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The advent of triaxial, piezoelectric force gages and the associated signal processing is a precursor to several dynamics testing innovations. This new technology is applicable to spacecraft programs that JPL manages. An application of force measurement is force limiting (when testing spacecraft in random vibration tests). Base-drive and acoustic modal testing is a potential application.
Pressure transducer is isolated from shock and vibration forces by a pressure-compensated shock mount. Silicone elastomer O-rings within the shock mount serve as shock and vibration-damping pads.
Limited data on extensional and flexural damping of small specimens of graphite/epoxy and unreinforced epoxy resin were obtained. Flexural damping was measured using a forced vibration technique based on resonant flexural vibration of shaker excited double cantilever specimens. Extensional damping was measured by subjecting similar specimens to low frequency sinusoidal oscillation in a servohydraulic tensile testing machine while plotting load versus extensional strain. Damping was found to vary slowly and continuously over the frequency range 0.01 - 1000 Hz, and no drastic transitions were observed. Composite damping was found to be less than neat resin damping. Comparison of small specimen damping values with assembled column damping values seems to indicate that, for those materials, material damping is more important than joint damping. The data reported was limited not by the test apparatus, but by signal conditioning and data acquisition. It is believed that filtering of the strain gage signals and the use of digital storage with slow playback will make it possible to extend the frequency and amplitude ranges significantly.
The current work presents an overview of the Viking 1975 environmental testing from an engineering standpoint. An extremely large vibration test fixture had to be designed, analyzed, and integrated into a test setup that employed hydrostatic bearings in a new fashion. A vibration control system was also required that would allow for thirty-six channels of sine-wave peak select control from acceleration, force-of-strain transducers. In addition, some 68 channels of peak limiting shutdown capability were needed for backup and monitoring of other data during the forced vibration test. Pretesting included analyses of the fixture design, overturning moment, control system capabilities, and response of the entire spacecraft/fixture/exciter system to the test environment. Closed-loop control for acoustic testing was a necessity due to the fact that the Viking spacecraft took up a major portion of the volume of the 10,000 cu ft chamber. The spacecraft emerged from testing undamaged.
The paper deals with finite actuators. A nonspinning three-axis stabilized space vehicle having a two-dimensional large structure and a rigid body at the center is chosen for analysis. The torquers acting on the vehicle are modeled as antisymmetric forces distributed in a small but finite area. In the limit they represent point torquers which also are treated as a special case of surface distribution of dipoles. Ordinary and partial differential equations governing the forced vibrations of the vehicle are derived by using Hamilton's principle. Associated modal inputs are obtained for both the distributed moments and the distributed forces. It is shown that the finite torquers excite the higher modes less than the point torquers. Modal cost analysis proves to be a suitable methodology to this end.
Equations of axisymmetric vibrational forces on liquid-filled thin-walled cylindrical shells
Report describes study of vibration-damping properties, in air and vacuum, of graphite/epoxy composite structural members joined by adhesives. Determines vibration-damping effects of specimens representative of members and joints of truss, particularly after gases and moisture trapped during manufacture released in vacuum. Damping ratios measured under free and forced vibrations and before and after outgassing in vacuum. Effects of end-support conditions and high and low temperatures on damping also measured.
An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.
An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler-Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.
An overview of the methods and concepts developed to enhance and predict structural dynamic characteristics of advanced aeropropulsion systems is presented. Aeroelasticity, vibration control, dynamic systems, and computational structural methods are four disciplines that make up the structural dynamic effort at LeRC. The aeroelasticity program develops analytical and experimental methods for minimizing flutter and forced vibration of aerospace propulsion systems. Both frequency domain and time domain methods were developed for applications on the turbofan, turbopump, and advanced turboprop. In order to improve life and performance, the vibration control program conceives, analyzes, develops, and demonstrates new methods for controlling vibrations in aerospace systems. Active and passive vibration control is accomplished with electromagnetic dampers, magnetic bearings, and piezoelectric crystals to control rotor vibrations. The dynamic systems program analyzes and verifies the dynamics of interacting systems, as well as develops concepts and methods for high-temperature dynamic seals. Work in this field involves the analysis and parametric identification of large, nonlinear, damped, stochastic systems. The computational structural methods program exploits modern computer science as an aid to the solutions of structural problems.
A flexural vibration test and associated equipment were developed to accurately measure the low strain dynamic modulus and damping of composite materials from -200 C to over 500 C. The basic test method involves the forced vibration of composite bars at their resonant free-free flexural modes in a high vacuum cryostat furnace. The accuracy of these expressions and the flexural test was verified by dynamic moduli and damping capacity measurements on 50 fiber volume percent boron/aluminum (B/Al) composites vibrating near 2000 Hz. The phase results were summarized to permit predictions of the B/Al dynamic behavior as a function of frequency, temperature, and fiber volume fraction.
An overview is given of the methods and concepts developed to enhance and predict structural dynamic characteristics of advanced aeropropulsion systems. Aeroelasticity, Vibration Control, Dynamic Systems, and Computational Structural Methods are four disciplines that make up the research program at NASA/Lewis Research Center. The Aeroelasticity program develops analytical and experimental methods to minimize flutter and forced vibration of aerospace propulsion systems. Both frequency domain and time domain methods have been developed for applications on the turbofan, turbopump, and advanced turboprop. To improve life and performance, the Vibration Control program conceives, analyzes, develops, and demonstrates new methods to control vibrations in aerospace systems. Active and passive vibration control is accomplished with electromagnetic dampers, magnetic bearings, and piezoelectric crystals to control rotor vibrations. The Dynamic Systems program analyzes and verifies the dynamics of interacting systems, as well as develops concepts and methods for high-temperature dynamic seals. The Computational Structural Methods program uses computer science to improve solutions of structural problems.
High performance aircraft-engine fan and compressor blades are vulnerable to aerodynamically forced vibrations generated by inlet flow distortions due to wakes from upstream blade and vane rows, atmospheric gusts, and maldistributions in inlet ducts. In this report, an analysis is developed to predict the flow-induced forced response of an aerodynamically detuned rotor operating in a supersonic flow with a subsonic axial component. The aerodynamic detuning is achieved by alternating the circumferential spacing of adjacent rotor blades. The total unsteady aerodynamic loading acting on the blading, as a result of the convection of the transverse gust past the airfoil cascade and the resulting motion of the cascade, is developed in terms of influence coefficients. This analysis is used to investigate the effect of aerodynamic detuning on the forced response of a 12-blade rotor, with Verdon's Cascade B flow geometry as a uniformly spaced baseline configuration. The results of this study indicate that, for forward traveling wave gust excitations, aerodynamic detuning is very beneficial, resulting in significantly decreased maximum-amplitude blade responses for many interblade phase angles.
The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided.
Vibration of germinating wheat seedlings at the levels experienced during the launch of the NASA Biosatellite II increases the frequency of developmental arrest in seedling organs. Severe vibrations lasted approximately 30 sec in two stages. Power spectral density was greatest at frequencies around 15-16 and 19-22 Hz on the entire vehicle. Vibration forces reaching the affected parts of individual seedlings could not be measured. One or more seedling organs may be expected to be absent in 11% of selected Earth-grown wheat plants. If subjected to simulated launch vibration between 12 and 27 hr after the start of germination, the number of abnormal plants rises to 21.6%. Lateral roots are most affected by vibration at this age. Seedlings which went into orbital weightlessness aboard Biosatellite II, or were grown for several days on a horizontal clinostat after vibration, showed only 5.3% abnormalities. Simulated weightlessness on the clinostat without prior vibration did not alter the number of abnormal plants. It is suggested that growth in weightlessness following exposure to vibration permits more extensive repair of injury produced by vibration than does growth in Earth's gravity.
Under driving conditions, a typical geared system may be subjected to large dynamic loads. Also, the vibration level of the geared system is directly related to the noise radiated from the gear box. The steady state dynamic behavior of the system is examined in order to design reliable and quiet transmissions. The scope is limited to a system containing a spur gear pair with backlash and periodically time varying mesh stiffness, and rolling element bearings with clearance type nonlinearities. The internal static transmission error at the gear mesh, which is of importance from high frequency noise and vibration control view point, is considered in the formulation in sinusoidal or periodic form. A dynamic finite element model of the linear time invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and forced vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solutions with the finite element model results. Using the reduced order formulations, a three degree of freedom dynamic model is developed which includes nonlinearities associated with radical clearances in the radial rolling element bearings, backlash between a spur gear pair and periodically varying gear mesh stiffness. As a limiting case, a single degree of freedom model of the spur gear pair with backlash is considered and mathematical conditions for tooth separation and back collision are defined. Both digital simulation technique and analytical models such as method of harmonic balance and the method of multiple scales were used to develop the steady state frequency response characteristics for various nonlinear and/or time varying cases.
Resonant vibrations of aircraft engine blades cause blade fatigue problems in engines, which can lead to thicker and aerodynamically lower performing blade designs, increasing engine weight, fuel burn, and maintenance costs. In order to mitigate undesirable blade vibration levels, active piezoelectric vibration control has been investigated, potentially enabling thinner blade designs for higher performing blades and minimizing blade fatigue problems. While the piezoelectric damping idea has been investigated by other researchers over the years, very little study has been done including rotational effects. The present study attempts to fill this void. The particular objectives of this study were: (a) to develop and analyze a multiphysics piezoelectric finite element composite blade model for harmonic forced vibration response analysis coupled with a tuned RLC circuit for rotating engine blade conditions, (b) to validate a numerical model with experimental test data, and (c) to achieve a cost-effective numerical modeling capability which enables simulation of rotating blades within the NASA Glenn Research Center (GRC) Dynamic Spin Rig Facility. A numerical and experimental study for rotating piezoelectric composite subscale fan blades was performed. It was also proved that the proposed numerical method is feasible and effective when applied to the rotating blade base excitation model. The experimental test and multiphysics finite element modeling technique described in this paper show that piezoelectric vibration damping can significantly reduce vibrations of aircraft engine composite fan blades.
The performance of potential passive damping concepts is investigted for a long tubular aluminum alloy member, and a two-bar grillage structure. The members are restrained partially at the ends and are of the type being considered by NASA for possible use in the construction of a future space station. Four different passive damping concepts are studied and include nylon brush, wool swab, copper brush, and silly putty in chamber dampers. Both free and forced vibration tests are conducted. It is found that the silly putty in chamber damper concept provides considerably greater passive damping as compared to that of the other three concepts. For the grillage natural vibration, a five wool swab damper configuration provides greater damping than the five silly putty dampers in chamber configuration. Due to the constrained motion imposed by the vibrator used in the tests, the effectiveness of the passive dampers could not be adequately evaluated for the individual member. However, it is found that for the grillage under forced vibration, the five silly putty dampers in chamber damper configuration provides very effective passive damping although only at and around the resonant frequency. At resonance, these dampers provide a 51 percent reduction in the dynamic magnification factor for this case.