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Shaker-structure interaction modeling and analysis for nonlinear force appropriation testing

Nonlinear force appropriation is an extension of its linear counterpart where sinusoidal excitation is applied to a structure with a modal shaker and phase quadrature is achieved between the excitation and response. While a standard practice in modal testing, modal shaker excitation has the potential to alter the dynamics of the structure under test. Previous studies have been conducted to address several concerns, but this work specifically focuses on a shaker-structure interaction phenomenon which arises during the force appropriation testing of a nonlinear structure. Under pure-tone sinusoidal forcing, a nonlinear structure may respond not only at the fundamental harmonic but also potentially at sub- or superharmonics, or it can even produce aperiodic and chaotic motion in certain cases. Shaker-structure interaction occurs when the response physically pushes back against the shaker attachment, producing non-fundamental harmonic content in the force measured by the load cell, even for pure tone voltage input to the shaker. This work develops a model to replicate these physics and investigates their influence on the response of a nonlinear normal mode of the structure. Experimental evidence is first provided that demonstrates the generation of harmonic content in the measured load cell force during a force appropriation test. This interaction is replicated by developing an electromechanical model of a modal shaker attached to a nonlinear, three-mass dynamical system. Several simulated experiments are conducted both with and without the shaker model in order to identify which effects are specifically due to the presence of the shaker. Finally, the results of these simulations are then compared to the undamped nonlinear normal modes of the structure under test to evaluate the influence of shaker-structure interaction on the identified system’s dynamics.

42 ENGINEERING↗

Vibration Response Models of a Stiffened Aluminum Plate Excited by a Shaker

Numerical models of structural-acoustic interactions are of interest to aircraft designers and the space program. This paper describes a comparison between two energy finite element codes, a statistical energy analysis code, a structural finite element code, and the experimentally measured response of a stiffened aluminum plate excited by a shaker. Different methods for modeling the stiffeners and the power input from the shaker are discussed. The results show that the energy codes (energy finite element and statistical energy analysis) accurately predicted the measured mean square velocity of the plate. In addition, predictions from an energy finite element code had the best spatial correlation with measured velocities. However, predictions from a considerably simpler, single subsystem, statistical energy analysis model also correlated well with the spatial velocity distribution. The results highlight a need for further work to understand the relationship between modeling assumptions and the prediction results.

Cabell, Randolph H.↗

Virtual Shaker Testing: Simulation Technology Improves Vibration Test Performance

In the field of vibration testing, the interaction between the structure being tested and the instrumentation hardware used to perform the test is a critical issue. This is particularly true when testing massive structures (e.g. satellites), because due to physical design and manufacturing limits, the dynamics of the testing facility often couples with the test specimen one in the frequency range of interest. A further issue in this field is the standard use of a closed loop real-time vibration control scheme, which could potentially shift poles and change damping of the aforementioned coupled system. Virtual shaker testing is a novel approach to deal with these issues. It means performing a simulation which closely represents the real vibration test on the specific facility by taking into account all parameters which might impact the dynamic behavior of the specimen. In this paper, such a virtual shaker testing approach is developed. It consists of the following components: (1) Either a physical-based or an equation-based coupled electro-mechanical lumped parameter shaker model is created. The model parameters are obtained from manufacturer's specifications or by carrying out some dedicated experiments; (2) Existing real-time vibration control algorithm are ported to the virtual simulation environment; and (3) A structural model of the test object is created and after defining proper interface conditions structural modes are computed by means of the well-established Craig-Bampton CMS technique. At this stage, a virtual shaker test has been run, by coupling the three described models (shaker, control loop, structure) in a co-simulation routine. Numerical results have eventually been correlated with experimental ones in order to assess the robustness of the proposed methodology.

Ricci, Stefano↗

Unsteady environments and responses of the shuttle combined loads orbiter test

Both separate and combined wind tunnel and vibration shaker tests were conducted on two structural panels representative of the Shuttle orbiter in the NASA LaRC 8-foot transonic pressure tunnel (TPT) to determine the effects of combined loads on the thermal protection system (TPS). The primary objective of this test was to provide a combined full-scale load environment and realistic time history of the dynamic pressures, Mach numbers (through transonic), and dynamic structural responses of these panels. The panels were selected from orbiter locations where interactive load sources such as aerodynamic shock waves, turbulent boundary layers, strut-induced vorticity, and substrate deformation combined to provide high bonding loads between the TPS and the orbiter structure. The test panels for this program were highly instrumented with static and dynamic pressure gages, accelerometers, deflectometers, strain gages, Schileren and high-speed photography, and special instrumentation necessary to determine TPS/structure interface loads and tile motions. Two test specimens of each orbiter panel were utilized. Both were high-fidelity representations of the selected orbiter location. The first panel (calibration panel) for each test was utilized to calibrate the tunnel and shaker system as well as provide a data-gathering source for applied static and dynamic loads. The second panel (test panel) for each test was subjected to flight time exposures only so that TPS characteristics as a function of flight mission exposure could be determined. These tests were the last in a series that was suce6ssfully completed and necessary to certify the TPS prior to the first launching of the Shuttle.

P. H. Schuetz↗

Aircraft interior noise prediction using a structural-acoustic analogy in NASTRAN modal synthesis

The noise induced inside a cylindrical fuselage model by shaker excitation is investigated theoretically and experimentally. The NASTRAN modal-synthesis program is used in the theoretical analysis, and the predictions are compared with experimental measurements in extensive graphs. Good general agreement is obtained, but the need for further refinements to account for acoustic-cavity damping and structural-acoustic interaction is indicated.

Grosveld, Ferdinand W.↗

State-space formulation of multi-shaker modal analysis

As modal testing techniques have improved in recent years, the demands placed on the accuracy of modal test results have increased. This paper describes a new multi-input, multi-output modal parameter estimation algorithm suitable for the identification of reduced-order models of structures. The method described is a frequency-domain method based on excitation and response spectra. The principal features of the algorithm are: (1) applicability to general linear, time-invariant systems, (2) direct use of multiple input and multiple response data, (3) identification of reduced-order models with minimum user interaction through the use of two automatic model-reduction techniques, (4) identification of a consistent set of modal parameters through the use of numerically stable least-squares techniques, and (5) complete user documentation.

Craig, Roy R., Jr.↗

Multi-axis transient vibration testing of space objects: Test philosophy, test facility, and control strategy

IABG has been using various servohydraulic test facilities for many years for the reproduction of service loads and environmental loads on all kinds of test objects. For more than 15 years, a multi-axis vibration test facility has been under service, originally designed for earthquake simulation but being upgraded to the demands of space testing. First tests with the DFS/STM showed good reproduction accuracy and demonstrated the feasibility of transient vibration testing of space objects on a multi-axis hydraulic shaker. An approach to structural qualification is possible by using this test philosophy. It will be outlined and its obvious advantages over the state-of-the-art single-axis test will be demonstrated by example results. The new test technique has some special requirements to the test facility exceeding those of earthquake testing. Most important is the high reproduction accuracy demanded for a sophisticated control system. The state-of-the-art approach of analog closed-loop control circuits for each actuator combined with a static decoupling network and an off-line iterative waveform control is not able to meet all the demands. Therefore, the future over-all control system is implemented as hierarchical full digital closed-loop system on a highly parallel transputer network. The innermost layer is the digital actuator controller, the second one is the MDOF-control of the table movement. The outermost layer would be the off-line iterative waveform control, which is dedicated only to deal with the interaction of test table and test object or non-linear effects. The outline of the system will be presented.

Lachenmayr, Georg↗

SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method

Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.

Uncertainty Quantification↗