Frequency response and transfer functions of a nuclear rocket engine system obtained from analog computer simulation
Frequency response and transport functions for NERVA-type rocket engine
FREQUENCY RESPONSE↗
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Ground vibration test of the laminar flow control JStar airplane
A ground vibration test was conducted on a Lockheed JetStar airplane that had been modified for the purpose of conducting laminar flow control experiments. The test was performed prior to initial flight flutter tests. Both sine-dwell and single-point-random excitation methods were used. The data presented include frequency response functions and a comparison of mode frequencies and mode shapes from both methods.
Kehoe, M. W.↗
Robust computer-aided synthesis and optimization of linear multivariable control systems with varying plant dynamics via AUTOCON
AUTOCON is an automated computer-aided design tool for the synthesis and optimization of linear multivariable control systems based upon user-defined control parameter optimization. Violations in stability and performance requirements are computed from constraints on Single Input/Single Output (SISO) open- and closed-loop transfer function frequency responses, and from constraints on the singular-value frequency responses of Multiple Input/Multiple Output (MIMO) transfer functions, for all critical plant variations. Optimum nonlinear programming algorithms are used in the search for local constrained solutions in which violations in stability and performance are caused either to vanish or be minimized for a proper selection of the control parameters. Classical control system stability and performance design can, in this way, be combined with modern multivariable robustness methods to offer general frequency response loop-shaping via a computer-aided design tool. Complete Nichols, Nyquist, Bode, singular-value Bode magnitude and transient response plots are produced, including user-defined boundary responses. AUTOCON is used to synthesize and optimize the lateral/directional flight control system for a typical high-performance aircraft.
Lefkowitz, C. P.↗
Shake test results of the MDHC test stand in the 40- by 80-foot wind tunnel
A shake test was conducted to determine the modal properties of the MDHC (McDonnell Douglas Helicopter Company) test stand installed in the 40- by 80- Foot Wind Tunnel at Ames Research Center. The shake test was conducted for three wind-tunnel balance configurations with and without balance dampers, and with the snubber engagement to lock the balance frame. A hydraulic shaker was used to apply random excitation at the rotor hub in the longitudinal and lateral directions. A GenRad 2515 computer-aided test system computed the frequency response functions at the rotor hub and support struts. From these response functions, the modal properties, including the natural frequency, damping ratio, and mode shape were calculated. The critical modes with low damping ratios are identified as the test-stand second longitudinal mode for the dampers-off configuration, the test-stand yaw mode for the dampers-on configuration, and the test stand first longitudinal mode for the balance-frame locked configuration.
Lau, Benton H.↗
Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test
The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.
Accelerance decoupling↗
Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test
The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.
Accelerance decoupling↗
Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test
The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.
Accelerance decoupling↗
Experimental Dynamic Characterization of a Reconfigurable Adaptive Precision Truss
The dynamic behavior of a reconfigurable adaptive truss structure with non-linear joints is investigated. The objective is to experimentally examine the effects of the local non-linearities on the global dynamics of the structure. Amplitude changes in the frequency response functions are measured at micron levels of motion. The amplitude and frequency variations of a number of modes indicate a non-linear Coulomb friction response. Hysteretic bifurcation behavior is also measured at an amplitude approximately equal to the specified free-play in the joint. Under the 1 g pre-load, however, the non-linearity was dominantly characteristic of Coulomb friction with little evidence of free-play stiffening.
Hinkle, J. D.↗
Numerical and experimental evaluation for single-axis control of an LSS laboratory model
One of the major problems of LSS attitude control design stems from the modeling uncertainties due to modal truncation errors and modal parameter estimation errors. This modeling problem is investigated by evaluating poles and zeros of the frequency response functions, described in terms of constrained or unconstrained modes. The frequency domain approach is utilized to evaluated the results of modal analyses and direct output feedback controller experiments using a simple flexible spacecraft model consisting of a rigid primary body and flexible aluminum beam(s) with a control moment gyro as an actuator. The modal data are compared under the conditions that the model is constrained as the canti-lever and it is rotationally free on a single-axis air bearing table. In addition, the open-loop responses are experimentally examined under the impulsive disturbance to the appendage. The results of the control experiments show that the first vibration mode of the appendage and the interacted rotational motion of the primary body are damped in a short time as predicted by the numerical analysis, to produce damping ratio of 10-20%.
Ohkami, Y.↗
Green Run Modal Test of the NASA Space Launch System Core Stage
The Core Stage of the new NASA Space Launch System (SLS) is a 212-foot tall rocket assembly—consisting primarily of two fuel tanks, an engine section, and four RS-25 rocket engines—capable of sending crew and large payloads to the moon and beyond with 1.6 million pounds of thrust. Currently, the Core Stage is in the B2 Test Stand at Stennis Space Center, undergoing a series of structural and functional tests, designated the Green Run test series. The ultimate goal of Green Run is to verify analytical models and confirm proper subsystem operation of the Core Stage. In January 2020, Green Run testing began with an experimental modal analysis test performed by the Marshal Space Flight Center modal test team. The desired free boundary condition of the Core Stage was achieved by suspending the massive spacecraft from the B2 Test Stand crane. Modal excitation was provided by a pair of 250-lb electro-dynamic shakers for multi-shaker random vibration testing, as well as a 12-pound impact hammer for impact testing. Modal response was measured with 550 accelerometers channels distributed on both the Core Stage and the B2 Test Stand crane. Following one very long night of testing, frequency response functions were calculated from the measured time histories in the target mode frequency range of 2.5 Hz to 15 Hz, and mode shapes, frequencies, and damping values were successfully extracted. The case-study presented in this paper will discuss the SLS Core Stage, the modal test setup and procedure, as well as a brief overview of the test results. Challenges associated with testing such a large, suspended structure in an outdoor environment will be discussed as well.
Green Run↗
Green Run Modal Test of the NASA Space Launch System Core Stage
The Core Stage of the new NASA Space Launch System (SLS) is a 212-foot-tall rocket assembly—consisting primarily of two cryogenic propellant tanks, an engine section, and four RS-25 rocket engines—that will send crew and large payloads to the moon and beyond for NASA’s Artemis program. Prior to SLS assembly, the Core Stage completed a series of structural and functional tests in the B-2 Test Stand at Stennis Space Center, designated Green Run. The goal of Green Run was to verify analytical models, confirm proper subsystem operation, and test-fire all four RS-25 engines of the Core Stage. In January 2020, Green Run testing began with an experimental modal analysis test, performed by the Marshal Space Flight Center modal test team. A free-boundary test condition of the Core Stage was simulated as close as possible by suspending the massive launch vehicle from the B-2 Test Stand crane. Modal excitation was provided by a pair of 250-lb electro-dynamic shakers for multi-shaker random vibration testing, as well as a 12-pound instrumented hammer for impact testing. Modal response was measured with 550 accelerometer channels distributed on both the Core Stage and the B-2 Test Stand derrick crane. Following one very long day of testing, frequency response functions were calculated from the measured time histories in the target mode frequency range of 5 Hz to 15 Hz, and mode shapes, frequencies, and damping values were successfully estimated. The case-study presented in this paper will discuss Green Run, the SLS Core Stage, the modal test setup and execution, as well as a brief overview of the test results. Challenges associated with testing such a large, suspended structure in an outdoor environment will be discussed as well.
Space Launch System↗
Algorithms for Efficient Computation of Transfer Functions for Large Order Flexible Systems
An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, still-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open- and closed-loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, the present method was up to two orders of magnitude faster than a traditional method. The present method generally showed good to excellent accuracy throughout the range of test frequencies, while traditional methods gave adequate accuracy for lower frequencies, but generally deteriorated in performance at higher frequencies with worst case errors being many orders of magnitude times the correct values.
Maghami, Peiman G.↗
Inverse Force Determination on a Small Scale Launch Vehicle Model Using a Dynamic Balance
A launch vehicle can experience large unsteady aerodynamic forces in the transonic regime that, while usually only lasting for tens of seconds during launch, could be devastating if structural components and electronic hardware are not designed to account for them. These aerodynamic loads are difficult to experimentally measure and even harder to computationally estimate. The current method for estimating buffet loads is through the use of a few hundred unsteady pressure transducers and wind tunnel test. Even with a large number of point measurements, the computed integrated load is not an accurate enough representation of the total load caused by buffeting. This paper discusses an attempt at using a dynamic balance to experimentally determine buffet loads on a generic scale hammer head launch vehicle model tested at NASA Ames Research Center's 11' x 11' transonic wind tunnel. To use a dynamic balance, the structural characteristics of the model needed to be identified so that the natural modal response could be and removed from the aerodynamic forces. A finite element model was created on a simplified version of the model to evaluate the natural modes of the balance flexures, assist in model design, and to compare to experimental data. Several modal tests were conducted on the model in two different configurations to check for non-linearity, and to estimate the dynamic characteristics of the model. The experimental results were used in an inverse force determination technique with a psuedo inverse frequency response function. Due to the non linearity, the model not being axisymmetric, and inconsistent data between the two shake tests from different mounting configuration, it was difficult to create a frequency response matrix that satisfied all input and output conditions for wind tunnel configuration to accurately predict unsteady aerodynamic loads.
testing↗
Model Validation of an RSRM Transporter Through Full-scale Operational and Modal Testing
The Reusable Solid Rocket Motor (RSRM) segments, which are part of the current Space Shuttle system and will provide the first stage of the Ares launch vehicle, must be transported from their manufacturing facility in Promontory, Utah, to a railhead in Corinne, Utah. This approximately 25-mile trip on secondary paved roads is accomplished using a special transporter system which lifts and conveys each individual segment. ATK Launch Systems (ATK) has recently obtained a new set of these transporters from Scheuerle, a company in Germany. The transporter is a 96-wheel, dual tractor vehicle that supports the payload via a hydraulic suspension. Since this system is a different design than was previously used, computer modeling with validation via test is required to ensure that the environment to which the segment is exposed is not too severe for this space-critical hardware. Accurate prediction of the loads imparted to the rocket motor is essential in order to prevent damage to the segment. To develop and validate a finite element model capable of such accurate predictions, ATA Engineering, Inc., teamed with ATK to perform a modal survey of the transport system, including a forward RSRM segment. A set of electrodynamic shakers was placed around the transporter at locations capable of exciting the transporter vehicle dynamics. Forces from the shakers with varying phase combinations were applied using sinusoidal sweep excitation. The relative phase of the shaker forcing functions was adjusted to match the shape characteristics of each of several target modes, thereby customizing each sweep run for exciting a particular mode. The resulting frequency response functions (FRF) from this series of sine sweeps allowed identification of all target modes and other higher-order modes, allowing good comparison to the finite element model. Furthermore, the survey-derived modal frequencies were correlated with peak frequencies observed during road-going operating tests. This correlation enabled verification of the most significant modes contributing to real-world loading of the motor segment under transport. After traditional model updating, dynamic simulation of the transportation environment was compared to the measured operating data to provided further validation of the analysis model. KEYWORDS Validation, correlation, modal test, rocket motor, transporter
Brillhart, Ralph↗
Influence of visual and motion cues on manual lateral stabilization
The ability of humans to detect and control their own lateral acceleration was measured by means of a closed-loop nulling task. Wide-field moving visual cues enhanced the operator's performance in nulling self-motion, especially at lower frequencies. Even visual cues, fixed relative to the operator, resulted in performance improvement relative to self-motion nulling in the dark. Describing function (frequency response) data was obtained for random acceleration conditions consisting of the visual field fixed relative to the laboratory, fixed relative to the subject, moving at constant velocity relative to the subject, and in the dark. The describing function data was corrected for the dynamics of operator manual control strategy. The resulting frequency responses were used to develop a linear model of self-motion detection which required a lead term of 1.5 rad/s to be added to the existing model in order to match the higher sensitivity at higher frequencies.
Huang, J.-K.↗
Vibratory response of a stiffened, floor equipped, composite cylinder
A structural modal analysis has been performed on a composite, filament wound cylindrical shell with floor, using a Computer Aided Test (CAT) system. The twelve foot (3.66 m) long shell is five and one half feet (1.68 m) in diameter and includes a half inch thick plywood floor attached to the shell 69 degrees from the vertical centerline through the bottom of the shell. The shell is composed of carbon fibers embedded in an epoxy resin. The cylinder is supported by two heavy, rigid endcaps simulating simply supported end conditions. Modal frequencies of the shell and floor have been extracted by measuring the frequency response functions from impulse excitation by an impact hammer. Reasonable agreement is obtained between the measured structural modal frequencies and mode shapes and analytical results from a computerized prediction model. The effects of floor location, fiber orientation, and skin thickness on the resonance frequencies of the shell and floor have been predicted for a stiffened and unstiffened cylinder.
Grosveld, Ferdinand W.↗
Modal Test of the NASA Mobile Launcher at Kennedy Space Center
The NASA Mobile Launcher (ML), located at Kennedy Space Center (KSC), has recently been modified to support the launch of the new NASA Space Launch System (SLS). The ML is a massive structure—consisting of a 345-foot tall tower attached to a two-story base, weighing approximately 10.5 million pounds—that will secure the SLS vehicle as it rolls to the launch pad on a Crawler Transporter, as well as provide a launch platform at the pad. The ML will also provide the boundary condition for an upcoming SLS Integrated Modal Test (IMT). To help correlate the ML math models prior to this modal test, and allow focus to remain on updating SLS vehicle models during the IMT, a ML-only experimental modal test was performed in June 2019. Excitation of the tower and platform was provided by five uniquely-designed test fixtures, each enclosing a hydraulic shaker, capable of exerting thousands of pounds of force into the structure. For modes not that were not sufficiently excited by the test fixture shakers, a specially-designed mobile drop tower provided impact excitation at additional locations of interest. The response of the ML was measured with a total of 361 accelerometers. Following the random vibration, sine sweep vibration, and modal impact testing, frequency response functions were calculated and modes were extracted for three different configurations of the ML in 0 Hz to 12 Hz frequency range. This paper will provide a case study in performing modal tests on large structures by discussing the Mobile Launcher, the test strategy, an overview of the test results, and recommendations for meeting a tight test schedule for a large-scale modal test.
Hydraulic shakers↗
Health Monitoring of Composite Material Structures Using a Vibrometry Technique
Non-destructive evaluation (NDE) methods for quantifying and locating damage are essential for inspecting structures to ensure safety and reliability. Transmittance function monitoring is a potentially new NDE technique being tested as a tool to detect, quantify, and locate damage on flexible structures. The technique has a large spatial range that is practical for detecting damage on large composite material structures such as a reusable launch vehicle. The Transmittance Function (TF) theory is based on structural dynamics principles that define how vibration at one point in a structure is related to a force at another point. This relationship is called the Frequency Response Function (FRF). A Transmittance Function (TF) is derived as the ratio of FRFs, and can detect damage because the FRFs change due to damage. If one excitation is used for the testing, the force does not need to be measured to compute the TF. In the damage detection procedure, the structure is subjected to wide-band vibration and TFs are computed between different accelerometers to detect changes in the structure, presumably due to damage. In the first year of the project the TF method was tested on a bolted panel, a curved panel, and beams, all made of fiberglass. It was shown that damage could be detected using low frequency vibration, 250 to 1,250 Hz. The technique is sensitive to damage, but it requires storage of historical or pre-damage TFs for the healthy structure. This would become a large data storage requirement for large structures. Thus one objective for the second year of the project was to eliminate the need to store historical data. The second year report gives details of how storage of historical data was eliminated. Further results of testing panel structures are also given.
Schulz, Mark J.↗