Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “deflection equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15

Critical stress of thin-walled cylinders in axial compression

Empirical design curves are presented for the critical stress of thin-wall cylinders loaded in axial compression. These curves are plotted in terms of the nondimensional parameters of small-deflection theory and are compared with theoretical curves derived for the buckling of cylinders with simply supported and clamped edges. An empirical equation is given for the buckling of cylinders having a length-radius ratio greater than about 0.75.

Batdorf, S B↗

Discussion of Boundary-Layer Characteristics Near the Wall of an Axial-Flow Compressor

The boundary-layer velocity profiles in the tip region of an axial-flow compressor downstream of the guide vanes and downstream of the rotor were measured by use of total-pressure and claw-type yaw probes. These velocities were resolved into two components: one along the streamline of the flow outside the boundary layer, and the other perpendicular to it. The affinity among all profiles was thus demonstrated with the boundary-layer thickness and the deflection of the boundary layer at the wall as the generalizing parameters. By use of these results and the momentum-integral equations, boundary-layer characteristics on the walls of an axial-flow compressor were qualitatively evaluated.

Mager, Artur↗

A Feasibility Study on Use of an Accelerometer to Measure the Dynamic Forces in Turning

Metal cutting is a highly dynamic process that generates continuously varying forces. Measurement of these forces is essential to characterizing a cutting process and to fully utilize the machine tool. A force dynamometer is often used to measure these varying forces; however, it is limited by the natural frequency of the sensor and can sometimes be hard to set up on a machine. Therefore, this study aims to estimate the dynamic component of the cutting force using an accelerometer placed directly below the cutting edge. The placement of the sensor helps achieving better signal to noise ratio (S/N). The cutting tool is modelled as a single degree of freedom (SDOF) system relative to the workpiece and dynamic loads are experimentally simulated on it. The measured acceleration is numerically integrated to obtain velocity and deflection, which along with the natural frequency (ω n ) and damping ratio (ζ), is used to predict the dynamic load using the system equation. The dynamic forces tested over a wide range of frequencies, show good agreement with the data from simultaneous dynamometer measurement and the force estimated using the proposed method. The study shows the feasibility of this method in a real cutting scenario and the capability to apply it to a multi DOF system. One major limitation is the inability to capture the static or quasi-static component of the cutting force.

Cutting vibrations↗

A non-linear dynamic lumped-parameter model of a rectangular plate.

A lumped-parameter model of a rectangular plate is developed by assuming fundamental mode solutions and using Hamilton's Principle and the Euler equations to set up the differential equation of motion for the system. The plate theory used may be described as the dynamic analogue of the von Karman large-deflection theory. Four sets of symmetrical boundary conditions are considered with the restriction of uniform pressure dynamic loads. The model takes the form of a mass on a cubic-hardening spring with each term defined by algebraic expressions of the plate parameters. The results for some specific problems are compared with two previous solutions. This method is less accurate but simpler to develop and apply.

Bayles, D. J.↗

Predicting Unsteady Aeroelastic Behavior

New method for predicting subsonic flutter, static deflections, and aeroelastic divergence developed. Unsteady aerodynamic loads determined by unsteady-vortex-lattice method. Accounts for aspect ratio and angle of attack. Equations for motion of wing and flow field solved iteratively and simultaneously. Used to predict transient responses to initial disturbances, and to predict steady-state static and oscillatory responses. Potential application for research in such unsteady structural/flow interactions as those in windmills, turbines, and compressors.

Strganac, Thomas W.↗

Influence of friction forces on the motion of VTOL aircraft during landing operations on ships at sea

Equations describing the friction forces generated during landing operations on ships at sea were formulated. These forces depend on the platform reaction and the coefficient of friction. The platform reaction depends on the relative sink rate and the shock absorbing capability of the landing gear. The friction coefficient varies with the surface condition of the landing platform and the angle of yaw of the aircraft relative to the landing platform. Landings by VTOL aircraft, equipped with conventional oleopneumatic landing gears are discussed. Simplifications are introduced to reduce the complexity of the mathematical description of the tire and shock strut characteristics. Approximating the actual complicated force deflection characteristic of the tire by linear relationship is adequate. The internal friction forces in the shock strut are included in the landing gear model. A set of relatively simple equations was obtained by including only those tire and shock strut characteristics that contribute significantly to the generation of landing gear forces.

Howard, J. C.↗

Large deflections of shallow conical membrane

Large deflections of a shallow elastic conical membrane fixed at the outer edge and loaded by either uniform or hydrostatic pressure are investigated. The overning equations were solved by the method of matched asymptotic expansions and by a finite difference method. Agreement between the two methods was excellent for the small values of the perturbation parameter.

Chang, W. H.↗

A recurrence matrix solution for the dynamic response of aircraft in gusts

A systematic procedure developed for the calculation of the structural response of aircraft flying through a gust by use of difference equations in the solution of dynamic problems is first illustrated by means of a simple-damped-oscillator example. A detailed analysis is then given which leads to a recurrence matrix equation for the determination of the response of an airplane in a gust. The method takes into account wing bending and twisting deformations, fuselage deflection, vertical and pitching motion of the airplane, and some tail forces. The method is based on aerodynamic strip theory, but compressibility and three-dimensional aerodynamic effects can be taken into account approximately by means of over-all corrections. Either a sharp-edge gust or a gust of arbitrary shape in the spanwise or flight directions may be treated. In order to aid in the application of the method to any specific case, a suggested computational procedure is included. The possibilities of applying the method to a variety of transient aircraft problems, such as landing, are brought out. A brief review of matrix algebra, covering the extent to which it is used in the analysis, is also included. (author)

Houbolt, John C↗

Investigation of Oxidation Profile in PMR-15 Polyimide using Atomic Microscope (AFM)

Nanoindentation measurements are made on thermosetting materials using cantiever deflection vs. piezoelectric scanner position behavior determined by AFM. The spring model is used to determine mechanical properties of materials. The generalized Sneddon's equation is utilized to calculate Young's moduli for thermosetting materials at ambient conditions. Our investigations show that the force-penetration depth curves during unloading in these materials can be described accurately by a power law relationship. The results show that the accuracy of the measurements can be controlled within 7%. The above method is used to study oxidation profiles in Pl\1R-15 polyimide. The thermo-mechanical profiles ofPNIR-15 indicate that the elastic modulus at the surface portion of the specimen is different from that at the interior of the material. It is also shown that there are two zones within the oxidized portion of the samples. Results confirm that the surface layer and the core material have substantially different properties.

Meador, Mary Ann B.↗

Simple torsion test for shear moduli determination of orthotropic composites

By means of torsion tests performed on test specimens of the same material having a minimum of two different cross sections (flat sheet of different widths), the effective in-plane (G13) and out-of-plane (G23) shear moduli were determined for two composite materials of uniaxial and angleply fiber orientations. Test specimens were 16 plies (nominal 2 mm) thick, 100 mm in length, and in widths of 6.3, 9.5, 12.5, and 15.8 mm. Torsion tests were run under controlled deflection (constant angle of twist) using an electrohydraulic servocontrolled test system. In-plane and out-of-plane shear moduli were calculated from an equation derived in the theory of elasticity which relates applied torque, the torsional angle of twist, the specimen width/thickness ratio, and the ratio of the two shear moduli G13/G23. Results demonstrate that torsional shear moduli, G23 as well as G13, can be determined by simple torsion tests of flat specimens of rectangular cross section. Neither the uniaxial nor angleply composite material were transversely isotropic.

Sumsion, H. T.↗

Acceleration of FDNS flow simulations using initial flowfields generated with a parabolized Navier-Stokes method

The capability of computational fluid dynamics (CFD) analysis to predict complex flowfields has been greatly advanced by the widespread use of flow simulation programs based on the Navier-Stokes (NS) equations. The flow physics are theoretically well represented, and with proper care the numerical solution should not introduce appreciable uncertainties. However, the computational cost of a typical simulation in terms of both memory and execution time are large by current standards. Therefore, the efficiency of the numerical algorithm in solving the set of model equations is one factor determining the usefulness of CFD tools. The objective of the present study is to reduce the execution time of the FDNS flow simulation code by using the parabolized Navier-Stokes (PNS) equations to provide a 'good' starting condition. The technique is not universal, however the PNS model can be applied to convection dominated flows with moderate deflection in geometries that are free of large obstructions.

Tenpas, Peter W.↗

Analysis of the Effects of Streamwise Lift Distribution on Sonic Boom Signature

The streamwise lift distribution of a wing-canard-stabilator-body configuration was varied to study its effect on the near-field sonic boom signature. The investigation was carried out via solving the three-dimensional Euler equation with the OVERFLOW-2 flow solver. The computational meshes were created using the Chimera overset grid topology. The lift distribution was varied by first deflecting the canard then trimming the aircraft with the wing and the stabilator while maintaining constant lift coefficient of 0.05. A validation study using experimental results was also performed to determine required grid resolution and appropriate numerical scheme. A wide range of streamwise lift distribution was simulated. The result shows that the longitudinal wave propagation speed can be controlled through lift distribution thus controlling the shock coalescence.

Yoo, Seung Yeun (Paul)↗

Flap noise prediction method for a powered lift system

A method is presented for estimating the noise generated by deflection of the engine exhaust for under-the-wing and over-the-wing versions of an externally blown flap configuration for powered lift. Correlation equations and curves are given for the overall sound pressure level and directivity and for spectra scaled to a high bypass 25,000-pound thrust size engine. Data are taken from TF34 engine tests and from large cold flow model tests. The correlations are empirical, and thus application of this prediction procedure is limited to geometrically similar configurations. Application of the method is illustrated by calculated sample footprints.

Clark, B.↗

Flap noise prediction method for a powered lift system

A method is presented for estimating the noise generated by deflection of the engine exhaust for under-the-wing and over-the-wing versions of an externally blown flap configuration for powered lift. Correlation equations and curves are given for the OASPL and directivity and for spectra scaled to a high bypass 25,000-pound thrust size engine. Data are taken from TF34 engine tests and from large cold flow model tests. The correlations are empirical, and thus application of this prediction procedure is limited to geometrically similar configurations. Application of the method is illustrated by calculated sample footprints.

Clark, B.↗

A finite element large deflection random response analysis of beams and plates subjected to acoustic loading

A finite element formulation is presented for the analysis of beams and rectangular plates undergoing large deflections subjected to Gaussian white noise excitations. Single-mode response is assumed in the present formulation. Root-mean-square (RMS) maximum deflections for simply supported and clamped beams and plates at various sound spectrum levels are obtained and compared with solutions using the Fokker-Planck-Kolmogorov equation and the equivalent linearization methods. RMS maximum stains and equivalent linear frequencies are compared with the equivalent linearization results for assessment of the accuracy of the finite element method.

Mei, Chuh↗

FORTRAN 4 computer program for calculating critical speeds of rotating shafts

A FORTRAN 4 computer program, written for the IBM DCS 7094/7044 computer, that calculates the critical speeds of rotating shafts is described. The shaft may include bearings, couplings, extra masses (nonshaft mass), and disks for the gyroscopic effect. Shear deflection is also taken into account, and provision is made in the program for sections of the shaft that are tapered. The boundary conditions at the ends of the shaft can be fixed (deflection and slope equal to zero) or free (shear and moment equal to zero). The fixed end condition enables the program to calculate the natural frequencies of cantilever beams. Instead of using the lumped-parameter method, the program uses continuous integration of the differential equations of beam flexure across different shaft sections. The advantages of this method over the usual lumped-parameter method are less data preparation and better approximation of the distribution of the mass of the shaft. A main feature of the program is the nature of the output. The Calcomp plotter is used to produce a drawing of the shaft with superimposed deflection curves at the critical speeds, together with all pertinent information related to the shaft.

Trivisonno, R. J.↗

Strain Gage Load Calibration of the Wing Interface Fittings for the Adaptive Compliant Trailing Edge Flap Flight Test

The safety-of-flight parameters for the Adaptive Compliant Trailing Edge (ACTE) flap experiment require that flap-to-wing interface loads be sensed and monitored in real time to ensure that the structural load limits of the wing are not exceeded. This paper discusses the strain gage load calibration testing and load equation derivation methodology for the ACTE interface fittings. Both the left and right wing flap interfaces were monitored; each contained four uniquely designed and instrumented flap interface fittings. The interface hardware design and instrumentation layout are discussed. Twenty-one applied test load cases were developed using the predicted in-flight loads. Pre-test predictions of strain gage responses were produced using finite element method models of the interface fittings. Predicted and measured test strains are presented. A load testing rig and three hydraulic jacks were used to apply combinations of shear, bending, and axial loads to the interface fittings. Hardware deflections under load were measured using photogrammetry and transducers. Due to deflections in the interface fitting hardware and test rig, finite element model techniques were used to calculate the reaction loads throughout the applied load range, taking into account the elastically-deformed geometry. The primary load equations were selected based on multiple calibration metrics. An independent set of validation cases was used to validate each derived equation. The 2-sigma residual errors for the shear loads were less than eight percent of the full-scale calibration load; the 2-sigma residual errors for the bending moment loads were less than three percent of the full-scale calibration load. The derived load equations for shear, bending, and axial loads are presented, with the calculated errors for both the calibration cases and the independent validation load cases.

Miller, Eric J.↗