Analytical Methods in Vibrations

This paper is an update of an earlier paper by Ibrahim (1987) and is aimed at reviewing the papers published during the last decade in the area of vibration of structures with parameter uncertainties Analytical, computational, and experimental studies conducted on probabilistic modeling of structural uncertainties and free and forced vibration of stochastically defined systems are discussed The review also covers developments in the areas of statistical modeling of high frequency vibrations and behavior of statistically disordered periodic systems

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Progress in structural dynamics with stochastic parameter variations: 1987-1998

The increasing demand for higher performance in rocketlaunchers promotes the development of nozzles with higherperformance, which basically is achieved by increasing theexpansion ratio. However, th ...

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Supersonic Flow Separation with Application to Rocket Engine Nozzles

The operation of rocket engines in the overexpanded mode, that is, with the ambient pressure considerably higher than the nozzle exit wall pressure, can result in dangerous lateral loads acting on the nozzle. These loads occur as the boundary layer separates from the nozzle wall and the pressure distribution deviates from its usual axisymmetric shape. Different aerodynamic or even coupled aerodynamic/structural mechanic reasons can cause an asymmetric pressure distribution. A number of subscale tests have been performed, and three potential origins of side loads were observed and investigated, namely, the pressure fluctuations in the separation and recirculation zone due to the unsteadiness of the separation location, the transition of separation pattern between free-shock separation and restricted-shock separation, and aeroelastic coupling, which indeed cannot cause but do amply existing side loads to significant levels. All three mechanisms are described in detail, and methods are presented to calculate their magnitude and pressure ratio at which they occur.

Side-Load Phenomena in Highly Overexpanded Rocket Nozzles

A detailed knowledge of the flow structure interaction in supersonic flows is important for the design of future space transportation systems. Therefore this work was devoted to the investigation of the shock wave boundary layer interaction on an elastic panel. During the wind tunnel experiments the panel deflection was measured with fast non-intrusive displacement sensors. On the flow side pressure, high-speed Schlieren photography and oil-film technique were used. The flow manipulation due to the panel deflection becomes manifest in a deformation of the impinging shock and the separation zone. The panel deflection consists of a constant and a dynamic component. The experimental results are discussed and compared to numerical results.

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Shock induced fluid structure interaction on a flexible wall in supersonic turbulent flow

Surveys of both the static and dynamic wall pressure signatures on the interior surface of a sub-scale, cold-flow and thrust optimized parabolic nozzle are conducted during fixed nozzle pressure ratios corresponding to FSS and RSS states. The motive is to develop a better understanding for the sources of off-axis loads during the transient start-up of overexpanded rocket nozzles. During FSS state, pressure spectra reveal frequency content resembling SWTBLI. Presumably, when the internal flow is in RSS state, separation bubbles are trapped by shocks and expansion waves; interactions between the separated flow regions and the waves produce asymmetric pressure distributions. An analysis of the azimuthal modes reveals how the breathing mode encompasses most of the resolved energy and that the side load inducing mode is coherent with the response moment measured by strain gauges mounted upstream of the nozzle on a flexible tube. Finally, the unsteady pressure is locally more energetic during RSS, albeit direct measurements of the response moments indicate higher side load activity when in FSS state. It is postulated that these discrepancies are attributed to cancellation effects between annular separation bubbles.

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Wall Pressure Unsteadiness and Side Loads in Overexpanded Rocket Nozzles

Two cold flow subscale nozzles were tested for side load characteristics during simulated nozzle start transients. The two test article contours were a truncated ideal and a parabolic. The current paper is an extension of a 2009 AIAA JPC paper on the test results for the same two nozzle test articles. The side load moments were measured with the strain tube approach in MSFC s Nozzle Test Facility. The processing techniques implemented to convert the strain gage signals into side load moment data are explained. Nozzle wall pressure profiles for separated nozzle flow at many NPRs are presented and discussed in detail. The effect of the test cell diffuser inlet on the parabolic nozzle s wall pressure profiles for separated flow is shown. The maximum measured side load moments for the two contours are compared. The truncated ideal contour s peak side load moment was 45% of that of the parabolic contour. The calculated side load moments, via mean-plus-three-standard-deviations at each nozzle pressure ratio, reproduced the characteristics and absolute values of measured maximums for both contours. The effect of facility vibration on the measured side load moments is quantified and the effect on uncertainty is calculated. The nozzle contour designs are discussed and the impact of a minor fabrication flaw in the nozzle contours is explained.

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Details of Side Load Test Data and Analysis for a Truncated Ideal Contour Nozzle and a Parabolic Contour Nozzle

During ground-tests of most production rocket engines over the last 30 years, large asymmetric transient side loads coming from the nozzle and related steady-state vibrational loads within the nozzle have been measured. The widely varying magnitude of these loads has been large enough to fail interfacing components as well as nozzles in these engines. This paper will discuss a comprehensive test and analysis program that has been undertaken to develop a methodology to accurately predict the character and magnitude of this loading. The project to-date has incorporated analytical modeling of both the fluid flow and the nozzle structure and testing of both full-scale and sub-scale rocket nodes. Examination of the test data indicates that one of the two-nodal diameter structural modes may be interacting with flow separation from the nozzle inside-wall in a self-excited or aeroelastic vibration phenomenon. If verified, this observation will be used to develop a methodology for design and analysis. A fuller understanding of the characteristics of this vibration will provide an increase in the accuracy and confidence of side load predictions, which will be critical for the successful construction of the next generation of low-cost, reliable rocket engines.

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Characterization of Side Load Phenomena Using Measurement of Fluid/Structure Interaction

A unique high temperature modal test and model correlation/update program has been performed on the composite nozzle of the FASTRAC engine for the NASA X-34 Reusable Launch Vehicle. The program was required to provide an accurate high temperature model of the nozzle for incorporation into the engine system structural dynamics model for loads calculation; this model is significantly different from the ambient case due to the large decrease in composite stiffness properties due to heating. The high-temperature modal test was performed during a hot-fire test of the nozzle. Previously, a series of high fidelity modal tests and finite element model correlation of the nozzle in a free-free configuration had been performed. This model was then attached to a modal-test verified model of the engine hot-fire test stand and the ambient system mode shapes were identified. A reduced set of accelerometers was then attached to the nozzle, the engine fired full-duration, and the frequency peaks corresponding to the ambient nozzle modes individually isolated and tracked as they decreased during the test. To update the finite-element model of the nozzle to these frequency curves, the percentage differences of the anisotropic composite moduli due to temperature variation from ambient, which had been used in the initial modeling and which were obtained by small sample coupon testing, were multiplied by an iteratively determined constant factor. These new properties were used to create high-temperature nozzle models corresponding to 10 second engine operation increments and tied into the engine system model for loads determination.

https://ntrs.nasa.gov/api/citations/20020016609/downloads/20020016609.pdf

Temperature Dependent Modal Test/Analysis Correlation of X-34 Fastrac Composite Rocket Nozzle

Realistic estimates of nozzle side loads, the off-axis forces that develop during engine start and shutdown, are important in the design cycle of a rocket engine. The estimated magnitude of the nozzle side loads has a large impact on the design of the nozzle shell and the engine s thrust vector control system. In 2004 Marshall Space Flight Center (MSFC) began developing a capability to quantify the relative magnitude of side loads caused by different types of nozzle contours. The MSFC Nozzle Test Facility was modified to measure nozzle side loads during simulated nozzle start. Side load results from cold flow tests on two nozzle test articles, one with a truncated ideal contour and one with a parabolic contour are provided. The experimental approach, nozzle contour designs and wall static pressures are also discussed

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Andrew M. Brown

Papers

Wall Pressure Unsteadiness and Side Loads in Overexpanded Rocket Nozzles

Details of Side Load Test Data and Analysis for a Truncated Ideal Contour Nozzle and a Parabolic Contour Nozzle

Characterization of Side Load Phenomena Using Measurement of Fluid/Structure Interaction

Temperature Dependent Modal Test/Analysis Correlation of X-34 Fastrac Composite Rocket Nozzle

Nozzle Side Load Testing and Analysis at Marshall Space Flight Center