Vibrations of a spherical shell under the action of a concentrated force
Spherical shell vibrations under continuosly distributed load over surface solved by Fourier method
VIBRATION↗
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Results for “Load Distribution”
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On the calculation of hanging roofings
Fundamental equations for nonaxisymmetrical case of circular hanging roof subjected to uniformly distributed load along with snow load
SNOW↗
Elastic plate spallation
The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.
Oline, L.↗
The prediction of rotor rotational noise using measured fluctuating blade loads
In tests conducted at the NASA Langley Research Center Helicopter Rotor Test Facility, simultaneous measurements of the high-frequency fluctuating aerodynamic blade loads and far-field radiated noise were made on a full-scale, nontranslating rotor system. After their characteristics were determined, the measured blade loads were used in an existing theory to predict the far-field rotational noise. A comparison of the calculated and measured rotational noise is presented with specific attention given to the effect of blade loading coefficients, chordwise loading distributions, blade loading phases, and observer azimuthal position on the predictions.
Hosier, R. N.↗
Helicopter rotor rotational noise predictions based on measured high-frequency blade loads
In tests conducted at the Langley helicopter rotor test facility, simultaneous measurements of up to 200 harmonics of the fluctuating aerodynamic blade surface pressures and far-field radiated noise were made on a full-scale nontranslating rotor system. After their characteristics were determined, the measured blade surface pressures were converted to loading coefficients and used in an existing theory to predict the far-field rotational noise. A comparison of the calculated and measured noise shows generally good agreement up to 300 to 600 Hz, depending on the discreteness of the loading spectrum. Specific attention is given to the effects of the blade loading coefficients, chordwise loading distributions, blade loading phases, and observer azimuthal position on the calculations.
Hosier, R. N.↗
Calculation of the longitudinal aerodynamic characteristics of upper-surface-blown wing-flap configurations
An engineering method for predicting the longitudinal aerodynamic characteristics of wing-flap configurations with upper surface blowing (USB) was developed. Potential flow models were incorporated into the prediction method: a wing and flap lifting surface model and a jet wake model. The wing-flap model used a vortex-lattice to represent the wing and flaps. The wing had an arbitrary planform and camber and twist, and the flap system was made up of a Coanda flap and other flap segments of arbitrary size. The jet wake model consisted of a series of closely spaced rectangular vortex rings. The wake was positioned such that it was tangent to the upper surface of the wing and flap between the exhaust nozzle and the flap trailing edge. It was specified such that the mass, momentum, and spreading rates were similar to actual USB jet wakes. Comparisons of measured and predicted pressure distributions, span load distributions, and total lift and pitching-moment coefficients on swept and unswept USB configurations are included. A wide range of thrust coefficients and flap deflection angles were considered at angles of attack up to the onset of stall.
Mendenhall, M. R.↗
Numerical procedures for the calculation of the stresses in monocoques III : calculation of the bending moments in fuselage frames
This report deals with the calculation of the bending moments in and the distortions of fuselage rings upon which known concentrated and distributed loads are acting. In the procedure suggested, the ring is divided into a number of beams each having a constant radius of curvature. The forces and moments caused in the end sections of the beams by individual unit displacements of the end sections are listed in a table designated as the operations table in conformity with Southwell's nomenclature. The operations table and the external loads are equivalent to a set of linear equations. For their solution the following three procedures are presented: 1) Southwell's method of systematic relaxations. This is a step-by-step approximation procedure guided by the physical interpretation of the changes in the values of the unknown. 2) The growing unit procedure in which the individual beams are combined successively into beams of increasing length until finally the entire ring becomes a single beam. In each step of the procedure a set of not more than three simultaneous linear equations is solved. 3) Solution of the entire set of simultaneous equations by the methods of the matrix calculus. In order to demonstrate the manner in which the calculations may be carried out, the following numerical examples are worked out: 1) Curved beam with both its end sections rigidly fixed. The load is a concentrated force. 2) Egg-shape ring with symmetric concentrated loads. 3) Circular ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 4) Same with V-braces incorporated in the ring. 5) Egg-shape ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 6) Same with V-braces incorporated in the ring. The results of these calculations are checked, whenever possible, by calculations carried out according to known methods of analysis. The agreement is found to be good. The amount of work necessary for the solution of ring problems by the methods described in the present report is practically independent of the degree of redundancy of the structure. For this reason the methods are recommended for use particularly in problems of rings having one or more internal bracing elements.
LOADS - FUSELAGES↗
A Method of Determining Aerodynamic-Influence Coefficients from Wind-Tunnel Data for Wings at Supersonic Speeds
A method is described for determining aerodynamic-influence coefficients from wind-tunnel data for calculating the steady-state load distribution on a wing with arbitrary angle-of-attack distribution at supersonic speeds. The method combines linearized theory with empirical adjustments in order to give accurate results over a wide range of angles of attack. The experimented data required are pressure distributions measured on a flat wing of the desired planform at the desired Mach number and over the desired range of angles of attack. The method has been tested by applying it to wind-tunnel data measured at Mach numbers of 1.61 and 2.01 on wings of the same planform but of different surface shapes. Influence coefficients adjusted to fit the flat wing gave good predictions of the spanwise and chord-wise distributions of loadings measured on twisted and cambered wings.
Gainer, Patrick A.↗
DACS II - A distributed thermal/mechanical loads data acquisition and control system
A distributed data acquisition and control system has been developed for the NASA Flight Loads Research Facility. The DACS II system is composed of seven computer systems and four array processors configured as a main computer system, three satellite computer systems, and 13 analog input/output systems interconnected through three independent data networks. Up to three independent heating and loading tests can be run concurrently on different test articles or the entire system can be used on a single large test such as a full scale hypersonic aircraft. Thermal tests can include up to 512 independent adaptive closed loop control channels. The control system can apply up to 20 MW of heating to a test specimen while simultaneously applying independent mechanical loads. Each thermal control loop is capable of heating a structure at rates of up to 150 F per second over a temperature range of -300 to +2500 F. Up to 64 independent mechanical load profiles can be commanded along with thermal control. Up to 1280 analog inputs monitor temperature, load, displacement and strain on the test specimens with real time data displayed on up to 15 terminals as color plots and tabular data displays. System setup and operation is accomplished with interactive menu-driver displays with extensive facilities to assist the users in all phases of system operation.
Zamanzadeh, Behzad↗
The Distribution of Loads on Rivets Connecting a Plate to a Beam under Transverse Loads
This report gives theoretical discussion of the distribution of leads on rivets connecting a plate to a beam under transverse leads. Two methods of solution are given which are applicable to loads up to the limit of proportionality; in the first the rivets are treated as discrete members, and in the second they are replaced by a continuous system of jointing. A method of solution is also given which is applicable to the case when nonlinear deformations occur in the rivets and the plate, but not in the beam. The methods are illustrated by numerical examples, and these show that the loads carried by the rivets and the plate are less than the values given by classical theory, which does not take into account the slip of the rivets, even below the limit of proportionality. The difference is considerably accentuated when nonlinear deformations occur in the restructure and the beam then carries the greater portion of the bending moment. If the material of the beam has a higher proportional limit and a higher ultimate strength than the material of the plate, there is thus a transfer of load from weaker to stronger material, and this is to the advantage of the structure. The methods given are of simple application and are recommended for use in the design of light-alloy structures when the design lead is likely to be above the proportional limit.
Vogt, F.↗
Growth characteristics of a plane crack subjected to three-dimensional loading
The closed form expressions for the stress intensity factors due to concentrated forces applied to the surfaces of a half plane crack in an infinite body are used to generate solutions for distributed loads in this geometry. The stress intensity factors for uniformly distributed loads applied over a rectangular portion of the crack surface are given in closed form. An example of non-uniformly distributed loads which can be treated numerically is also included. In particular, combinations of normal and shear stresses on the crack which simulate the case of loading at an angle to the crack front are considered. The resulting stress intensity factors are combined with the strain energy density fracture criterion for the purpose of predicting the most likely direction of crack propagation. The critical value of the energy density factor can then be used for determining the allowable load on a specimen with a crack front not perpendicular to the tensile axis.
Hartranft, R. J.↗
The cylindrical antenna with non-reflecting resistive loading
Distribution of current along center-driven cylindrical antenna with variable internal impedance per unit length
ANTENNA↗
Application of Theodorsen's Theory to Propeller Design
A theoretical analysis is presented for obtaining by use of Theodorsen's propeller theory the load distribution along a propeller radius to give the optimum propeller efficiency for any design condition.The efficiencies realized by designing for the optimum load distribution are given in graphs, and the optimum efficiency for any design condition may be read directly from the graph without any laborious calculations. Examples are included to illustrate the method of obtaining the optimum load distributions for both single-rotating and dual-rotating propellers.
Crigler, John L↗
Application of Theodorsen's theory to propeller design
A theoretical analysis is presented for obtaining, by use of Theodorsen's propeller theory, the load distribution along a propeller radius to give the optimum propeller efficiency for any design condition. The efficiencies realized by designing for the optimum load distribution are given in graphs, and the optimum efficiency for any design condition may be read directly from the graph without any laborious calculations. Examples are included to illustrate the method of obtaining the optimum load distributions for both single-rotating and dual-rotating propellers.
Crigler, John L↗
Load support system analysis high speed input pinion configuration
An analysis and a series of computerized calculations were carried out to explore competing prototype design concepts of a shaft and two taper-roller bearings systems to support the high-speed input pinion of an advanced commercial helicopter transmission. The results were used to evaluate designs both for a straddle arrangement where the pinion gear is located between the bearings and for a cantilever arrangement where the pinion is outboard of the two bearings. Effects of varying parameters including applied gear load, preload, wall thickness, interference fits, bearing spacing and pinion gear location on system rigidity, load distribution and bearing rating life were assessed. A comparison of the bearing load distributions for these designs demonstrated that the straddle more equally distributes both radial and axial loads. The performance of these designs over a range of shaft rotational speeds, with lubrication and friction effects included, is also discussed.
Gassel, S. S.↗
Reduction of structural loads using maneuver load control on the Advanced Fighter Technology Integration (AFTI)/F-111 mission adaptive wing
A transonic fighter-bomber aircraft, having a swept supercritical wing with smooth variable-camber flaps was fitted with a maneuver load control (MLC) system that implements a technique to reduce the inboard bending moments in the wing by shifting the spanwise load distribution inboard as load factor increases. The technique modifies the spanwise camber distribution by automatically commanding flap position as a function of flap position, true airspeed, Mach number, dynamic pressure, normal acceleration, and wing sweep position. Flight test structural loads data were obtained for loads in both the wing box and the wing root. Data from uniformly deflected flaps were compared with data from flaps in the MLC configuration where the outboard segment of three flap segments was deflected downward less than the two inboard segments. The changes in the shear loads in the forward wing spar and at the roots of the stabilators also are presented. The camber control system automatically reconfigures the flaps through varied flight conditions. Configurations having both moderate and full trailing-edge flap deflection were tested. Flight test data were collected at Mach numbers of 0.6, 0.7, 0.8, and 0.9 and dynamic pressures of 300, 450, 600, and 800 lb/sq ft. The Reynolds numbers for these flight conditions ranged from 26 x 10(exp 6) to 54 x 10(exp 6) at the mean aerodynamic chord. Load factor increases of up to 1.0 g achieved with no increase in wing root bending moment with the MLC flap configuration.
Thornton, Stephen V.↗
Plotting max/min data envelopes
Study of maximum and minimum load distributions along structural section is aided by visual display of load distribution data. Maximum/minimum envelope plot program plots these envelopes of the stresses and shear loads at selected points in beam modeled by series of finite elements. Digital output for engineers and management is presented for quick analysis and understanding.
Furuike, T.↗
Evaluation of 3D Inverse Code Using Rotor 67 as Test Case
A design modification of Rotor 67 is carried out with a full 3D inverse method. The blade camber surface is modified to produce a prescribed pressure loading distribution, with the blade tangential thickness distribution and the blade stacking line at midchord kept the same as the original Rotor 67 design. Because of the inviscid-flow assumption used in the current version of the method, Rotor 67 geometry is modified for use at a design point different from the original design value. A parametric study with the prescribed pressure loading distribution yields the following results. In the subsonic section, smooth pressure loading shapes generally produce blades with well-behaved blade surface pressure distributions. In the supersonic section, the study shows that the strength and position of the passage shock correlate with the characteristics of the blade pressure loading shape. In general, "smooth" prescribed blade pressure loading distributions generate blade designs with reverse cambers which have the effect of weakening the passage shock.
Dang, T.↗