Search NASA⌕ Search

SEARCH · Search NASA

Results for “CANTILEVER BEAM”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Modelling of piezoelectric actuator dynamics for active structural control

The paper models the effects of dynamic coupling between a structure and an electrical network through the piezoelectric effect. The coupled equations of motion of an arbitrary elastic structure with piezoelectric elements and passive electronics are derived. State space models are developed for three important cases: direct voltage driven electrodes, direct charge driven electrodes, and an indirect drive case where the piezoelectric electrodes are connected to an arbitrary electrical circuit with embedded voltage and current sources. The equations are applied to the case of a cantilevered beam with surface mounted piezoceramics and indirect voltage and current drive. The theoretical derivations are validated experimentally on an actively controlled cantilevered beam test article with indirect voltage drive.

Hagood, Nesbitt W.↗
NASA NTRS2007

Displacement Theories for In-Flight Deformed Shape Predictions of Aerospace Structures

Displacement theories are developed for a variety of structures with the goal of providing real-time shape predictions for aerospace vehicles during flight. These theories are initially developed for a cantilever beam to predict the deformed shapes of the Helios flying wing. The main structural configuration of the Helios wing is a cantilever wing tubular spar subjected to bending, torsion, and combined bending and torsion loading. The displacement equations that are formulated are expressed in terms of strains measured at multiple sensing stations equally spaced on the surface of the wing spar. Displacement theories for other structures, such as tapered cantilever beams, two-point supported beams, wing boxes, and plates also are developed. The accuracy of the displacement theories is successfully validated by finite-element analysis and classical beam theory using input-strains generated by finite-element analysis. The displacement equations and associated strain-sensing system (such as fiber optic sensors) create a powerful means for in-flight deformation monitoring of aerospace structures. This method serves multiple purposes for structural shape sensing, loads monitoring, and structural health monitoring. Ultimately, the calculated displacement data can be visually displayed to the ground-based pilot or used as input to the control system to actively control the shape of structures during flight.

Ko, William L.↗
NASA NTRS1992

Vibration transmission through rolling element bearings. IV - Statistical energy analysis

A theoretical broadband coupling-loss factor is developed analytically for use in the statistical energy analysis (SEA) of a shaft-bearing-plate system. The procedure is based on the solution of the boundary-value problem at the plate-bearing interface and incorporates a bearing-stiffness matrix developed by the authors. Three examples are utilized to illustrate the SEA incorporating the coupling-loss factor including: (1) a shaft-bearing-plate system; (2) a plate-cantilevered beam; and (3) a circular-shaft-bearing plate. The coupling-loss factor in the case of the thin plate-cantilevered beam is found to be more accurate than that developed by Lyon and Eichler (1964). The coupling-loss factor is described for the bearing system and extended to describe the mean-square vibratory response of a rectangular plate. The proposed techniques are of interest to the study of vibration and noise in rotating machinery such as gearboxes.

Lim, T. C.↗
NASA NTRS1987

An Investigation of the Dynamic Response of Spur Gear Teeth with Moving Loads

Two concepts relating to gear dynamics were studied. The first phase of the analysis involved the study of the effect of the speed of a moving load on the dynamic deflections of a gear tooth. A single spur gear tooth modelled using finite elements was subjected to moving loads with variable velocities. The tooth tip deflection time histories were plotted, from which it was seen that the tooth tip deflection consisted of a quasistatic response with an oscillatory response superimposed on it whose amplitude was dependent on the type of load engagement. Including the rim in the analysis added flexibility to the model but did not change the general behavior of the system. The second part of the analysis involved an investigation to determine the effect on the dynamic response of the inertia of the gear tooth. A simplified analysis using meshing cantilever beams was used. In one case, the beams were assumed massless. In the other, the mass (inertia) of the beams was included. From this analysis it was found that the inertia of the tooth did not affect the dynamic response of meshing cantilever beams.

Passerello, C. E.↗
NASA NTRS1984

Extensions of the Ritz-Galerkin method for the forced, damped vibrations of structural elements

The Ritz-Galerkin methods were used to obtain approximate solutions for free undamped, vibration problems. It is demonstrated that these same methods may be used straightforwardly to analyze forced vibrations with damping without requiring the free vibration eigenfunctions. It was shown that the Galerkin method is an effective technique for these types of problems. The Ritz method has the advantage that it does not need to satisfy the force-type boundary conditions, which is particularly important for plates and shells. Proper functionals representing the forcing and damping terms were developed. Two types of damping--viscous and material (hysteretic) are discussed. Distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. The rates of convergence of the solutions are shown. Approximate solutions from the present methods are compared with the exact solutions for the cantilever beam.

Leissa, A. W.↗
NASA NTRS1978

Simplified modeling for wind turbine modal analysis using NASTRAN

A detailed finite element model of the MOD-0 wind turbine tower was reduced to six beam elements (stick model). The method used to calculate the properties of the beam elements in the stick model was explained and the accuracy of the stick model in predicting natural frequencies and mode shapes was examined. Computer times were compared and several applications where the stick model was used are described. From results obtained from the MOD-0 tower it is concluded that a tower of this type can be modeled as a simple cantilever beam for modal analysis. However, this model should be limited to tower torsional modes and tower bending modes where the mode shape resembles a cantilever beam first bending mode shape.

Sullivan, T. L.↗
NASA NTRS1988

Electro optical performance of an improved deformable mirror device

The design, fabrication, and performance of an improved 128 x 128 deformable mirror device (DMD) are discussed. The present DMD consists of a monolithically formed array of cantilever beams which are electrostatically deflected by an underlying MOS transistor address matrix. In contrast to an earlier version, the improved DMD on-chip address circuitry supports a single video input to the chip, with all demux operations performed on-chip. The cantilever beams are formed by two layers of high-reflectivity aluminum alloy. The dynamic range of the DMD in the Fourier plane at the Nyquist frequency has been determined at greater than 45 dB.

Wu, Wen R.↗
NASA NTRS1992

Discrete distributed strain sensing of intelligent structures

Techniques are developed for the design of discrete highly distributed sensor systems for use in intelligent structures. First the functional requirements for such a system are presented. Discrete spatially averaging strain sensors are then identified as satisfying the functional requirements. A variety of spatial weightings for spatially averaging sensors are examined, and their wave number characteristics are determined. Preferable spatial weightings are identified. Several numerical integration rules used to integrate such sensors in order to determine the global deflection of the structure are discussed. A numerical simulation is conducted using point and rectangular sensors mounted on a cantilevered beam under static loading. Gage factor and sensor position uncertainties are incorporated to assess the absolute error and standard deviation of the error in the estimated tip displacement found by numerically integrating the sensor outputs. An experiment is carried out using a statically loaded cantilevered beam with five point sensors. It is found that in most cases the actual experimental error is within one standard deviation of the absolute error as found in the numerical simulation.

Anderson, Mark S.↗
NASA NTRS1997

Validation of a Deterministic Vibroacoustic Response Prediction Model

This report documents the recently completed effort involving validation of a deterministic theory for the random vibration problem of predicting the response of launch pad structures in the low-frequency range (0 to 50 hertz). Use of the Statistical Energy Analysis (SEA) methods is not suitable in this range. Measurements of launch-induced acoustic loads and subsequent structural response were made on a cantilever beam structure placed in close proximity (200 feet) to the launch pad. Innovative ways of characterizing random, nonstationary, non-Gaussian acoustics are used for the development of a structure's excitation model. Extremely good correlation was obtained between analytically computed responses and those measured on the cantilever beam. Additional tests are recommended to bound the problem to account for variations in launch trajectory and inclination.

Caimi, Raoul E.↗
DOE OSTI2021

Transforming a Simple Structure Model to Represent a Complex Dynamic System with Unknown Boundary Restraints

Imposing a boundary condition on a structure can significantly alter its dynamic properties. However, sometimes the specifics of the new boundary conditions are not known. When the effects of a boundary condition are uncertain or there is not enough information, engineers need to excite the complex structure to obtain these modified properties. In order to experimentally obtain the new properties, engineers need multiple experiments and many outputs for interpolation in order to sufficiently represent the entire structure. In this study, the researchers attached a stinger to a cantilever beam, acting as a new transverse restraint of unknown properties. This paper presents a conversion expression that predicts the dynamic behavior of any point in the system with the new boundary condition. This expression relies only on one impact hammer experiment with one output and the model of the stinger-free cantilever beam, referred to as the simple structure. Researchers estimated the Transfer Function (TRF) of the beam and compared it with an experimentally measured TRF to validate the method. The mean absolute error of the estimated TRF compared to the experimental TRF is 1.99 dB. This demonstrates the use of the proposed method for estimating unmeasured TRFs in a system with an uncertain boundary condition using a single input, single output (SISO) test and a model of the simple structure.

42 ENGINEERING↗
NASA NTRS1991

Comparison of advanced reduced-basis methods for transient structural analysis

Two advanced reduced-basis methods for linear, transient structural analysis, the force-derivative method and the Lanczos method, are compared to two widely-used modal methods, the mode-displacement method and the mode-acceleration method. Comparisons are made for two linear example problems: a proportionally-damped cantilevered beam subject to a discrete tip load which varies linearly with time, and a discretely-damped multispan beam subject to a uniformly distributed load which varies as a quintic function of time. Results from the methods are compared in terms of the number of basis vectors required to obtain a desired level of accuracy and the associated computational times. The results are problem dependent, and it is shown that for the cantilevered beam problem, the mode-acceleration and force-derivative methods are the most efficient in terms of the number of basis vectors and computational time. The force-derivative method is shown to be the most effective method for solving the multispan beam problem with closely-spaced frequencies. In general, the force-derivative method is shown to produce an accurate solution using very few basis vectors and to require less computational time as compared to the other methods studied.

Mcgowan, David M.↗
NASA NTRS1991

Interlaminar fracture characterization: A current review

Interlaminar fracture characterization has been investigated for several years. Only now is it well enough understood for standardization organizations to attempt to write standard test methods. A review of the current philosophies in characterizing interlaminar fracture is presented. First, the mode 1, double cantilever beam test (DCB) for measuring G(sub 1c) and the end notched flexure (ENF) test for measuring G(sub 2c) are discussed. These tests have undergone the most extensive research throughout the years and are furthest towards standardization. In addition, the mode 2, end loaded split (ELS) specimen is discussed. Mixed mode fracture is also discussed and the recently developed mixed mode bending (MMB) test is detailed. Then, tests for evaluating mode 3 fracture toughness, including the split cantilever beam (SCB), are reviewed. Finally, the work done on interlaminar fracture characterization in fatigue is reviewed.

Martin, Roderick H.↗
DOE OSTI2023

An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

Abstract In this work, we present a boundary oriented graph embedding (BOGE) approach for the graph neural network to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10 ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based finite element analysis (FEA) results, which cannot be realized by other machine-learning-based surrogate methods. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model achieves the regression with mean square error (MSE) of 0.011 706 (2.41% mean absolute percentage error) for stress field prediction and 0.002 735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and Computer Aided Design (CAD) design-related areas.

42 ENGINEERING↗
NASA NTRS2006

Mode I Toughness Measurements of Core/Facesheet Bonds in Honeycomb Sandwich Structures

Composite sandwich structures will be used in many future applications in aerospace, marine and offshore industries due to the fact that the strength and stiffness to mass ratios surpass any other structural type. Sandwich structure also offers advantages over traditional stiffened panels such as ease of manufacturing and repair. During the last three decades, sandwich structure has been used extensively for secondary structure in aircraft (fuselage floors, rudders and radome structure). Sandwich structure is also used as primary structure in rotorcraft, the most common example being the trailing edge of rotor blades. As with other types of composite construction, sandwich structure exhibits several types of failure mode such as facesheet wrinkling, core crushing and sandwich buckling. Facesheet/core debonding has also been observed in the marine and aerospace industry. During this failure mode, peel stresses applied to an existing facesheet/core debond or an interface low in toughness, results in the facesheet being peeled from the core material, possibly leading to a significant loss in structural integrity of the sandwich panel. In an incident during a test on a liquid hydrogen fuel tank of the X-33 prototype vehicle, the outer graphite/epoxy facesheet and honeycomb core became debonded from the inner facesheet along significant areas, leading to failure of the tank. As a consequence of the accident; significant efforts were made to characterize the toughness of the facesheet/core bond. Currently, the only standardized method available for assessing the quality of the facesheet/core interface is the climbing drum peel test (ASTM D1781). During this test a sandwich beam is removed from a panel and the lip of one of the facesheets is attached to a drum, as shown in Fig. 1. The drum is then rotated along the sandwich beam, causing the facesheet to peel from the core. This method has two major drawbacks. First, it is not possible to obtain quantitative fracture data from the test and so the results can only be used in a qualitative manner. Second, only sandwich structure with thin facesheets can be tested (to facilitate wrapping of the facesheet around the climbing drum). In recognition of the need for a more quantitative facesheet/core fracture test, several workers have devised experimental techniques for characterizing the toughness of the facesheet/core interface. In all of these cases, the tests are designed to yield a mode I-dominated fracture toughness of the facesheet/core interface in a manner similar to that used to determine mode I fracture toughness of composite laminates. In the current work, a modified double cantilever beam is used to measure the mode I-dominated fracture toughness of the interface in a sandwich consisting of glass/phenolic honeycomb core reinforced with graphite epoxy facesheets. Two specimen configurations were tested as shown in Fig 2. The first configuration consisted of reinforcing the facesheets with aluminum blocks (Fig. 2a). In the second configuration unreinforced specimens were tested (Fig. 2b). Climbing drum peel tests were also conducted to compare the fracture behavior observed between this test and the modified double cantilever beam. This paper outlines the test procedures and data reduction strategies used to compute fracture toughness values from the tests. The effect of specimen reinforcement on fracture toughness of the facesheet/core interface is discussed.

Nettles, Alan T.↗
NASA NTRS1982

Structural fatigue test results for large wind turbine blade sections

In order to provide quantitative information on the operating life capabilities of wind turbine rotor blade concepts for root-end load transfer, a series of cantilever beam fatigue tests was conducted. Fatigue tests were conducted on a laminated wood blade with bonded steel studs, a low cost steel spar (utility pole) with a welded flange, a utility pole with additional root-end thickness provided by a swaged collar, fiberglass spars with both bonded and nonbonded fittings, and, finally, an aluminum blade with a bolted steel fitting (Lockheed Mod-0 blade). Photographs, data, and conclusions for each of these tests are presented. In addition, the aluminum blade test results are compared to field failure information; these results provide evidence that the cantilever beam type of fatigue test is a satisfactory method for obtaining qualitative data on blade life expectancy and for identifying structurally underdesigned areas (hot spots).

Faddoul, J. R.↗
NASA NTRS1987

Positive position feedback control for large space structures

A new technique for vibration suppression in large space structures is investigated in laboratory experiments on a thin cantilever beam. This technique, called Positive Position Feedback, makes use of generalized displacement measurements to accomplish vibration suppression. Several features of Positive Position Feedback make it attractive for the large space structure control environment: The realization of the controller is simple and straightforward. Global stability conditions can be derived which are independent of the dynamical characteristics of the structure being controlled, i.e., all spillover is stabilizing. The method cannot be destabilized by finite actuator dynamics, and the technique is amenable to a strain-based sensing approach. The experiments control the first six bending modes of a cantilever beam, and make use of piezoelectric materials for actuators and sensors, simulating a piezoelectric active-member. The modal damping ratios are increased by factors ranging from 2 to 130.

Fanson, J. L.↗
NASA NTRS1998

Computational Investigation and Validation of Twin-Tail Buffet Response Including Dynamics and Control

Multidisciplinary tools for prediction of single rectangular-tail buffet are extended to single swept-back-tail buffet in transonic-speed flow, and multidisciplinary tools for prediction and control of twin-tail buffet are developed and presented. The configuration model consists of a sharp-edged delta wing with single or twin tails that are oriented normal to the wing surface. The tails are treated as cantilevered beams fixed at the root and allowed to oscillate in both bending and torsion. This complex multidisciplinary problem is solved sequentially using three sets of equations on a dynamic single or multi-block grid structure. The first set is the unsteady, compressible, Reynolds-averaged Navier-Stokes equations which are used for obtaining the flow field vector and the aerodynamic loads on the tails. The Navier-Stokes equations are solved accurately in time using the implicit, upwind, flux-difference splitting, finite volume scheme. The second set is the coupled bending and torsion aeroelastic equations of cantilevered beams which are used for obtaining the bending and torsion deflections of the tails. The aeroelastic equations'are solved accurately in time using, a fifth-order-accurate Runge-Kutta scheme. The third set is the grid-displacement equations and the rigid-body dynamics equations, which are used for updating the grid coordinates due to the tail deflections and rigid-body motions. The tail-buffet phenomenon is predicted for highly-swept, single vertical tail placed at the plane of geometric symmetry, and for highly-swept, vertical twin tails placed at three different spanwise separation distances. The investigation demonstrates the effects of structural inertial coupling and uncoupling of the bending and torsion modes of vibration, spanwise positions of the twin-tail, angle of attack, and pitching and rolling dynamic motions of the configuration model on the tail buffet loading and response. The fundamental issue of twin-tail buffet alleviation is addressed using two active flow-control methods. These methods are the tangential leading-edge blowing and the flow suction from the leading-edge vortex cores along their paths. Qualitative and quantitative comparisons with the available experimental data are presented. The comparisons indicate that the present multidisciplinary aeroelastic analysis tools are robust, accurate and efficient.

Kandil, Osama A.↗
NASA NTRS2009

Applications of Ko Displacement Theory to the Deformed Shape Predictions of the Doubly-Tapered Ikhana Wing

The Ko displacement theory, formulated for weak nonuniform (slowly changing cross sections) cantilever beams, was applied to the deformed shape analysis of the doubly-tapered wings of the Ikhana unmanned aircraft. The two-line strain-sensing system (along the wingspan) was used for sensing the bending strains needed for the wing-deformed shapes (deflections and cross-sectional twist) analysis. The deflection equation for each strain-sensing line was expressed in terms of the bending strains evaluated at multiple numbers of strain-sensing stations equally spaced along the strain-sensing line. For the preflight shape analysis of the Ikhana wing, the strain data needed for input to the displacement equations for the shape analysis were obtained from the nodal-stress output of the finite-element analysis. The wing deflections and cross-sectional twist angles calculated from the displacement equations were then compared with those computed from the finite-element computer program. The Ko displacement theory formulated for weak nonlinear cantilever beams was found to be highly accurate in the deformed shape predictions of the doubly-tapered Ikhana wing.

Ko, William L.↗