Bayesian inference is a technique that researchers have recently employed to solve inverse problems in structural dynamics and acoustics. More specifically, this technique can identify the spatial correlation of a distributed set of pressure loads generated during vibroacoustic testing. In this context, Bayesian inference augments the experimenter’s prior knowledge of the acoustic field prior to testing with vibration measurements at several locations on the test article to update these pressure correlations. One method to incorporate prior knowledge is to use a theoretical form of the correlations; however, theoretical forms only exist for a few special cases, e.g., a diffuse field or uncorrelated pressures. For more complex loading scenarios, such as those arising in a direct-field acoustic test, utilizing one of these theoretical priors may not be able to accurately reproduce the acoustic loading generated during the experiment. As such, this work leverages the pressure correlations generated from an acoustic simulation as the Bayesian prior to increase the accuracy of the inference for complex loading scenarios.
Piezoelectric stack actuators can convert an electrical stimulus into a mechanical displacement, which facilitates their use as a vibration-excitation mechanism for modal and vibration testing. Due to their compact nature, they are especially suitable for applications where typical electrodynamic shakers may not be physically feasible, e.g., on small-scale centrifuge/vibration (vibrafuge) testbeds. As such, this work details an approach to extract modal parameters using a distributed set of stack actuators incorporated into a vibrafuge system to provide the mechanical inputs. A derivation that considers a lumped-parameter stack actuator model shows that the transfer functions relating the mechanical responses to the piezoelectric voltages are in a similar form to conventional transfer functions relating the mechanical responses to mechanical forces, which enables typical curve-fitting algorithms to extract the modal parameters. An experimental application consisted of extracting modal parameters from a simple research structure on the centrifuge’s arm excited by the vibrafuge’s stack actuators. A modal test that utilized a modal hammer on the same structure with the centrifuge arm stationary produced similar modal parameters as the modal parameters extracted from the combined-environments testing with low-level inertial loading.
Aerospace structures are often subjected to combined inertial acceleration and vibration environments during operation. Traditional qualification approaches independently assess a system under inertial and vibration environments but are incapable of addressing couplings in system response under combined environments. Considering combined environments throughout the design and qualification of a system requires development of both analytical and experimental capabilities. Recent ground testing efforts have improved the ability to replicate flight conditions and aid qualification by incorporating combined centrifuge acceleration and vibration environments in a “vibrafuge” test. Modeling these loading conditions involves the coupling of multiple physical phenomena to accurately capture dynamic behavior. In this work, finite element analysis and model validation of a simple research structure was conducted using Sandia’s SIERRA analysis suite. Geometric preloading effects due to an applied inertial load were modeled using SIERRA coupled analysis capability, and structural dynamics analysis was performed to evaluate the updated structural response compared to responses under vibration environments alone. Results were validated with vibrafuge testing, using a test setup of amplified piezoelectric actuators on a centrifuge arm.
Systems subjected to dynamic loads often require monitoring of their vibrational response, but limitations on the total number and placement of the measurement sensors can hinder the data-collection process. This paper presents an indirect approach to estimate a system's full-field dynamic response, including all uninstrumented locations, using response measurements from sensors sparsely located on the system. This approach relies on Bayesian inference that utilizes a system model to estimate the full-field response and quantify the uncertainty in these estimates. By casting the estimation problem in the frequency domain, this approach utilizes the modal frequency response functions as a natural, frequency-dependent weighting scheme for the system mode shapes to perform the expansion. This frequency-dependent weighting scheme enables an accurate expansion, even with highly correlated mode shapes that may arise from spatial aliasing due to the limited number of sensors, provided these correlated modes do not have natural frequencies that are closely spaced. Furthermore, the inherent regularization mechanism that arises in this Bayesian-based procedure enables the utilization of the full set of system mode shapes for the expansion, rather than any reduced subset. This approach can produce estimates when considering a single realization of the measured responses, and with some modification, it can also produce estimates for power spectral density matrices measured from many realizations of the responses from statistically stationary random processes. A simply supported beam provides an initial numerical validation, and a cylindrical test article excited by acoustic loads in a reverberation chamber provides experimental validation.
Kelley, Christopher R.; Lopp, Garret K.;
Kauffman, Jeffrey L.
Modern turbomachinery blades have extremely low inherent damping, which can lead to high transient vibrations and failure through high-cycle fatigue. Smart materials enable vibration reduction while meeting strict blade requirements such as weight and aerodynamic efficiency. In particular, piezoelectric-based vibration reduction offers the potential to reduce vibration semi-actively while simultaneously harvesting sufficient energy to power the implementation. The placement and the size of the piezoelectric material is critical to the vibration reduction capabilities of the system. Furthermore, the implementation should target multiple vibration modes. In this study, we develop a procedure to optimize electromechanical coupling across multiple vibration modes for a representative turbomachinery blade with surface-mounted piezoelectric patches. Experimental validation demonstrates good coupling across three targeted modes with a single piezoelectric patch. Placing the piezoelectric material in regions of high signed strain energy for all targeted modes enables vibration reduction across all of the targeted modes.