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A review is presented of the NASA program of design analysis methods for vibrations (DAMVIBS) whose objective was to establish the technology base needed for developing an advanced FEM-based dynamics design capability for vibrations. New experimental/analytical studies have been performed to identify an airframe's components that require better representation in the finite element model for improved correlation with test results.
Helicopter airframe vibration is examined using calculation and measurements for the SA349/2 research helicopter. The hub loads, which transmit excitation to the fuselage, are predicted using a comprehensive rotorcraft analysis and correlated with measured hub loads. The predicted and measured hub loads are then coupled with finite element models representing the SA349/2 fuselage. The resulting vertical acceleration at the pilot seat is examined. Adjustments are made to the airframe structural models to examine the sensitivity of predicted vertical acceleration to the model. Changes of a few percent to the damping and frequency of specific modes lead to large reductions in predicted vibration and to major improvements in the correlations with measured pilot seat vertical acceleration.
Techniques for defining a finite element model (FEM) for analysis of nonlinear vibrations in beam structures subjected to harmonic excitation are presented. The resulting model covers longitudinal deformation and inertial effects. The nonlinear oscillations of a beam element under forced excitation are modeled by a harmonic force matrix based on first order approximations of the Jacobian elliptic forcing function. Harmonic force and nonlinear stiffness matrices are derived and the nonlinear forced responses of beams are calculated under various boundary conditions. The results of FEM computations for simply-supported and clamped beams show that midplane stretching caused by large deflections increases the nonlinearity. Axially-restrained beams experience only hardening nonlinearity, while axially-free beams have reduced nonlinearity in deformation and inertia and an increase in linearity due to large deflection.
An analysis of an idealized passive vibration-cancelling two-terminal mount with one degree of freedom at each mechanical terminal isolating a nonrigid machine from a nonrigid foundation is presented. To evaluate a vibration-cancelling (VC) mount, its effectiveness as a function of frequency is compared with the effectiveness of both conventional and compound mounts isolating a rigid machine from a nonrigid foundation. The comparisons indicate that a carefully designed and manufactured VC mount should provide substantially greater vibration reduction at its cancellation frequency than either a conventional or compound mount having the same low frequency stiffness, i.e., stiffness at the natural frequency of the machine mount system.
Applying distributed parameter concepts of propagation and reflection to dynamics and controls analysis of bending vibrations in flexible aerospace vehicles
The application of FEM modeling techniques to the analysis of torsional vibrations in complex rotating systems is described and demonstrated, summarizing results reported by Soares (1985). A substructuring approach is used for determination of torsional natural frequencies and resonant-mode shapes, steady-state frequency-sweep analysis, identification of dynamically unstable speed ranges, and characterization of transient linear and nonlinear systems. Results for several sample problems are presented in diagrams, graphs, and tables. STORV, a computer code based on this approach, is in use as a preliminary design tool for drive-train torsional analysis in the High Altitude Wind Tunnel at NASA Lewis.
Under a NASA research program designated DAMVIBS (Design Analysis Methods for VIBrationS), four U. S. helicopter industry participants (Bell Helicopter, Boeing Vertol, McDonnell Douglas Helicopter, and Sikorsky Aircraft) are to apply existing analytical methods for calculating coupled rotor-fuselage vibrations of the AH-1G helicopter for correlation with flight test data from an AH-1G Operational Load Survey (OLS) test program. Bell Helicopter, as the manufacturer of the AH-1G, was asked to provide pertinent rotor data and to collect the OLS flight vibration data needed to perform the correlations. The analytical representation of the fuselage structure is based on a NASTRAN finite element model (FEM) developed by Bell which has been extensively documented and correlated with ground vibration tests.The AH-1G FEM was provided to each of the participants for use in their coupled rotor-fuselage analyses. This report describes the AH-1G OLS flight test program and provides the flight conditions and measured vibration data to be used by each participant in their correlation effort. In addition, the mechanical, structural, inertial and aerodynamic data for the AH-1G two-bladed teetering main rotor system are presented. Furthermore, modifications to the NASTRAN FEM of the fuselage structure that are necessary to make it compatible with the OLS test article are described. The AH-1G OLS flight test data was found to be well documented and provide a sound basis for evaluating currently existing analysis methods used for calculation of coupled rotor-fuselage vibrations.
Under the NASA-sponsored Design Analysis Methods for Vibrations program, a series of ground vibration tests and NASTRAN finite element model correlations were conducted on the Bell AH-1G helicopter gunship to investigate the effects of difficult components on the vibration response of the airframe. Secondary structure and damping were found to have significant effects on the frequency response of the airframe above 15 Hz. The nonlinear effects of thrust stiffening and elastomeric mounts on the low-frequency pylon modes below the main rotor were also significant.
The initial detections of IR vibration-rotation bands in polyatomic molecular ions by recent spectroscopic advances were guided by ab initio prediction of vibrational frequencies. The present calculations predict the vibrational frequencies of additional ions which are candidates for laboratory analysis. Neutral molecule vibrational frequencies were computed at three levels of theory and then compared with experimental data; the effect of scaling was also investigated, in order to determine how accurately vibrational frequencies could be predicted. For 92 percent of the frequencies examined, the relatively simple HF/6-31G theory's vibrational frequencies were within 100/cm of experimental values, with a mean absolute error of 49/cm. On this basis, the frequencies of 30 molecular ions (many possessing astrophysical significance) were computed.
Several assertions are argued regarding mode analysis of structural vibration. The idea of a "mode' is, in essence, a mathematical one. It is highly unlikely that any real structure can vibrate exactly so that all its points move in unison; in other words, it is highly unlikely that any structure has any modes. As an approximation, however, the use of a mode is an excellent one for many structures, especially for the "lower modes'. The agreement between experiment and theory for the "higher modes' tends to become weaker. In this approximate sense, most structures have a very large number of modes. It is elementary to show, however, that no real structure has an infinite number of modes. The only utility of the "infinite modes' idea is within the purely mathematical domain. Many "error indices' can be defined as guidelines for structural modal order reduction. Simple modal truncation, although suggested by experience with slender rods, is naive. The proper process is mode selection, based on a appropriate error criterion.
A wind tunnel balance system was designed to determine the wind-induced vibrations of a space shuttle model. The balance utilizes a flexible sting mounting in conjunction with a geometrically scaled rigid model. Bending and torsional displacements are determined through strain-gauge-instrumented spring bar mechanisms. The natural frequency of the string-model system can be varied continuously throughout the expected scaled frequency range of the shuttle vehicle while a test is in progress by the use of moveable riders on the spring bar mechanism. Through the use of a frequency analyzer, the output can be used to determine troublesome vibrational frequencies. A dimensional analysis of the wind-induced vibration problem is also presented which suggests a test procedure. In addition a computer program for analytical studies of the forced vibration problem is presented.
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BACKGROUND: This study was conducted with the primary interest of providing data that would inform Vibration Isolation and Stabilization (VIS) system design and performance for the European Enhanced Exploration Exercise Device (E4D). In preparation for the International Space Station (ISS) in-flight demonstration, a list of critical Human Health Countermeasures (HHC) exercises was compiled [1]. The goal of this study was to assess the ground reaction forces and moments imposed by an exercising subject in each of the six VIS Degrees of Freedom (DOFs) during a comprehensive set of these critical exercises performed on the E4D. METHODS AND RESULTS: The ISS in-flight demonstration list of critical exercises included seated aerobic rowing, bent-over rowing, cycling, front squats, back squats, conventional deadlifts, Romanian deadlifts, heel raises, overhead presses, reverse chops, and power clean presses. At the NASA Johnson Space Center (JSC) Prototype Immersive Technology (PIT) laboratory, motion capture data were collected on critical E4D exercises for six subjects. At the NASA JSC Active Response Gravity Offload System (ARGOS) facility, additional motion capture and load cell data were collected on offloaded trials for four subjects. Select data were extrapolated to represent a 5th percentile female subject and a 95th percentile male subject. A previous investigation comparing the forces obtained from the load cell and from motion capture based data found a satisfactory level of agreement between the two measurements [2]. The motion capture based data were analyzed for this study since it is driven by the subject’s trajectory alone, automatically excluding any forces exerted on the subject by the ARGOS offloading harness. The OpenSim [3, 4] biomechanical simulation inverse kinematics tool was used to calculate the joint angles based on the locations of motion capture markers placed at key positions on the subject’s body. An OpenSim plugin was then used to obtain the forces and moments generated by the subject during each trial, with the moments computed relative to the equilibrium location of the subject’s feet [5]. The force of gravity was also removed to simulate the loads generated by the exercise when performed in microgravity. The load plots for each trial were generated and visually analyzed to obtain the magnitudes of the peak loads for each exercise in each DOF. The typical period of exercise for each trial was also estimated and used to calculate the frequency for each trial. The exercise loads data was then organized in multiple ways to capture different aspects of the data. As a result of this study, we present a summary of the load magnitudes observed during these critical exercises utilizing the E4D.
This presentation discusses fractured leads on field-programmable gate array (FPGA) during flight vibration. Actions taken to determine root cause and resolution of the failure include finite element analysis (FEA) and vibration testing and scanning electron microscopy (with X-ray microanalysis) and energy dispersive spectrometry (SEM/EDS) failure assessment. Bonding methods for surface mount parts is assessed, including critical analysis and assessment of random fatigue damage. Regarding ceramic quad flat pack (CQFP) lead fracture, after disassembling the attitude control electronics (ACE) configuration, photographs showed six leads cracked on FPGA RTSX72SU-1 CQ208B package located on the RWIC card. An identical package (FPGA RTSX32SU-1 CQ208B) mounted on the RWIC did not results in cracked pins due to vibration. FPGA lead failure theories include workmanship issues in the lead-forming, material defect in the leads of the FPGA packages, and the insecure mounting of the board in the card guides, among other theories. Studies were conducted using simple calculations to determine the response and fatigue life of the package. Shorter packages exhibited more response when loaded by out-of-plane displacement of PCB while taller packages exhibit more response when loaded by in-plane acceleration of PCB. Additionally, under-fill did not contribute to reducing stress in leads due to out-of-plane PCB loading or from component twisting, as much as corner bonding. The combination of corner bond and under-fill is best to address mechanical and thermal S/C environment. Test results of bonded parts showed reduced (dampened) amplitude and slightly shifted peaks at the un-bonded natural frequency and an additional response at the bonded frequency. Stress due to PCBB out-of-plane loading was decreased on in the corners when only a corner bond was used. Future work may address CQFP fatigue assessment, including the investigation of discrepancy in predicted fatigue damage, as well as comparing fatigue life and fatigue damage cycle ration computed using FEA and Miner's rule to results from a fatigue assessment software program.
Under the NASA-sponsored DAMVIBS (Design Analysis Methods for VIBrationS) program, a series of ground vibration tests and NASTRAN finite element model (FEM) correlations were conducted on the Bell AH-1G helicopter gunship to investigate the effects of difficult components on the vibration response of the airframe. Previous correlations of the AG-1G showed good agreement between NASTRAN and tests through 15 to 20 Hz, but poor agreement in the higher frequency range of 20 to 30 Hz. Thus, this effort emphasized the higher frequency airframe vibration response correlations and identified areas that need further R and T work. To conduct the investigations, selected difficult components (main rotor pylon, secondary structure, nonstructural doors/panels, landing gear, engine, furl, etc.) were systematically removed to quantify their effects on overall vibratory response of the airframe. The entire effort was planned and documented, and the results reviewed by NASA and industry experts in order to ensure scientific control of the testing, analysis, and correlation exercise. In particular, secondary structure and damping had significant effects on the frequency response of the airframe above 15 Hz. Also, the nonlinear effects of thrust stiffening and elastomer mounts were significant on the low frequency pylon modes below main rotor 1p (5.4 Hz). The results of the NASTRAN FEM correlations are given.
In the last progress report (Feb. 1988) some results were presented for a parametric analysis on the vibrational power flow between two coupled plate structures using the mobility power flow approach. The results reported then were for changes in the structural parameters of the two plates, but with the two plates identical in their structural characteristics. Herein, limitation is removed. The vibrational power input and output are evaluated for different values of the structural damping loss factor for the source and receiver plates. In performing this parametric analysis, the source plate characteristics are kept constant. The purpose of this parametric analysis is to determine the most critical parameters that influence the flow of vibrational power from the source plate to the receiver plate. In the case of the structural damping parametric analysis, the influence of changes in the source plate damping is also investigated. The results obtained from the mobility power flow approach are compared to results obtained using a statistical energy analysis (SEA) approach. The significance of the power flow results are discussed together with a discussion and a comparison between the SEA results and the mobility power flow results. Furthermore, the benefits derived from using the mobility power flow approach are examined.
The variational principle, differential equations, and boundary conditions considered appropriate to the analysis of transverse vibrations of hollow thin-walled cylindrical beams are shown. General solutions for the modes and frequencies of cantilever and free-free cylindrical beams of arbitrary cross section but of uniform thickness are given. The combined influence of the secondary effects of transverse shear deformation, shear lag, and secondary effects of transverse shear deformation, shear lag, and longitudinal inertia is shown in the form of curves for cylinders of rectangular cross section and uniform thickness. The contribution of each of the secondary effects to the total reduction in the actual frequency is also indicated. (author)
The space shuttle introduced a new dimension in the complexity of the structural dynamics of a space vehicle. The four-body configuration exhibited structural frequencies as low as 2 hertz with a model density on the order of 10 modes per hertz. In the verification process, certain mode shapes and frequencies were identified by the users as more important than others and, as such, the test objectives were oriented toward experimentally extracting those modes and frequencies for analysis and test correlation purposes. To provide the necessary experimental data, a series of ground vibration tests (GVT's) was conducted using test articles ranging from the 1/4-scale structural replica of the space shuttle to the full-scale vehicle. The vibration test and analysis program revealed that the mode shapes and frequency correlations below 10 hertz were good. The quality of correlation of modes between 10 and 20 hertz ranged from good to fair and that of modes above 20 hertz ranged from poor to good. Since the most important modes, based on user preference, were below 10 hertz, it was judged that the shuttle structural dynamic models were adequate for flight certifications.