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The bellows flow excitation mechanism and results of comprehensive test program are summarized. The analytical model for predicting bellows flow induced stress is refined. The model includes the effects of an upstream elbow, arbitrary geometry, and multiple piles. A refined computer code for predicting flow induced stress is described which allows life prediction if a material S-N diagram is available.
Space Shuttle Main Engine/Structural Tailoring of Engine Blades (SSME/STAEBL) was developed by systematically modifying and enhancing the STAEBL code developed by Pratt and Whitney under contract to NASA Lewis Research Center. STAEBL was designed for application to gas turbine blade design. Typical design variables include blade thickness distribution and root chord. Typical constraints include resonance margins, root stress, and root to chord ratios. In this program, the blade is loaded by centrifugal forces only. Additions and modifications of STAEBL included in SSME/STAEBL include (1) thermal stress analysis; (2) gas dynamic (pressure) loads; (3) temperature dependent material and thermal properties; (4) forced vibrations; (5) tip displacement constraints; (6) single crystal material analysis; (7) blade cross section stacking offsets; and (8) direct time integration algorithm for transient dynamic response. Capabilities are also included which permit data transfer from finite element models and stand-alone analysis.
High surface temperatures and temperature gradients can affect the vibratory characteristics and stability of aircraft structures. Aircraft designers are relying more on finite-element model analysis methods to ensure sufficient vehicle structural dynamic stability throughout the desired flight envelope. Analysis codes that predict these thermal effects must be correlated and verified with experimental data. Experimental modal data for aluminum, titanium, and fiberglass plates heated at uniform, nonuniform, and transient heating conditions are presented. The data show the effect of heat on each plate's modal characteristics, a comparison of predicted and measured plate vibration frequencies, the measured modal damping, and the effect of modeling material property changes and thermal stresses on the accuracy of the analytical results at nonuniform and transient heating conditions.
Noise transmission measurements were made for a 0.020-inch panel with and without air flow on its surface. Tests were conducted with both an absorbent and reverberant chamber behind the panel. Panel stresses for some of these tests were also determined. Noise spectra obtained inside the absorbent chamber with flow attached and flow not attached to the panel appeared to contain several peaks corresponding in frequency to panel vibration modes. These peaks were notably absent when the chamber was reverberant. The noise reduction through the test panel measured with the aid of an absorbent chamber for the flow-not-attached case is in general agreement with values predicted by the theoretical weight law, which assumes negligible panel stiffness. Corresponding data for the flow-attached case do not follow the weight law but rather indicate less noise reduction at the high frequencies. The main stress responses of the panel without air flow occurred at its fundamental vibration mode. In the presence of air flow the main response occurs in a vibration mode having a node line perpendicular to the direction of air flow.
The temperature distributions encountered in thin solid wings subjected to aerodynamic heating induce thermal stresses that may effectively reduce the stiffness of the wing. The effects of this reduction in stiffness were investigated experimentally by rapidly heating the edges of a cantilever plate. The midplane thermal stresses imposed by the nonuniform temperature distribution caused the plate to buckle torsionally, increased the deformations of the plate under a constant applied torque, and reduced the frequency of the first two natural modes of vibration. By using small-deflection theory and employing energy methods, the effect of nonuniform heating on the plate stiffness was calculated. The theory predicts the general effects of the thermal stresses, but becomes inadequate as the temperature difference increases and plate deflections become large.
The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the true stress, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Rayleigh-Ritz method of finding upper limits. The theory of the lower-limit procedure has been given by Trefftz, but, in the present application, the method differs from that of Trefftz in a way that makes it inherently more quickly convergent. It is expected that in other buckling problems and in some vibration problems the Lagrangian multiplier method of finding upper and lower limits may be advantageously applied to the calculation of buckling stresses and natural frequencies.
A flow-generating rotor has been designed under NASA contract NAS3-7614 to enable three transonic stators to be tested. The stators were designed by NASA in conjunction with the Contractor. Design analyses were conducted and the results indicate that the rotor will produce the required inlet flow to the stators. Structural and vibration analyses indicate that resonances and critical speeds occur outside the operating range and that the component stresses will be well within the capabilities of the materials used. Design details of the flow generation rotor and the three transonic stators are presented.
Report presents theoretical and experimental study of stiffness of lightweight, jointed pressure vessels made of wound graphite fibers and epoxy. Specimens fabricated from layers of graphite fibers, wet with epoxy, on aluminum mandrel. Segment ends thickened with interspersed layers of axially oriented fibers to reduce pinhole bearing stresses and local deformations. Segments cured at 390 degrees F (199 degrees C). Report presents results of vibrational tests of one-quarter-scale models of wound-filament pressure vessels.
Nonlinear equations of motion of symmetrically laminated anisotropic plates are derived accounting for von Karman strains. The effect of transverse shear is included in the formulation and the rotatory inertia effect is ignored. Using a single-mode Galerkin procedure the nonlinear modal equation is obtained. Direct equivalent linearization is employed. The response of acoustic excitation on moderately thick composite panels is studied. Further, the effects of transverse shear on large deflection vibration of laminates under random excitation are studied. Mean-square deflection and mean-square inplane stresses are obtained for some symmetric graphite-epoxy laminates. Using equilibrium equations and the continuity requirements, the mean-square transverse shear stresses are calculated. The results obtained will be useful in the sonic fatigue design of composite aircraft panels. The analysis is presented in detail for simply supported plate. The analogous equations for a clamped case are given in the appendix.
Nonlinear equations of motion of symmetrically laminated anisotropic plates are derived accounting for von Karman strains. The effect of transverse shear is included in the formulation. Using a single-mode Galerkin procedure, the nonlinear modal equation is obtained. The direct equivalent linearization method is employed for solution of this equation. The response to acoustic excitation of moderately thick composite panels is studied. Further, the effects of transverse shear on large deflection vibration of laminates under random excitation are studied. Mean-square deflections and mean-square inplane stresses are obtained for symmetric graphite-epoxy laminates. Using equilibrium equations and the continuity requirements, the mean-square transverse shear stresses are calculated. The results obtained will be useful in the sonic fatigue design of composite aircraft panels. The analysis is presented in detail for simply supported plates. The analogous equations for a clamped case are also obtained.
Special needs are imposed on the design and operation of a sensor test and integration lab. Cryogenic temperature, vibration isolation for electro-optical equipment, contamination control, thermal control to reduce or minimize thermally induced stresses on mirrors and supporting metering structure, thermal vacuum chamber shroud temperature uniformity, and varying temperature control capability to bring optical equipment from cryogenic temperature to ambient environment, and real time processing are some of the stringent needs that must be addressed before a facility can be accepted to perform sensor test and integration. Most of the sensor tests are performed at cryogenic temperature, and thermal isolation of the test article from the ambient temperature is a strong consideration for the thermal vacuum chamber design. Also, equipment heat and parasitic heat sources must be able to be removed from the chamber without exceeding the chamber shroud temperature gradients. How these needs were met in the design, build, and acceptance test of the Grumman Sensor Test and Integration Lab (STIL) is described.
Elastic and shear moduli were determined for two aluminum matrix composites containing 20 and 40 volume percent discontinuous silicon carbide, respectively, using transverse, longitudinal, and torsional vibrational modes of specimens prepared as thin beams. These moduli are consistent with those determined from stress-strain measurements. The damping factors for these modes were also determined. Thermal properties are used to show that part of the damping of transverse modes is caused by the transverse thermal currents discussed by C. Zener (thermo-elastic damping); this damping is frequency-dependent with a maximum damping factor of approximately 0.002. The remaining damping is frequency-independent, and has roughly similar values in transverse, longitudinal, and torsional modes: approximately 0.0001.
The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the truss, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Raleigh-Rite method of finding upper limits. The theory of the lower-limit procedure has been given by Trefftz but, in the present application, the method differs from that of Trefftz in a way that makes it inherently more quickly convergent. It is expected that in other buckling problems and in some vibration problems problems the Lagrangian multiplier method finding upper and lower limits may be advantageously applied to the calculation of buckling stresses and natural frequencies.
An integrated computerized approach for design and stress analysis of low-noise spiral bevel gear drives with adjusted bearing contact is proposed. The procedure of computations is an iterative process that requires four separate procedures and provide: (a) a parabolic function of transmission errors that is able to reduce the effect of errors of alignment on noise and vibration, and (b) reduction of the shift of bearing contact caused by misalignment. Application of finite element analysis enables us to determine the contact and bending stresses and investigate the formation of the bearing contact. The design of finite element models and boundary conditions is automated and does not require intermediate CAD computer programs for application of general purpose computer program for finite element analysis.
Calcium related injuries to plants grown in controlled environments under conditions which maximize plant growth rates are described. Procedures to encourage movement of calcium into developing leaves of lettuce plants were investigated. The time course and pattern of calcium accumulation was determined to develop effective control procedures for this injury, termed tipburn. Procedures investigated were: (1) increasing the relative humidity to saturation during the dark period and altering root temperatures, (2) maximizing water stress during light and minimizing water stress during dark periods, (3) shortening the light-dark cycle lengths in combination with elevated moisture levels during the dark cycles, (4) reducing nutrient concentrations and (5) vibrating the plants. Saturated humidities at night increased the rate of growth and the large fluctuation in plant water potential encouraged calcium movement to the young leaves and delayed tipburn. Root temperature regulation between 15 and 26 C was not effective in preventing tipburn. Attempts to modulate water stress produced little variation, but no difference in tipburn development. Variations in light-dark cycle lengths also had no effect on calcium concentrations within developing leaves and no variation in tipburn development. Low concentrations of nutrient solution delayed tipburn, presumably because of greater calcium transport in the low concentration plants. Shaking of the plants did not prevent tipburn, but did delay it slightly.
Development in the modeling and simulation of shock and vibration phenomena are considered. Predicting the noise exposure of payloads in the space shuttle, prediction for step-stress fatigue, pyrotechnique shock simulation using metal-to-metal impact, and prediction of fragment velocities and trajectories are among the topics covered.
An approximate theory of laminated plates is developed by assuming that the extensioral and thickness mode of vibration are coupled. The mixed boundary value crack problem of a four layered composite plate is solved. Dynamic stress intensity factors for a crack subjected to suddenly applied stress are found to vary as a function of time and depend on the material properties of the laminate. Stress intensification in the region near the crack front can be reduced by having the shear modulus of the inner layers to be larger than that of the outer layers.
A survey is presented of recently published papers in the field of optimum structural design of plates, largely with respect to the minimum-weight design of plates subject to such constraints as fundamental frequency maximization. It is shown that, due to the availability of powerful computers, the trend in optimum plate design is away from methods tailored to specific geometry and loads and toward methods that can be easily programmed for any kind of plate, such as finite element methods. A corresponding shift is seen in optimization from variational techniques to numerical optimization algorithms. Among the topics covered are fully stressed design and optimality criteria, mathematical programming, smooth and ribbed designs, design against plastic collapse, buckling constraints, and vibration constraints.