Randy L. Mayes

Experimental Investigation of Fluid-Structure Interactions in Compressible Cavity Flows

Experiments were performed to understand the complex fluid-structure interactions that occur during internal store carriage. A cylindrical store was installed in a cavity having a length-to-depth ratio of 3.33 and a length-to-width ratio of 1. The Mach number ranged from 0.6 – 2.5 and the incoming turbulent boundary layer thickness was about 30-40% of the cavity depth. Fast-response pressure measurements provided aeroacoustic loading in the cavity, while triaxial accelerometers and laser Doppler vibrometry provided simultaneous store response. Despite occupying only 6% of the cavity volume, the store significantly altered the cavity acoustics. The store responded to the cavity flow at its natural structural frequencies, as previously determined with modal hammer tests, and it exhibited a directional dependence to cavity resonance. Specifically, cavity tones excited the store in the streamwise and wall-normal directions consistently, while a spanwise response was observed only occasionally. The streamwise and wall-normal responses were attributed to the known pressure gradients in these directions. Furthermore, spanwise vibrations were greater at the downstream end of the cavity, attributable to decreased levels of flow coherence near the aftwall. Collectively, the data indicate the store response to be dependent on direction of vibration and position along the length of the store.

Health monitoring of operational structures -- Initial results

Two techniques for damage localization (Structural Translational and Rotational Error Checking -- STRECH and MAtriX COmpletioN -- MAXCON) are described and applied to operational structures. The structures include a Horizontal Axis Wind Turbine (HAWT) blade undergoing a fatigue test and a highway bridge undergoing an induced damage test. STRECH is seen to provide a global damage indicator to assess the global damage state of a structure. STRECH is also seen to provide damage localization for static flexibility shapes or the first mode of simple structures. MAXCON is a robust damage localization tool using the higher order dynamics of a structure. Several options arc available to allow the procedure to be tailored to a variety of structures.

Converting a Driven Base Vibration Test to a Fixed Base Modal Analysis

Qualification vibration tests are routinely performed on prototype hardware. Model validation cannot generally be done from the qualification vibration test because of multiple uncertainties, particularly the uncertainty of the boundary condition. These uncertainties can have a dramatic effect on the modal parameters extracted from the data. It would be valuable if one could extract a modal model of the test article with a known boundary condition from the qualification vibration test. This work addresses an attempt to extract fixed base modes on a 1.2 meter tall test article in a random vibration test on a 1.07 meter long slip table. The slip table was supported by an oil film on a granite block and driven by a 111,000 Newton shaker, hereinafter denoted as the big shaker. This approach requires obtaining dominant characteristic shapes of the bare table. A vibration test on the full system is performed. The characteristic table generalized coordinates are constrained to zero to obtain fixed base results. Results determined the first three fixed base bending mode frequencies excited by the shaker within four percent. A stick-slip nonlinearity in the shaker system had a negative effect on the final damping ratios producing large errors. An alternative approach to extracting the modal parameters directly from transmissibilities proved to be more accurate. Even after accounting for distortion due to the Hann window, it appears that dissipation physics in the bare shaker table provide additional damping beyond the true fixed base damping.

Experimental Based Substructuring Using a Craig-Bampton Transmission Simulator Model

Recently, a new experimental based substructure formulation was introduced which reduces ill-conditioning due to experimental measurement noise by imposing the connection constraints on substructure modal coordinates instead of the physical interface coordinates. The experimental substructure is tested in a free-free configuration, and the interface is exercised by attaching a flexible transmission simulator. An analytical representation of the fixture is then used to subtract its effects from the experimental substructure. The resulting experimental component is entirely modal based, and can be attached in an indirect manner to other substructures by constraining the modal degrees of freedom of the transmission simulator to those substructures. This work explores a different alternative in which the transmission simulator is modeled with a Craig-Bampton model, a model that may be more appropriate when the interfaces are connected rigidly. The new method is compared to the authors’ previous approaches to evaluate the errors due to modal truncation using finite element models of several beam systems including one in which the transmission simulator is connected to the component of interest at two points, potentially producing an ill-conditioned inverse problem.

Formulation of a Craig-Bampton Experimental Substructure Using a Transmission Simulator

Recently, a new experimental based substructure formulation was introduced, called Modal Constraint for Fixture and Subsystem (MCFS). This method reduces ill-conditioning by imposing constraints on substructure modal coordinates instead of the physical interface coordinates. The experimental substructure is tested in a free-free configuration, and the interface is exercised by attaching a flexible transmission simulator. An analytical representation of the fixture is then used to subtract its effects from the experimental substructure. The resulting experimental component is entirely modal based, and can be attached in an indirect manner to other substructures using MCFS. In contrast, this work presents a formulation in which the analytical representation of the transmission simulator is in the form of a Craig-Bampton (CB) substructure including fixed-interface modal coordinates and physical interface coordinates. The negative of the analytical representation of the transmission simulator is constrained to the experimental modal model using MCFS by eliminating the fixed-interface modal coordinates. The resulting experimental substructure contains a hybrid set of coordinates, including modal coordinates and the physical interface degrees of freedom, analogous to a CB representation. This new formulation offers the improved conditioning of the MCFS approach, but can be directly connected through the physical interface coordinates to other finite element based substructures.

Excitation Methods for a 60 kW Vertical Axis Wind Turbine

A simple modal test to determine the first tower bending mode of a 60 kW (82 feet tall) vertical axis wind turbine was performed. The minimal response instrumentation included accelerometers mounted only at easily accessible locations part way up the tower and strain gages near the tower base. The turbine was excited in the parked condition with step relaxation, random human excitation, and wind excitation. The resulting modal parameters from the various excitation methods are compared.

Examples of Hybrid Dynamic Models Combining Experimental and Finite Element Substructures

Substructuring methods have been used for many years to reduce the size of FE dynamic models and maintain satisfactory response for a limited bandwidth of interest. However, experimental substructures have been used only in a very limited number of cases, generally where there was only a single connection point idealized to six connection degrees of freedom. This is because it is difficult to experimentally characterize the moments and rotations at multiple connection points. Mayes and Allen developed a method to practically characterize continuity and equilibrium at multiple connection points through the instrumentation of a flexible fixture. The instrumented fixture is transformed into a force and response sensor that is expressed in terms of the modal connection forces and modal connection responses of the fixture. The sensor is called the transmission simulator. Two previous results of the method for coupling R&D pieces of hardware are given. The primary emphasis of this paper is on a set of representative system hardware, for which two designs of a transmission simulator are compared with the view to discover design characteristics that optimize the sensor effectiveness. Frequency response functions (FRF) from the assembled system hardware are measured and designated as the truth against which to compare. The accuracy of the experimental substructure is evaluated by attaching it to a finite element substructure and predicting full system response FRFs which are compared against the truth FRFs. The result is that the transmission simulator design is relatively robust to the stiffness chosen, although the stiff transmission simulator appears to be a slightly better choice in the structure evaluated in this work. Substructure modes tend to maintain the shapes of the bare transmission simulator if it is stiff. A one piece transmission simulator design with no joints is easier to model accurately, which is of value in this methodology.

Experimental Modal Substructuring with Nonlinear Modal Iwan Models to Capture Nonlinear Subcomponent Damping

This work proposes a means whereby weak nonlinearity in a substructure, as typically arises due to friction in bolted interfaces, can be captured experimentally on a mode-by-mode basis and then used to predict the nonlinear response of an assembly. The method relies on the fact that the modes of a weakly nonlinear structure tend to remain uncoupled so long as their natural frequencies are distinct and higher harmonics generated by the nonlinearity do not produce significant response in other modes. Recent experiments on industrial hardware with bolted joints has shown that this type of model can be quite effective, and that a single degree-of-freedom (DOF) system with an Iwan joint, which is known as a modal Iwan model, effectively captures the way in which the stiffness and damping depend on amplitude. Once the modal Iwan models have been identified for each mode of the subcomponent(s) of interest, they can be assembled using standard techniques and used with a numerical integration routine to compute the nonlinear transient response of the assembled structure. The proposed methods are demonstrated by coupling a modal model of a 3DOF system with three discrete Iwan joints to a linear model for a 2DOF system.

Efficient Method of Measuring Effective Mass of a System

Effective mass is a system property that is used in the aerospace industry in predicting the forces of an elastic payload on the delivery system in a specific direction. Effective mass is usually calculated with the finite element model. Experimental effective mass can be used to validate calculated effective mass from a finite element model. Measuring the effective mass of a system, however, has been difficult and has been attempted by putting force sensors between the payload and a test base. A much more tractable method amenable to a payload mounted on a slip table is provided here. The method measures a driving point and a base frequency response function and uses a recently developed method to constrain the base response and calculate the effective mass. This theory will be demonstrated with an analytical system and example hardware.

A Color-Coded Complex Mode Indicator Function for Selecting a Final Mode Set

Many test articles exhibit slight nonlinearities which result in natural frequencies shifting between data from different references. This shifting can confound mode fitting algorithms because a single mode can appear as multiple modes when the data from multiple references are combined in a single data set. For this reason, modal test engineers at Sandia National Laboratories often fit data from each reference separately. However, this creates complexity when selecting a final set of modes, because a given mode may be fit from a number of reference data sets. The color-coded complex mode indicator function was developed as a tool that could be used to reduce a complex data set into a manageable figure that displays the number of modes in a given frequency range and also the reference that best excites the mode. The tool is wrapped in a graphical user interface that allows the test engineer to easily iterate on the selected set of modes, visualize the MAC matrix, quickly resynthesize data to check fits, and export the modes to a report-ready table. This tool has proven valuable, and has been used on very complex modal tests with hundreds of response channels and a handful of reference locations.