is a compressed-air-operated rubber diaphragm with motor-driven valves to cycle the pressure between appropriate limits.
Molecular flow velocity of N2 was measured in a supersonic wind tunnel using inverse Raman spectroscopy. This technique employs the large Doppler shift exhibited by the molecules when the pump and probe laser beams are counter-propagating (backward scattering). A retrometer system is employed to yield a vibration-free optical configuration which has the additional advantage of obtaining both the forward and backward scattered spectra simultaneously. The linebreadths and their relative Doppler shift can be used to determine the static pressure, translational temperature, and molecular flow velocity. A demonstration of the concept was performed in a supersonic wind tunnel and included: (1) measurements over the Mach number range 2.50 to 4.63; (2) static pressure measurements (at Mach 2.50) corresponding to a Reynolds number per foot range of 1 to 5 x 10 to the 6th power; and (3) measurements behind the shock wave of a flat plate model.
Recent research activities at NASA Lewis Research Center to computationally evaluate the effects of interply layer progressive weakening (degradation) on the structural response of a composite beam are summarized. The structural responses of interest include: (1) bending, (2) buckling, (3) free vibrations, (4) periodic excitation, and (5) impact. Finite element analysis was used for the computational evaluations. The interply layer degradation effects on the various structural responses were determined and assessed as a function of the interply layer modulus varying from 1 million psi down to 1000 psi and even lower for some limiting cases. The results obtained show that the interply layer degradation has generally negligible effects on composite structural response and, therefore, structural integrity, unless the interply layer modulus degrades to about 10,000 psi or less.
The paper describes the development of an eight-node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices. Numerical test results of free vibration analyses are presented in detail for the newly developed eight-node element and also the corresponding four-node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures. Such results indicate a superior pattern of solution convergence of the presently developed dynamic element.
A vibration free fluid compressor particularly adapted for Stirling cycle cryogenic refrigeration apparatus comprises a pair of identical opposing ferromagnetic pistons located in a housing and between a gas spring including a sealed volume of a working fluid such as gas under pressure. The gas compresses and expands in accordance with movement of the pistons to generate a compression wave which can be vented to other apparatus, for example, a displacer unit in a Stirling cycle engine. The pistons are urged outwardly due to the pressure of the gas; however, a fixed electromagnetic coil assembly located in the housing adjacent the pistons, is periodically energized to produce a magnetic field which interlinks the pistons in such a fashion that the pistons are mutually attracted to one another. The mass of the pistons, in conjunction with the compressed gas between them, form a naturally resonant system which, when the pistons are electromagnetically energized, produces an oscillating compression wave in the entrapped fluid medium.
Recent research activities at NASA Lewis Research Center to computationally evaluate the effects of interply layer progressive weakening (degradation) on the structural response of a composite beam are summarized. The structural responses of interest include: (1) bending, (2) buckling, (3) free vibrations, (4) periodic excitation, and (5) impact. Finite element analysis was used for the computational evaluations. The interply layer degradation effects on the various structural responses were determined and assessed as a function of the interply layer modulus varying from 1 million psi down to 1000 psi and even lower for some limiting cases. The results obtained show that the interply layer degradation has generally negligible effectss on composite structural response and, therefore, structural integrity, unless the interply layer modulus degrades to about 10,000 psi or less.
The paper is concerned with the development of novel numerical procedures for the solution of static, stability, free vibration and dynamic response analysis of large, complex practical structures. Thus, details of numerical algorithms evolved for dynamic analysis of usual non-rotating and also rotating structures as well as finite dynamic elements are presented in the paper. Furthermore, the article provides some description of a general-purpose computer program STARS specifically developed for efficient analysis of complex practical structures.