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NASA NTRS2012

Design of a Variable Thickness Plate to Focus Bending Waves

This paper describes the design of a thin plate whose thickness is tailored in order to focus bending waves to a desired location on the plate. Focusing is achieved by smoothly varying the thickness of the plate to create a type of lens, which focuses structural-borne energy. Damping treatment can then be positioned at the focal point to efficiently dissipate energy with a minimum amount of treatment. Numerical simulations of both bounded and unbounded plates show that the design is effective over a broad frequency range, focusing traveling waves to the same region of the plate regardless of frequency. This paper also quantifies the additional energy dissipated by local damping treatment installed on a variable thickness plate relative to a uniform plate.

Schiller, Noah H.↗

NASA NTRS2014

Robot Arm with Tendon Connector Plate and Linear Actuator

A robotic system includes a tendon-driven end effector, a linear actuator, a flexible tendon, and a plate assembly. The linear actuator assembly has a servo motor and a drive mechanism, the latter of which translates linearly with respect to a drive axis of the servo motor in response to output torque from the servo motor. The tendon connects to the end effector and drive mechanism. The plate assembly is disposed between the linear actuator assembly and the tendon-driven end effector and includes first and second plates. The first plate has a first side that defines a boss with a center opening. The second plate defines an accurate through-slot having tendon guide channels. The first plate defines a through passage for the tendon between the center opening and a second side of the first plate. A looped end of the flexible tendon is received within the tendon guide channels.

Ihrke, Chris A.↗

NASA NTRS2017

Shed Vortex Structure and Phase-Averaged Velocity Statistics in Symmetric/Asymmetric Turbulent Flat Plate Wakes

The near wake of a flat plate is investigated via direct numerical simulations (DNS). Many earlier experimental investigations have used thin plates with sharp trailing edges and turbulent boundary layers to create the wake. This results in large theta divided by D (sub TE) values (theta is the boundary layer momentum thickness towards the end of the plate and D (sub TE) is the trailing edge thickness). In the present study the emphasis is on relatively thick plates with circular trailing edges (CTE) resulting in theta divided by D values less than one (D is the plate thickness and the diameter of the CTE), and vigorous vortex shedding. The Reynolds numbers based on the plate length and D are 1.255 x 10 (sup 6) and 10,000, respectively. Two cases are computed; one with turbulent boundary layers on both the upper and lower surfaces of the plate (statistically the same, symmetric wake, Case TT) and, a second with turbulent and laminar boundary layers on the upper and lower surfaces, respectively (asymmetric case, Case TL). The data and understanding obtained is of considerable engineering interest, particularly in turbomachinery where the pressure side of an airfoil can remain laminar or transitional because of a favorable pressure gradient and the suction side is turbulent. Shed-vortex structure and phase-averaged velocity statistics obtained in the two cases are compared here. The upper negative shed vortices in Case TL (turbulent separating boundary layer) are weaker than the lower positive ones (laminar separating boundary layer) at inception (a factor 1.27 weaker in terms of peak phase-averaged spanwise vorticity at first appearance of a peak). The upper vortices weaken rapidly as they travel downstream. A second feature of interest in Case TL is a considerable increase in the peak phase-averaged, streamwise normal intensity (random component) with increasing streamwise distance (x divided by D) that occurs nears the positive vortex cores. This behavior is observed for a few diameters in the near wake. This is counter to Case TT where the peak value essentially decreases with increasing x divided by D. Both these effects are examined in detail and the important contributors are identified.

direct numerical simulations↗

NASA NTRS2024

Scalability in SLA lattice through lattice orientation and hybrid frame and plate architectures

Lightweighting has been a key goal for engineers and designers, with lattice structures widely explored as the building blocks for structural components. Cellular structure-inspired lattice truss frame designs made of struts, have been extensively studied. All plate-based lattice designs have superior mechanical performance. Limits in scalability occur from formation of closed pockets limiting uv curing in processes like stereolithography (SLA). We examine hybrid frame and plate body-centered cubic-simply cubic (BCC-SC) lattices under compression. Unit cells and scaled up lattice exhibit an increase in yield stress and modulus with the addition of plates. The loading direction on the hybrid frame and plate unit cells affected the magnitude of improvement. Simulations and measurements indicated that the optimal lightweight lattice was determined to be when two plates were placed opposite each other with plates buttressing the struts, inhibiting buckling of the struts aligned with the loading direction. This lattice resulted in 63% improvement in specific modulus, a 137% improvement in specific yield point, and a 360% improvement in specific energy absorption (SEA) and the scaled up 4 × 4 × 4 scaled-up structures, showed a 107%, 148%, and 297% in specific modulus, specific yield point, and SEA, respectively A combined stretching-bending behavior was identified in optimal orientations reflecting the delayed buckling mechanism paired to a rising stress-strain curve past the elastic yield indicating bending resistance. The mass moment of inertia was found to be a key parameter correlating optimum orientation for the same number of plates added to the BCC-SC frame.

Mahan Ghosh↗

NASA NTRS1993

Flow and acoustic field due to an inclined plate with a downstream splitter

In the present work, the high Reynolds number flow past an inclined plate with a splitter plate placed in its wake is considered numerically. A numerical conformal mapping technique is employed to transform the two-plate system into the same number of cylinders: the flow field is assumed to be two-dimensional. The vortex shedding from the inclined plate is modelled using the discrete vortex method. It is shown that the splitter plate has a profound effect on the development of the flow over a range of values of a suitably defined offset parameter and for a range of positions of the leading edge of the splitter plate. The acoustic field is also calculated and the spectrum reflects the flow results.

DISCRETE VORTEX METHOD↗

NASA NTRS1942

Square plate with clamped edges under normal pressure producing large deflections

A theoretical analysis is given for the stresses and deflections of a square plate with clamped edges under normal pressure producing large deflections. Values of the bending stress and membrane stress at the center of the plate and at the midpoint of the edge are given for center deflections up to 1.9 times the plate thickness. The shape of the deflected surface is given for low pressures and for the highest pressure considered. Convergence of the solution is considered and it is estimated that the possible error is less than 2 percent. The results are compared with the only previous approximate analysis known to the author and agree within 5 percent. They are also shown to compare favorably with the known exact solutions for the long rectangular plate and the circular plate.

PLATES-PRESSURE↗

NASA NTRS1951

Torsion and transverse bending of cantilever plates

The problem of combined bending and torsion of cantilever plates of variable thickness, such as might be considered for solid thin high-speed airplane or missile wings, is considered in this paper. The deflections of the plate are assumed to vary linearly across the chord; minimization of the potential energy by means of the calculus of variations then leads to two ordinary linear differential equations for the bending deflections and the twist of the plate. Because the cantilever is analyzed as a plate rather than as a beam, the effect of constraint against axial warping in torsion is inherently included. The application of this method to specific problems involving static deflection, vibration, and buckling of cantilever plates is presented. In the static-deflection problems, taper and sweep are considered.

WINGS, SOLID↗

NASA NTRS1965

Adherent protective coatings plated on magnesium-lithium alloy

Zinc is plated on a magnesium-lithium alloy by using a modification of the standard zinc-plate immersion bath. Further protection is given the alloy by applying a light plating of copper on the zinc plating. Other metals are plated on the copper by using conventional plating baths.

Source record↗

NASA NTRS1972

Design analysis for a nutating plate drive 4

A simplified design analysis was conducted on a nutating plate type drive system for a 2500 horsepower helicopter main rotor gear box. A drive system that split the output torque evenly between two nutating plates for the purpose of reducing the load on each nutating plate was analyzed. Needle bearings were used on the nutating plate pins. The results of the analysis indicate that the required load capacity of the pin bearings and the speed of the nutating plate bearings were beyond the state-of-the-art capacity of rolling-element bearings. The analysis further indicates that the nutating plate drive is less efficient, and results in a higher weight per horsepower than a conventional planetary helicopter transmission with similar design specifications.

Loewenthal, S. H.↗

NASA NTRS1972

Elastostatic stress analysis of orthotropic rectangular center-cracked plates

A mapping-collocation method was developed for the elastostatic stress analysis of finite, anisotropic plates with centrally located traction-free cracks. The method essentially consists of mapping the crack into the unit circle and satisfying the crack boundary conditions exactly with the help of Muskhelishvili's function extension concept. The conditions on the outer boundary are satisfied approximately by applying the method of least-squares boundary collocation. A parametric study of finite-plate stress intensity factors, employing this mapping-collocation method, is presented. It shows the effects of varying material properties, orientation angle, and crack-length-to-plate-width and plate-height-to-plate-width ratios for rectangular orthotropic plates under constant tensile and shear loads.

Gyekenyesi, G. S.↗

NASA NTRS1972

Lumped parameter analysis of a stringer reinforced plate excited by band limited noise

The maximum root-mean-square response of a square clamped plate, subjected to a stationary random excitation, was determined both theoretically and empirically. For the tests, a 40 x 40 x 1/4 aluminum sheet was milled out to provide a thin waffle plate with 9 panels. The plate was acoustically excited, with the frequency range limited between 25 Hz and 500 Hz. The root-mean-square power of the random excitations, 149 decibels, was nearly constant for all natural frequencies of the plate system. Strain gage readings at 14 points were plotted as power spectral densities and root-mean-square displacements. A modal damping ratio matrix was determined from the response curves. Damping ratios were found to be a function of frequency, but not of location on the plate. For comparisons with the theoretical response, the plate was subdivided into 14 modes and anlayzed as a damped, lumped parameter system by use of an approximate normal-mode method. This method gave the best predictions of the power spectral densities for the lower frequencies. That prediction errors increased for the higher frequencies is attributed to improper assumptions for mass distribution and the insufficient number of lumped mass points.

Bilyeu, D. J.↗

NASA NTRS1972

Prediction and measurement of heat transfer rates for the shock-induced unsteady laminar boundary layer on a flat plate

The unsteady laminar boundary layer induced by the flow-initiating shock wave passing over a flat plate mounted in a shock tube was theoretically and experimentally studied in terms of heat transfer rates to the plate for shock speeds ranging from 1.695 to 7.34 km/sec. The theory presented by Cook and Chapman for the shock-induced unsteady boundary layer on a plate is reviewed with emphasis on unsteady heat transfer. A method of measuring time-dependent heat-transfer rates using thin-film heat-flux gages and an associated data reduction technique are outlined in detail. Particular consideration is given to heat-flux measurement in short-duration ionized shocktube flows. Experimental unsteady plate heat transfer rates obtained in both air and nitrogen using thin-film heat-flux gages generally agree well with theoretical predictions. The experimental results indicate that the theory continues to predict the unsteady boundary layer behavior after the shock wave leaves the trailing edge of the plate even though the theory is strictly applicable only for the time interval in which the shock remains on the plate.

Cook, W. J.↗

NASA NTRS1973

Acoustic radiation from plates excited by flow noise.

Theoretical formulation of noise radiation from thin, rectangular, flexible plates excited by turbulent wall pressure fluctuations. An extensive parametric study including surface roughness and both plate and flow parameters is presented. From the results, presented graphically, it is possible to predict the spectrum of the total radiated power provided that the power spectral density of the wall-pressure fluctuations, the flow velocity, the plate dimensions and the plate modal damping parameters are known. Along with the parametric study, an estimate of the dependence of the noise radiation on plate boundary conditions based on a consideration of the wavenumber-frequency selectivity of the plate is presented. The parametric study is based on the assumption that the wave number/frequency spectrum of the wall-pressure fluctuations can be described by a Fourier transform of a Corcos model of the cross spectral density. The results indicate that at frequencies above the hydrodynamic-coincidence frequency the radiated power is dependent on the low-wave-number spectrum of the excitation. The dependence on the high-wave-number spectrum, however, is limited to a narrow band of frequencies below the hydrodynamic-coincidence frequency.

Aupperle, F. A.↗

NASA NTRS1974

A model of convergent plate margins based on the recent tectonics of Shikoku, Japan

A viscoelastic finite element plate tectonic model is applied to displacement data for the island of Shikoku, Japan. The flow properties and geometry of the upper portions of the earth are assumed known from geophysical evidence, and the loading characteristics are determined from the model. The nature of the forces acting on the Philippine Sea plate, particularly in the vicinity of the Nankai trough, is determined. Seismic displacement data related to the 1946 Nankaido earthquake are modeled in terms of a thick elastic plate overlying a fluidlike substratum. The sequence of preseismic and seismic displacements can be explained in terms of two independent processes operating on elastic lithospheric plates: a strain accumulation process caused by vertical downward forces acting on or within the lithosphere in the vicinity of the trench, and a strain release process caused by plate failure along a preexisting zone on weakness. This is a restatement of Reid's elastic rebound theory in terms of elastic lithospheric plates.

Bischke, R. E.↗

NASA NTRS1975

Flutter of laminated plates in supersonic flow

A solution procedure was developed using linear small deflection theory for the flutter of simply supported laminated plates. For such plates, the bending and extensional governing equations are coupled and have cross-stiffness terms which do not appear in classical plate theory. An extended Galerkin method is used to obtain approximate solutions to the governing equations, and the aerodynamic pressure loading used in the analysis is that given by linear piston theory with flow at arbitrary cross-flow angle. A limited parametric study was conducted for typical laminated composite plates. The calculations show that both the bending-extensional coupling and the cross-stiffness terms have a large destabilizing effect on flutter. Since classical plate theory does not consider bending-extensional coupling and cross stiffness terms, it usually gives inaccurate and nonconservative flutter boundaries for laminated plates.

Sawyer, J. W.↗

NASA NTRS1977

Impact on multilayered composite plates

Stress wave propagation in a multilayer composite plate due to impact was examined by means of the anisotropic elasticity theory. The plate was modelled as a number of identical anisotropic layers and the approximate plate theory of Mindlin was then applied to each layer to obtain a set of difference-differential equations of motion. Dispersion relations for harmonic waves and correction factors were found. The governing equations were reduced to difference equations via integral transforms. With given impact boundary conditions these equations were solved for an arbitrary number of layers in the plate and the transient propagation of waves was calculated by means of a Fast Fourier Transform algorithm. The multilayered plate problem was extended to examine the effect of damping layers present between two elastic layers. A reduction of the interlaminar normal stress was significant when the thickness of damping layer was increased but the effect was mostly due to the softness of the damping layer. Finally, the problem of a composite plate with a crack on the interlaminar boundary was formulated.

Kim, B. S.↗

NASA NTRS1978

Gaussian step-pressure loading of rigid viscoplastic plates

The response of a thin, rigid viscoplastic plate subjected to a spatially axisymmetric Gaussian step pressure impulse loading was studied analytically. A Gaussian pressure distribution in excess of the collapse load was applied to the plate, held constant for a length of time, and then suddenly removed. The plate deforms with monotonically increasing deflections until the dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid viscoplastic materials. For the small deflection bending response of the plate, the governing system of equations is essentially nonlinear. Transverse shear stress is neglected in the yield condition and rotary inertia in the equations of dynamic equilibrium. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and to obtain the analytical solutions in the form of eigenvalue expansions. The effects of load concentration, of an order of magnitude change in the viscosity of the plate material, and of load duration were examined while holding the total impulse constant.

Hayduk, R. J.↗

NASA NTRS1980

Stability optimization of laminated composite plates

The optimum design of plates with orthotropic layers under axial compression and shear is discussed. The plates considered are the laminates of N orthotropic layers whose principal material axes coincide with the plate axes. Each layer is assumed to have the same thickness and an equal number of fibers in the direction of + alpha sub i and - alpha sub i with respect to the plate axis. The fiber directions which give the highest axial buckling stress and the highest shear buckling stress are found by utilizing a mathematical optimization technique for various aspect ratios of the plates. Inhomogeneity in the direction of the plate thickness (stacking sequence) is taken into account in this analysis.

Hirano, Y.↗