Matrix methods for calculating cantilever-beam deflections
Explore the source record for details and available documents.
BEAMS, CANTILEVER - VIBRATION↗
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.
Simulation of large motions of nonuniform beams in orbit. I - The cantilever beam
An algorithm is developed for producing numerical simulations of large motions of a nonuniform cantilever beam in orbit. Special emphasis is given to the effective formulation of equations of motion and to the use of the finite element method to construct modal functions. Finite element methods are used to generate modal functions in such a way as to permit a particularly harmonious relationship to be established between the disciplines of rigid body dynamics and structural analysis. Sufficient information is provided to enable a reader to create, with relatively little effort, his own simulation program; simulation results are reported, both to provide check cases for other investigators and to illustrate certain important facets of the behavior of flexible spacecraft.
Levinson, D. A.↗
Analytical determination of coupled bending-torsion vibrations of cantilever beams by means of station functions
Explore the source record for details and available documents.
TURBINES - BLADES - VIBRATION↗
Analytical and experimental investigation of effect of twist on vibrations of cantilever beams
Explore the source record for details and available documents.
BEAMS, CANTILEVER - BENDING & TORSION↗
Finite element modeling of a cantilever beam
Finite element modeling of uniform cantilever beams and computation of transverse frequencies due to combinations of bending with rotatory inertia and shear flexibility
CANTILEVER BEAM↗
Effect of Centrifugal Force on the Elastic Curve of a Vibrating Cantilever Beam
A study was made to determine the effect of rotation on the dynamic-stress distribution in vibrating cantilever beams. The results of a mathematical analysis are presented together with experimental results obtained by means of stroboscopic photographs and strain gages. The theoretical analysis was confined to uniform cantilever beams; the experimental work was extended to include a tapered cantilever beam to simulate an aircraft propeller blade. Calculations were made on nondimensional basis for second and third mode vibration; the experiments were conducted on beams of various lengths, materials, and cross sections for second-mode vibration. From this investigation it was concluded that high vibratory-stress positions are unaffected by the addition of centrifugal force. Nonrotating vibration surveys of blades therefore are valuable in predicting high vibratory-stress locations under operating conditions.
Simpkinson, Scott H↗
Design, modeling and experimental validation of a micro cantilever beam with an electro-controllable twisting ability
The structure design of micro cantilever beams (MCBs), which has a significant effect on MCBs' controllable actuation range, is usually restricted by the establishment of the inner electric circuit. This paper proposes the design of a micro electro-controllable twisting cantilever beam (METCB). The architecture and the fabrication diagram of the proposed METCB are presented before its features are theoretically and experimentally validated. In detail, the analytical validation includes a sequence of two models: electro-thermal and thermo-mechanical. Through these two models, the thermal distribution along the METCB and the deformation brought by the thermal distribution are investigated, respectively. On the basis of the design and equations, the METCB samples have been manufactured using a planar deposition technique with an e-beam evaporator. Two in-site experiments are then conducted to sequentially figure out the upper voltage limit of the inner electric circuit and the maximum temperature limit of the METCB. Finally, another experiment is carried out to explore the relation between the applied voltage and the relative twisting angle of the METCB sample. Here, the theoretical prediction and the observed experiment result both prove the feasibility of the proposed METCB and its electro-controllable twisting ability.
36 MATERIALS SCIENCE↗
Effect of centrifugal force on flutter of uniform cantilever beam at subsonic speeds with application to compressor and turbine blades
Explore the source record for details and available documents.
BEAMS - BENDING & TORSION↗
Modal Analysis and Testing of a Cantilever Beam: Results and Guide
This report discusses modal analysis and testing of a cantilever beam including an introduction to modal testing, simulation, analysis, and a comparison of results. An accompanying presentation can be found from the LLNL CASIS website. Modal testing and analysis are essential for characterizing the response of a structure during vibration environments. Determining natural frequencies and mode shapes helps determine whether resonances will be reached during operations and if so, how the structure will respond and how the response can be tuned. The goal of this work is to convey the basics of modal testing and analysis through a simple project. This can be applied later to more complex, applicable structures. This includes a variety of work including data collection, finite element analysis and data processing. For this project a cantilever beam was chosen because it is a simple, well-characterized structure.
42 ENGINEERING↗
Evaluation of the split cantilever beam for Mode 3 delamination testing
A test rig for testing a thick split cantilever beam for scissoring delamination (mode 3) fracture toughness was developed. A 3-D finite element analysis was conducted on the test specimen to determine the strain energy release rate, G, distribution along the delamination front. The virtual crack closure technique was used to calculate the G components resulting from interlaminar tension, GI, interlaminar sliding shear, GII, and interlaminar tearing shear, GIII. The finite element analysis showed that at the delamination front no GI component existed, but a GII component was present in addition to a GIII component. Furthermore, near the free edges, the GII component was significantly higher than the GIII component. The GII/GIII ratio was found to increase with delamination length but was insensitive to the beam depth. The presence of GII at the delamination front was verified experimentally by examination of the failure surfaces. At the center of the beam, where the failure was in mode 3, there was significant fiber bridging. However, at the edges of the beam where the failure was in mode 3, there was no fiber bridging and mode 2 shear hackles were observed. Therefore, it was concluded that the split cantilever beam configuration does not represent a pure mode 3 test. The experimental work showed that the mode 2 fracture toughness, GIIc, must be less than the mode 3 fracture toughness, GIIIc. Therefore, a conservative approach to characterizing mode 3 delamination is to equate GIIIc to GIIc.
Martin, Roderick H.↗
Evaluation of the split cantilever beam for mode III delamination testing
A test rig for testing a thick split cantilever beam for scissoring delamination (mode 3) fracture toughness was developed. A 3-D finite element analysis was conducted on the test specimen to determine the strain energy release rate, G, distribution along the delamination front. The virtual crack closure technique was used to calculate the G components resulting from interlaminar tension, GI, interlaminar sliding shear, GII, and interlaminar tearing shear, GIII. The finite element analysis showed that at the delamination front no GI component existed, but a GII component was present in addition to a GIII component. Furthermore, near the free edges, the GII component was significantly higher than the GIII component. The GII/GIII ratio was found to increase with delamination length but was insensitive to the beam depth. The presence of GII at the delamination front was verified experimentally by examination of the failure surfaces. At the center of the beam, where the failure was in mode 3, there was significant fiber bridging. However, at the edges of the beam where the failure was in mode 3, there was no fiber bridging and mode 2 shear hackles were observed. Therefore, it was concluded that the split cantilever beam configuration does not represent a pure mode 3 test. The experimental work showed that the mode 2 fracture toughness, GIIc, must be less than the mode 3 fracture toughness, GIIIc. Therefore, a conservative approach to characterizing mode 3 delamination is to equate GIIIc to GIIc.
Martin, Roderick, H.↗
Free and forced vibrations of cantilever beams with viscous damping
Free and forced vibrations of cantilever beam with viscous damping - equations of motion for shear, deflection, velocity, bending moment, and acceleration
MOTION EQUATION↗
Bending and shear stresses developed by the instantaneous arrest of the root of a cantilever beam rotating with constant angular velocity about a transverse axis through the root
A theoretical investigation was made of the behavior of a cantilever beam in rotational motion about a transverse axis through the root determining the stresses, the deflections, and the accelerations that occur in the beam as a result of the arrest of motion. The equations for bending and shear stress reveal that, at a given percentage of the distance from root to tip and at a given trip velocity, the bending stresses for a particular mode are independent of the length of the beam and the shear stresses vary inversely with the length. When examined with respect to a given angular velocity instead of a given tip velocity, the equations reveal that the bending stress is proportional to the length of the beam whereas the shear stress is independent of the length. Sufficient experimental verification of the theory has previously been given in connection with another problem of the same type.
BEAMS - VIBRATION↗
Damping characteristics of built-up cantilever beams in a vacuum environment
Structural vibration damping of solid, reinforced cantilever beams in vacuum chamber
STRUCTURAL VIBRATION↗
Forced response of a cantilever beam with a dry friction damper attached. I - Theory. II - Experiment
A theoretical and experimental study of the forced vibration response of a cantilevered beam with Coulomb damping nonlinearity is described. Viscous damping in the beam is neglected. Beam and dry friction damper configurations of interest for applications to turbine blade vibrations are considered. It is shown that the basic phenomena found by Dowell (1983) for a simply supported beam with an attached dry friction damper of specific geometry also apply to a cantilevered beam and a more general representation of the dry friction damper and its associated mass and stiffness.
Dowell, E. H.↗
Characterizing Face Sheet/Core Disbonding Using the Single Cantilever Beam Test: Results from an International Round Robin
Test results from an international round robin are presented. The single cantilever beam (SCB) test was used to characterize face sheet/core disbonding in sandwich components in an effort to help standardization. Each of the seven participating laboratories performed a set of five baseline tests using the same protocol, however, using their own specific equipment. In addition, each laboratory performed two sets of tests with altered tests conditions which included using a test fixture with a translating carriage and performing the tests with different loading and unloading speeds. The orientation of the disbond front with respect to the honeycomb core cells was varied and the effect on the fracture toughness was also studied. Additional factors that could influence test results were investigated, such as the use of a saw cut starter disbond as an alternative to Teflon® release film, and the effects of using a face sheet doubler to increase the bending stiffness. For each set of tests, summary results such as load/displacements plots, observed disbond growth location and calculated energy release rates are reported and a comparison of results between labs is presented. Critical strain energy release rate measurements from SCB tests are also compared with measurements made from an alternative test, namely the double cantilever beam with uneven bending moments (DCB-UBM) test, which has been studied extensively at the Technical University of Denmark and proposed as a mixed-mode test standard. A set of recommendations are made with respect to improving the SCB test and a path to standardization is presented.
Ronald Krueger↗
Characterization of Interlaminar Crack Growth in Composites with the Double Cantilever Beam Specimen
A project to examine the double cantilever beam specimen as a quantitative test method to assess the resistance of various composite materials to interlaminar crack growth is discussed. A second objective is to investigate the micromechanics of failure for composites with tough matrix resins from certain generic types of polymeric systems: brittle thermosets, toughened thermosets, and thermoplastics. Emphasis is given to a discussion of preliminary results in two areas: the effects of temperature and loading rate for woven composites, and the effects of matrix toughening in woven and unidirectional composites.
Hunston, D. L.↗
Strain energy release rate distributions for double cantilever beam specimens
A 24-ply composite double cantilever-beam specimen under mode I (opening) loading has been analyzed by a 3D FEM code that calculated along a straight delamination starter for several different specimen materials. An isotropic specimen was found to have a strain-energy release rate distribution which varied along its delamination front due to the boundary-layer effect and another effect associated with the anticlastic curvature of the bent specimen arms. A 0-deg graphite-reinforced epoxy specimen had a nearly-uniform strain-energy release rate distribution which dropped only near the edge, due to the boundary-layer effect, and a +/- 45-deg graphite/epoxy specimen exhibited a pronounced strain-energy release rate variation across the specimen width.
Crews, J. H., Jr.↗