SEARCH · Search NASA

Results for “mode shape”

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.

SourceResearch connectionFrom yearThrough year

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

At least 325 records · Page 18

All sources NASA NTRS DOE OSTI

NASA NTRS1986

Senstitivty analysis and optimization of nodal point placement for vibration reduction

A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location - for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed.

Pritchard, J. I.↗

NASA NTRS1987

Sensitivity derivatives and optimization of nodal point locations for vibration reduction

A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location; for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed.

Pritchard, Jocelyn I.↗

NASA NTRS1987

Sensitivity analysis and optimization of nodal point placement for vibration reduction

Pritchard, J. I.↗

NASA NTRS2003

Fiber-Optic Bragg Gratings and Optical Holography Compared as Vibration Detectors

The NASA Glenn Research Center is interested in determining structural damage in engine components during flight to evaluate the health of aerospace propulsion systems. On the ground, we can use holography to detect structural damage by examining the characteristic mode shapes and frequencies of vibrating objects. We are studying the feasibility of using embedded fiber Bragg gratings (FBGs) to accomplish this goal in a flight-worthy system, by using the minimal intrusion and high sensitivity afforded by fiber optics. We have recently compared holographically imaged modes of vibrating plates with the corresponding dynamic strains detected by embedded FBGs. We constructed an experimental setup for studying the responses of FBGs to dynamic excitations. One of the plates was made of a polymer matrix composite (PMC) with an FBG embedded in it, and the other one was made of copper with surface-mounted FBGs. The instrumented plates were mounted and vibrated, and time-averaged holography was used to measure their surface displacements. Simultaneously, the signals from the FBGs were detected and sent via fiber-optic cable to a quiet location about 20 m away for interrogation. The the test configuration used for the PMC plate is shown. Experimental results are also shown. The FBG was embedded in the middle of the PMC plates, roughly within the center circular fringe in each of the interferograms shown. Two resonant excitation frequencies were used: 706 and 3062 Hz. The plot in this paper shows a larger FBG signal at the higher frequency; this is because the plate bends more at higher order resonant modes, causing higher strain. This contrasts to the smaller displacements characteristic of higher frequencies, which are measured by holographic techniques.

Adamovsky, Grigory↗

NASA NTRS2016

Measurements in a Transitioning Cone Boundary Layer at Freestream Mach 3.5

An experimental study was conducted in the Supersonic Low-Disturbance Tunnel to investigate naturally-occurring instabilities in a supersonic boundary layer on a 7 deg half- angle cone. All tests were conducted with a nominal freestream Mach number of M(sub infinity) = 3:5, total temperature of T(sub 0) = 299:8 K, and unit Reynolds numbers of Re(sub infinity) x 10(exp -6) = 9:89, 13.85, 21.77, and 25.73 m(exp -1). Instability measurements were acquired under noisy- ow and quiet- ow conditions. Measurements were made to document the freestream and the boundary-layer edge environment, to document the cone baseline flow, and to establish the stability characteristics of the transitioning flow. Pitot pressure and hot-wire boundary- layer measurements were obtained using a model-integrated traverse system. All hot- wire results were single-point measurements and were acquired with a sensor calibrated to mass ux. For the noisy-flow conditions, excellent agreement for the growth rates and mode shapes was achieved between the measured results and linear stability theory (LST). The corresponding N factor at transition from LST is N 3:9. The stability measurements for the quiet-flow conditions were limited to the aft end of the cone. The most unstable first-mode instabilities as predicted by LST were successfully measured, but this unstable first mode was not the dominant instability measured in the boundary layer. Instead, the dominant instabilities were found to be the less-amplified, low-frequency disturbances predicted by linear stability theory, and these instabilities grew according to linear theory. These low-frequency unstable disturbances were initiated by freestream acoustic disturbances through a receptivity process that is believed to occur near the branch I locations of the cone. Under quiet-flow conditions, the boundary layer remained laminar up to the last measurement station for the largest Re1, implying a transition N factor of N greater than 8:5.

King, Rudolph A.↗

NASA NTRS1993

Numerical and experimental investigation of the bending response of thin-walled composite cylinders

A numerical and experimental investigation of the bending behavior of six eight-ply graphite-epoxy circular cylinders is presented. Bending is induced by applying a known end-rotation to each end of the cylinders, analogous to a beam in bending. The cylinders have a nominal radius of 6 inches, a length-to-radius ratio of 2 and 5, and a radius-to-thickness ratio of approximately 160. A (+/- 45/0/90)S quasi-isotropic layup and two orthotropic layups, (+/- 45/0 sub 2)S and (+/- 45/90 sub 2)S, are studied. A geometrically nonlinear special-purpose analysis, based on Donnell's nonlinear shell equations, is developed to study the prebuckling responses and gain insight into the effects of non-ideal boundary conditions and initial geometric imperfections. A geometrically nonlinear finite element analysis is utilized to compare with the prebuckling solutions of the special-purpose analysis and to study the buckling and post buckling responses of both geometrically perfect and imperfect cylinders. The imperfect cylinder geometries are represented by an analytical approximation of the measured shape imperfections. Extensive experimental data are obtained from quasi-static tests of the cylinders using a test fixture specifically designed for the present investigation. A description of the test fixture is included. The experimental data are compared to predictions for both perfect and imperfect cylinder geometries. Prebuckling results are presented in the form of displacement and strain profiles. Buckling end-rotations, moments, and strains are reported, and predicted mode shapes are presented. Observed and predicted moment vs. end-rotation relations, deflection patterns, and strain profiles are illustrated for the post buckling responses. It is found that a geometrically nonlinear boundary layer behavior characterizes the prebuckling responses. The boundary layer behavior is sensitive to laminate orthotropy, cylinder geometry, initial geometric imperfections, applied end-rotation, and non-ideal boundary conditions. Buckling end-rotations, strains, and moments are influenced by laminate orthotropy and initial geometric imperfections. Measured buckling results correlate well with predictions for the geometrically imperfect specimens. The postbuckling analyses predict equilibrium paths with a number of scallop-shaped branches that correspond to unique deflection patterns. The observed postbuckling deflection patterns and measured strain profiles show striking similarities to the predictions in some cases. Ultimate failure of the cylinders is attributed to an interlaminar shear failure mode along the nodal lines of the postbuckling deflection patterns.

Fuchs, J. P.↗

NASA NTRS1991

Structural damage identification using mathematical optimization techniques

An identification procedure is proposed to identify damage characteristics (location and size of the damage) from dynamic measurements. This procedure was based on minimization of the mean-square measure of difference between measurement data (natural frequencies and mode shapes) and the corresponding predictions obtained from the computational model. The procedure is tested for simulated damage in the form of stiffness changes in a simple fixed free spring mass system and symmetric cracks in a simply supported Bernoulli Euler beam. It is shown that when all the mode information is used in the identification procedure it is possible to uniquely determine the damage properties. Without knowing the complete set of modal information, a restricted region in the initial data space has been found for realistic and convergent solution from the identification process.

Shen, Mo-How Herman↗

NASA NTRS1993

A model for the selective amplification of spatially coherent waves in a centrifugal compressor on the verge of rotating stall

A simple model for the stability zones of a low speed centrifugal compressor is developed, with the goal of understanding the driving mechanism for the changes in stalling behavior predicted for, and observed in, the Purdue Low Speed Centrifugal Research Compressor Facility. To this end, earlier analyses of rotating stall suppression in centrifugal compressors are presented in a reduced form that preserves the essential parameters of the model that affect the stalling behavior of the compressor. The model is then used to illuminate the relationship between compressor geometry, expected mode shape, and regions of amplification for weak waves which are indicative of the susceptibility of the system to rotating stall. The results demonstrate that increasing the stagger angle of the diffuser vanes, and consequently the diffusion path length, results in the compressor moving towards a condition where higher-order spatial modes are excited during stall initiation. Similarly, flow acceleration in the diffuser section caused by an increase in the number of diffuser vanes also results in the excitation of higher modes.

Lawless, Patrick B.↗

NASA NTRS2018

Advanced Mirror Technology Development (AMTD) II Modal Test of A 1.5 m Glass Slumped Mirror

The Advanced Mirror Technology Development (AMTD) project is in Phase 2 of a multiyear effort initiated in Fiscal Year 2012 to mature toward the next technology readiness level critical technologies required to enable 4-m-or-larger monolithic or segmented ultraviolet, optical, and infrared (UVOIR) space telescope primary-mirror assemblies for general astrophysics and ultra-high-contrast observations of exoplanets. As part of AMTD II, a free-free modal test was performed of a light weighted slumped 1.5 m mirror made of Corning Ultra Low Expansion (ULE®) material. The test article and support structure were suspended via bungee to simulate a free-free environment. Modes were excited by roaming an instrumented modal test hammer and responses were measured. Predicted and measured frequencies are presented as well as Modal Assurance Criteria (MAC) results to compare the mode shapes. The finite element mirror model used for pre-test predictions and posttest comparisons was provided by the mirror vendor, Harris Corporation. The mirror FEM included deformations of the ribs that were a result of the slumping process. Modal test frequencies matched predictions within the 5% target with the exception of one mode and that pair differed by 5.2%. Of the seven modes measured and predicted, four had MAC values meeting the target of ≥ 0.90, one was just under and two were notably below the target.

Knight, J. Brent↗

NASA NTRS1989

Effect of control surface mass unbalance on the stability of a closed-loop active control system

The effects on stability of inertial forces arising from closed-loop activation of mass-unbalanced control surfaces are studied analytically using inertial energy approach, similar to the aerodynamic energy approach used for flutter suppression. The limitations of a single control surface like a leading-edge (LE) control or a trailing-edge (TE) control are demonstrated and compared to the superior combined LE-TE mass unbalanced system. It is shown that a spanwise section for sensor location can be determined which ensures minimum sensitivity to the mode shapes of the aircraft. It is shown that an LE control exhibits compatibility between inertial stabilization and aerodynamic stabilization, and that a TE control lacks such compatibility. The results of the present work should prove valuable, both for the purpose of flutter suppression using mass unbalanced control surfaces, or for the stabilization of structural modes of large space structures by means of inertial forces.

Nissim, E.↗

NASA NTRS1977

NASTRAN hydroelastic modal studies. Volume 1: Introduction, theory, and results

The implementation of a general three-dimensional hydroelastic capability in the NASTRAN computer program is described. A method for analyzing the combined mode shapes of arbitrary fluid and structure finite element models was developed. The fluid was modeled with three-dimensional solid elements with options for tetrahedron, wedge, and hexahedron shapes. The elements were then connected to fluid grid points which defined the pressure in the fluid at the specified location. Matrices were formulated to provide efficient solutions for large-order problems. The structure matrices were processed separately and could be reduced using matrix condensation procedures or through a modal formulation using the normal modes of the empty structure as solution coordinates. The fluid/structure interface and the free surface were defined by the user with special NASTRAN boundary elements. A special purpose mesh generator program was provided to generate the actual NASTRAN data cards for the fluid, the structure, and the boundary elements for typical tank-type models.

Source record↗

NASA NTRS1989

Accurate calculation of control-augmented structural eigenvalue sensitivities using reduced-order models

A method is presented for generating mode shapes for model order reduction in a way that leads to accurate calculation of eigenvalue derivatives and eigenvalues for a class of control augmented structures. The method is based on treating degrees of freedom where control forces act or masses are changed in a manner analogous to that used for boundary degrees of freedom in component mode synthesis. It is especially suited for structures controlled by a small number of actuators and/or tuned by a small number of concentrated masses whose positions are predetermined. A control augmented multispan beam with closely spaced natural frequencies is used for numerical experimentation. A comparison with reduced-order eigenvalue sensitivity calculations based on the normal modes of the structure shows that the method presented produces significant improvements in accuracy.

Livne, Eli↗

NASA NTRS1998

Fastrac Rocket Engine Combustion Chamber Acoustic Cavities

A three dimensional modal analysis was performed using finite fluid elements. The analysis shows four distinct modes of the Fastrac chamber plus cavities near the frequency of the chamber first tangential mode. The mode shapes illustrate the complexity of fluid oscillations in a three dimensional chamber and acoustic cavity. In addition, a first tangential forcing function was applied to the chamber with three different acoustic cavity fluid temperatures. It was observed that the acoustic cavity fluid temperature has a significant effect on the response of the chamber to first tangential mode oscillations.

Christensen, Eric↗

NASA NTRS1967

Matrix Analysis of Longitudinal and Torsional Vibrations in Nonuniform Multibranch Beams

Since longitudinal modes and frequencies provide basic data for dynamic analyses of arbitrary beam-like structures and since closed-form solutions for the modes are generally not feasible to obtain, an approximate method is developed for computing the natural frequencies and the corresponding mode shapes for a variable-section, unconstrained multibranch beam. A lumped mass analogy employing influence coefficients is used to represent the beam. The simultaneous equations of motion for the lumped mass system are derived in matrix form and algebraically manipulated to yield a classical eigenvalue equation solvable by standard procedures. The orthogonality relationship of the natural modes is derived and used to form the basis of an orthogonal sweeping process for determination of modes above the fundamental. Numerical examples including an application to a solid-fuel launch system are presented. Also, a detailed discussion is devoted to the theoretical verifications of the approximate modes and frequencies.

Wingate, Robert T.↗

NASA NTRS2003

Task II: Three-dimensional Rotating Stall Inception and Effects of Rotating Tip Clearance Asymmetry in Axial Compressors

The effects of two types of flow non-uniformity on stall inception behavior were assessed with linearized stability analyses of two compressor flow models. Response to rotating tip clearance asymmetries induced by a whirling rotor shaft or rotor height variations were investigated with a two-dimensional flow model. A 3-D compressor model was also developed to study the stability of both full-span and part-span rotating stall modes in annular geometries with radial flow variations. The studies focussed on (1) understanding what compressor designs were sensitive to these types of circumferential and spanwise flow non-uniformities, and (2) situations where 2-D stability theories were inadequate because of 3-D flow effects. Rotating tip clearance non-uniformity caused the greatest performance loss for shafts whirling at the rotating stall frequency. A whirling shaft displacement of 1 percent chord caused the stalling mass flow to rise by as much as 10 percent and the peak pressure rise to decrease by 6 percent. These changes were an order of magnitude larger than for equivalent-sized stationary or rotor-locked clearance asymmetries. Spanwise flow non-uniformity always destabilized the compressor, so that 2-D models over-predicted that stall margin compared to 3-D theory. The difference increased for compressors with larger spanwise variations of characteristic slope and reduced characteristic curvature near the peak. Differences between 2-D and 3-D stall point predictions were generally unacceptable (2 - 4 percent of flow coefficient) for single-stage configurations, but were less than 1 percent for multistage compressors. 2-D analyses predicted the wrong stall mode for specific cases of radial inlet flow distortion, mismatching and annulus area contraction, where higher-order radial modes led to stall. The stability behavior of flows with circumferential or radial non-uniformity was unified through a single stability criterion. The stall point for both cases was set by the integral around the annulus of the pressure rise characteristic slope, weighted by the amplitude of the mode shape. For the case of steady circumferential variations, this criterion reduced to the integrated mean slope (IMS) condition associated with steady inlet distortions. The rotating tip clearance asymmetry model was also used to demonstrate the feasibility of actively controlling the shaft position to suppress rotating stall. In axisymmetric mean flow, this method only stabilized the first harmonic mode, increasing the operating range until surge or higher harmonic modes became unstable.

Suder, Kenneth↗

NASA NTRS2005

Operating Deflection Shapes for the Space Shuttle Partial Stack Rollout

In November of 2003 a rollout test was performed to gain a better understanding of the dynamic environment for the Space Shuttle during transportation from the Vehicle Assembly Building to the launch pad. This was part of a study evaluating the methodology for including the rollout dynamic loads in the Space Shuttle fatigue life predictions. The rollout test was conducted with a partial stack consisting of the Crawler Transporter, Mobile Launch Platform, and the Solid Rocket Boosters with an interconnecting crossbeam. Instrumentation included over 100 accelerometers. Data was recorded for steady state speeds, start-ups and stops, and ambient wind excitations with the vehicle at idle. This paper will describe the operating deflection shape analysis performed using the measured acceleration response data. The response data for the steady state speed runs were dominated by harmonics of the forcing frequencies, which were proportional to the vehicle speed. Assuming a broadband excitation for the wind, analyses of the data sets with the vehicle at idle were used to estimate the natural frequencies and corresponding mode shapes. Comparisons of the measured modal properties with numerical predictions are presented.

Buehrle, Ralph D.↗

NASA NTRS2015

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL Multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. This work builds upon previous efforts to verify the use of the acoustic velocity potential equation (AVPE) laid out by Campos. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, del squared psi - (lambda/c) squared psi - M x [M x del((del)(psi))] - 2((lambda)(M)/c + M x del(M) x (del)(psi) - 2(lambda)(psi)[M x del(1/c)] = 0. with M as the Mach vector, c as the speed of sound, and λ as the complex eigenvalue. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, axial velocity, exit velocity). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The one way coupled analysis is perform four times utilizing geometries determined through traditional SRM modeling procedures. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Fischbach, S. R.↗

NASA NTRS2015

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework [1, 2, 3]. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick [4, 5]. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, no slip boundary conditions, and the hybrid outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, thrust, ect.). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the Acoustic Velocity Potential Equation (AVPE). The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob [2, 3]. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Fischbach, Sean R.↗