Bending and Shear Stresses Developed by the Instantaneous Arrest of the Root of a Cantilever Beam with a Mass at Its Tip
Explore the source record for details and available documents.
BEAMS, CANTILEVER-STRESSES↗
SEARCH · Search NASA
Results for “BENDING VIBRATION”
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.
Supersonic Stall Flutter of High Speed Fans
An analytical model is developed for predicting the onset of supersonic stall bending flutter in axial flow compressors. The analysis is based on a modified two dimensional, compressible, unsteady actuator disk theory. It is applied to a rotor blade row by considering a cascade of airfoils whose geometry and dynamic response coincide with those of a rotor blade element at 85 percent of the span height (measured from the hub). The rotor blades are assumed to be unshrouded (i.e., free standing) and to vibrate in their first flexural mode. The effects of shock waves and flow separation are included in the model through quasi-steady, empirical, rotor total-pressure-loss and deviation-angle correlations. The actuator disk model predicts the unsteady aerodynamic force acting on the cascade blading as a function of the steady flow field entering the cascade and the geometry and dynamic response of the cascade. Calculations show that the present model predicts the existence of a bending flutter mode at supersonic inlet Mach numbers. This flutter mode is suppressed by increasing the reduced frequency of the system or by reducing the steady state aerodynamic loading on the cascade. The validity of the model for predicting flutter is demonstrated by correlating the measured flutter boundary of a high speed fan stage with its predicted boundary. This correlation uses a level of damping for the blade row (i.e., the log decrement of the rotor system) that is estimated from the experimental flutter data. The predicted flutter boundary is shown to be in good agreement with the measured boundary.
Adamczyk, J. J.↗
Approximate method for calculating free vibrations of a large-wind-turbine tower structure
A set of ordinary differential equations were derived for a simplified structural dynamic lumped-mass model of a typical large-wind-turbine tower structure. Dunkerley's equation was used to arrive at a solution for the fundamental natural frequencies of the tower in bending and torsion. The ERDA-NASA 100-kW wind turbine tower structure was modeled, and the fundamental frequencies were determined by the simplified method described. The approximate fundamental natural frequencies for the tower agree within 18 percent with test data and predictions analyzed.
Das, S. C.↗
Crossover from hydrogen to chemical bonding
Hydrogen bonds (H-bonds) can be interpreted as a classical electrostatic interaction or as a covalent chemical bond if the interaction is strong enough. As a result, short strong H-bonds exist at an intersection between qualitatively different bonding descriptions, with few experimental methods to understand this dichotomy. The [F-H-F] − ion represents a bare short H-bond, whose distinctive vibrational potential in water is revealed with femtosecond two-dimensional infrared spectroscopy. It shows the superharmonic behavior of the proton motion, which is strongly coupled to the donor-acceptor stretching and disappears on H-bond bending. In combination with high-level quantum-chemical calculations, we demonstrate a distinct crossover in spectroscopic properties from conventional to short strong H-bonds, which identify where hydrogen bonding ends and chemical bonding begins.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Investigation of empirical damping laws for the space shuttle
An analysis of dynamic test data from vibration testing of a number of aerospace vehicles was made to develop an empirical structural damping law. A systematic attempt was made to fit dissipated energy/cycle to combinations of all dynamic variables. The best-fit laws for bending, torsion, and longitudinal motion are given, with error bounds. A discussion and estimate are made of error sources. Programs are developed for predicting equivalent linear structural damping coefficients and finding the response of nonlinearly damped structures.
Bernstein, E. L.↗
Shaft flexibility effects on the forced response of a bladed-disk assembly
A model analysis approach is used to study the forced response of an actual flexible bladed-disk-shaft system. Both in-plane and out-of-plane flexible deformations of the bladed-disk assembly are considered, in addition to its rigid-body translations and rotations, resulting from the bending of the supporting flexible shaft in two orthogonal planes. The effects of Coriolis forces and structural coupling between flexible and rigid disk motions on the system's response are investigated. Aerodynamic loads acting on the rotating and vibrating bladed-disk assembly are accounted for through a simple quasi-steady representation, to evaluate their influence, combined with shaft flexibility and Coriolis effects.
Khader, N.↗
A Multi-Mode Blade Damping Control using Shunted Piezoelectric Transducers with Active Feedback Structure
The Structural Dynamics and. Mechanics branch (RXS) is developing smart adaptive structures to improve fan blade damping at resonances using piezoelectric (PE) transducers. In this presentation, only one shunted PE transducer was used to demonstrate active control of multi-mode blade resonance damping on a titanium alloy (Ti-6A1-4V) flat plate model, regardless of bending, torsion, and 2-stripe modes. This work would have a significant impact on the conventional passive shunt damping world because the standard feedback control design tools can now be used to design and implement electric shunt for vibration control. In other words, the passive shunt circuit components using massive inductors and. resistors for multi-mode resonance control can be replaced with digital codes. Furthermore, this active approach with multi patches can simultaneously control several modes in the engine operating range. Dr. Benjamin Choi presented the analytical and experimental results from this work at the Propulsion-Safety and. Affordable Readiness (P-SAR) Conference in March, 2009.
Choi, Benjamin↗
Parameter estimation in truss beams using Timoshenko beam model with damping
Truss beams with members having viscous damping are modeled with a Timoshenko beam. Procedures for deriving the equivalent bending rigidity, transverse shear rigidity, and damping are presented. Explicit expressions for these equivalent beam properties are obtained for a specific truss beam. The beam model thus established is then used to investigate the effect of damping in free vibration. Finally, the beam is employed in the estimation of structural parameters in a simply-supported truss beam using a random search algorithm.
Sun, C. T.↗
Predicting Flutter Of A Propfan
Report discusses theoretical model and associated computer program for prediction of subsonic bending-torsion cascade flutter in propfans. Predictions of model compared with results of experiments. Additional parametric studies illustrate effects upon flutter speed of steady aeroelastic deformations, angle at which blade set, speed of rotation, structural damping, and number of vibrational modes. Calculations performed by parts of ASTROP computer code: ASTROP 2, based on two-dimensional, subsonic, unsteady aerodynamics; and ASTROP 3, based on three-dimensional, subsonic, steady and unsteady aerodynamics.
Kaza, K. R. V.↗
Member vibration effects on LSS behavior
This paper evaluates the sensitivity of modal characteristics of large deployable lattice-type space structures to joint boundary conditions. The evaluation of joint rotational boundary conditions is accomplished by a review of modal strain energy among elements of the analytic dynamic model. This review shows that space structure designs having no bending energy in lattice members in the low frequency range are insensitive to joint rotational boundary conditions in that frequency range. Evaluation of joint translation boundary conditions is accomplished by the 'modal freeplay method' which is described in this paper. The modal freeplay method relates modal frequency to joint translational freeplay and to amplitude of applied forces.
White, Charles W.↗
Inelastic Triatom-Atom Quantum Close-Coupling Dynamics in Full Dimensionality: All Rovibrational Mode Quenching of Water Due to the H Impact on a Six-Dimensional Potential Energy Surface
The rovibrational level populations, and subsequent emission in various astrophysical environments, are driven by inelastic collision processes. The available rovibrational rate coefficients for water have been calculated using a number of approximations. We present a numerically exact calculation for the rovibrational quenching for all water vibrational modes due to collisions with atomic hydrogen. The scattering theory implements a quantum close-coupling (CC) method on a high level ab initio six-dimensional (6D) potential energy surface (PES). Total rovibrational quenching cross sections for excited bending levels were compared with earlier results on a 4D PES with the rigid-bender closecoupling (RBCC) approximation. General agreement between 6D-CC and 4DRBCC calculations are found, but differences are evident including the energy and amplitude of low-energy orbiting resonances. Quenching cross sections from the symmetric and asymmetric stretch modes are provided for the first time. The current 6D-CC calculation provides accurate inelastic data needed for astrophysical modeling.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Microwave spectrum, structure, dipole moment, and Coriolis coupling of 1,1-difluoroallene
Microwave spectra from 12.4 to 40.0 GHz were recorded for five isotopic species of 1,1-difluoroallene. A-type transitions were observed and R-branch assignments were made for the ground state and two vibrationally excited states. Several structural parameters of the compounds were determined. The dipole moment value obtained from Stark splitting was 2.07 plus or minus 0.03 D. A Coriolis coupling was observed between the two-low-frequency C = C = C bending modes.
Durig, J. R.↗
Passively Shunted Piezoelectric Damping of Centrifugally-Loaded Plates
Researchers at NASA Glenn Research Center have been investigating shunted piezoelectric circuits as potential damping treatments for turbomachinery rotor blades. This effort seeks to determine the effects of centrifugal loading on passively-shunted piezoelectric - damped plates. Passive shunt circuit parameters are optimized for the plate's third bending mode. Tests are performed both non-spinning and in the Dynamic Spin Facility to verify the analysis, and to determine the effectiveness of the damping under centrifugal loading. Results show that a resistive shunt circuit will reduce resonant vibration for this configuration. However, a tuned shunt circuit will be required to achieve the desired damping level. The analysis and testing address several issues with passive shunt circuit implementation in a rotating system, including piezoelectric material integrity under centrifugal loading, shunt circuit implementation, and tip mode damping.
Duffy, Kirsten P.↗
Active control of a flexible structure using a modal positive position feedback controller
The feasibility of a new Modal Positive Position Feedback (MPPF) strategy in controlling the vibration of a complex flexible structure using a single piezo-electric active structural member is demonstrated. The control strategy generates its control forces by manipulating only the modal position signals of the structure to provide a damping action to undamped modes. This is in contrast to conventional modal controllers that rely in their operation on negative feedback of both the modal position and velocity. The proposed strategy is very simple to design and implement as it designs the controller at the uncoupled modal level and utilizes simple first order filters to achieve the Positive Position Feedback effect. The performance of the new strategy is enhanced by augmenting it with a time sharing strategy to share a small number of actuators between larger number of modes. The effectiveness of the new strategy is validated experimentally on a flexible box-type structure that has four bays and its first two bending modes are 2.015 and 6.535 Hz respectively. A single piezo-electric actuator is utilized as an active structural member to control several transverse bending modes of the structure. The performance of the active control system is determined in the time and the frequency domains. The results are compared with those obtained when using the Independent Modal Space Control (IMSC) of Meirovitch. The experimental results suggest the potential of the proposed strategy as a viable means for controlling the vibration of large flexible structures in real time.
Poh, S.↗
Active control of a flexible structure using a modal positive position feedback controller
The feasibility of a new Modal Positive Position Feedback (MPPF) strategy in controlling the vibration of a complex flexible structure using a single piezo-electric active structural member is demonstrated. The control strategy generates its control forces by manipulating only the modal position signals of the structure to provide a damping action to undamped modes. This is in contrast to conventional modal controllers that rely in their operation on negative feedback of both the modal position and velocity. The proposed strategy is very simple to design and implement as it designs the controller at the uncoupled modal level and utilizes simple first order filters to achieve the Positive Position Feedback effect. The performance of the new strategy is enhanced by augmenting it with a time sharing strategy to share a small number of actuators between larger number of modes. The effectiveness of the new strategy is validated experimentally on a flexible box-type structure that has four bays and its first two bending modes are 2.015 and 6.535 Hz, respectively. A single piezo-electric actuator is utilized as an active structural member to control several transverse bending modes of the structure. The performance of the active control system is determined in the time and the frequency domains. The results are compared with those obtained when using the Independent Modal Space Control (IMSC) of Meirovitch. The experimental results suggest the potential of the proposed strategy as a viable means for controlling the vibration of large flexible structures in real time.
Poh, S.↗
Aeroelastic Tests of an Eight Percent Scale Saturn C-1 Block II
Buffet and flutter characteristics of Saturn Apollo mission were studied using a dynamically scaled model. The model was built around a central aluminum tube for scaled stiffness distribution and strength to resist loads imposed during testing. Styrofoam sections attached to the core provided the correct external contours. Lead weights were added for correct mass distribution. An electromagnetic shaker was used to excite the model in its flexible modes of vibration during portions of the test. The model was supported on a sting, mounted by leaf springs, cables and torsion bars. The support system provided for simulating the full scale rigid body pitch frequency with minimum restraint imposed on elastic deflections. Bending moments recorded by sensors on the aluminum tube. Several modified nose configurations were tested: The basic configuration was tested with and without a flow separator disk on the escape rocket motor, tests also were made with the escape tower and rocket motor removed completely. For the final test, the Apollo capsule was replaced with a Jupiter nose cone. The test program consisted of determining model response throughout the transonic speed range at angles of attack up to 6 degrees and measuring the aerodynamic damping over the same range for the basic model and the modified configurations. Signals from the model pickup were recorded on tape for later analysis. The data obtained were used to estimate bending moments that would be produced on the full-scale vehicle by aerodynamic forces due to buffeting.
EXPERIMENTS↗
Behavior of Hydrogarnet‐Type Defects in Hydrous Stishovite at Various Temperatures and Pressures
Abstract Dense polymorphs of silica have been demonstrated experimentally to incorporate from 1.5 wt% to as much as 11.6 wt% H 2 O as OH groups, with implications for the hydrogen budgets of Earth and other planets. This OH is thought to enter the SiO 2 structure via a charge‐balanced substitution in which silicon vacancies (V Si ) are compensated by protonating four of the surrounding six oxygen atoms, often referred to as a hydrogarnet‐type defect. There are many possible configurations for this defect structure in dense silica, but the nature of these configurations and whether they can be distinguished experimentally is unknown. We present here density functional theory calculations that systematically assess the possible configurations of a hydrogarnet‐type defect in stishovite (rutile‐type SiO 2 ), with direct comparisons to experimental vibrational spectroscopy data. We predict that stishovite synthesized at 450 K and 10 GPa quenched to room temperature is dominated by a single defect type with tetrahedral geometry. This leads to OH stretching modes (2,500–3,000 cm −1 ) and SiOH bending modes (∼1,400–1,450 cm −1 ) largely consistent with experimentally observed modes. One remaining issue is that our calculations produce results compatible with experimental data on H to D exchange, but do not explain why a considerable fraction of the 1,420 cm −1 mode shifts by only 40 cm −1 in deuterated samples. At elevated pressures and temperatures, we find that a second square planar defect configuration also becomes favorable, leading to modes that should allow differentiation from the tetrahedral configuration.
Geochemistry & Geophysics↗
Preliminary investigation of stability of a fin-stiffened slender strut
A fin-stiffened strut concept which possesses high bending stiffness and low packaged volume has been identified for use on large space structures. The concept incorporates three curved fins which deploy from a core tube to increase the effective cross-sectional moment of inertia, the buckling load, and the vibration frequency of the strut. A strut design incorporating welded fin connections provides an upper bound of the strut buckling load. A strut design which allows the individual fins and core to move independently in the strut axial direction provides a lower bound of the strut buckling load which is approximately 20 to 25 percent of the upper bound. A practical strut design, incorporating hinge assemblies which constrain the fins to move together but independently of the core tube in the strut axial direction, provides a buckling load which is 75 to 80 percent of the upper bound. Euler's equation can be used to accurately predict buckling loads for the bounding designs. Flat plate finite element models of all designs give results that agree to within 10 percent of the experimental values. Equivalent beam models of the strut give results which are slightly less accurate.
Lake, Mark S.↗