The time-average power flow between two linearly coupled oscillators excited by independent white-noise sources is shown to be proportional to the difference in the time-average energies of the oscillators. This proportionality is independent of the strength of the coupling if the oscillator energies are correctly defined. Power balance and energy sharing in the two oscillator systems are investigated, and the power-flow energydifference proportionality relation is extended to a group of N linear oscillators, all with the same natural frequencies and damping ratios and each coupled to all the others by identical springs and masses. The coupled-oscillator results are applied to a simple coupled-beam example, in which two almost identical Bernoulli-Euler beams are lightly coupled together by stiffness terms. Experimental measurements for this system provide verification of the power-flow equations provided that the coupling loss factor be correctly computed.
A randomly excited single-degree-of-freedom oscillator in which an idealized form of plastic deformation can take place is studied. Through the use of an artificial process, statistics of this nonlinear, hysteretic system are deduced from linear system-response statistics in two rdgimes of operation. The expected accumulated plastic deformation is found as a function of time and some other statistics derivable from the artificial process are indicated. A numerical example is given that illustrates the use of the method with low-cycle fatigue data.
The transmission of vibrational energy in a planar, three-element plate/beam/plate structure is analyzed. Theoretical predictions of average energy (or acceleration) ratios in frequency bands are developed, using concepts of energy flow in multimodal systems that have been described previously. Interstructure coupling parameters are calculated for torsional and flexural motions of the central connecting member (beam), and the energy transfer contributed by each type of motion is also calculated. It is found that the energy transfer is dominated by beam flexure in the lower-frequency bands, but torsional motion contributes significantly at the higher frequencies. Experimental analysis of a model of the structure is consistent with the theoretical predictions.
The flow of high-frequency vibratory energy to a shroud-enclosed spacecraft is discussed. Two paths of energy flow are considered: first, the acoustical path along which energy flows from the external exciting field through the shroud and interior acoustic space to the spacecraft; and, second, the mechanical path along which energy flows from the external field through the shroud and spacecraft mounting trusses to the spacecraft. Theoretically predicted response levels in octave frequency bands for a model of the OGO spacecraft assembly are presented. These predictions show that the spacecraft response to energy transmitted along the acoustic path is at least a factor of 10 greater than the response due to energy transmitted along the mechanical path over the frequency range 250–8000 Hz. Methods to reduce the spacecraft response are discussed. [Research supported by National Aeronautics and Space Administration.]
Due to its simplicity, the valveless pulsejet may be an ideal low cost propulsion system. In this paper, a new acoustic model is described, which can accurately predict the operating frequency of a valveless pulsejet. Experimental and computational methods were used to investigate how the inlet and exhaust area and the freestream velocity affect the overall performance of a 50cm pulsejet. Pressure and temperature were measured at several axial locations for different fuel flow rates and different geometries. Computer simulations were performed for exactly the same geometries and fuel flow rates using a commercial CFD package (CFX) to develop further understanding of the factors that affect the performance of a valveless pulsejet. An acoustic model was developed to predict the frequency of these valveless pulsejets. The new model treats the valveless pulsejet engine as a combination of a Helmholtz resonator and a wave tube. This new model was shown to accurately predict geometries for maximum thrust. The model was further extended to account for the effect of freestream velocity. Evidence is provided that valveless pulsejet generates the highest thrust when the inherent inlet frequency matches the inherent exhaust frequency.
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