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.
In general, existing methods to develop an effective input for multiple-input/multiple-output (MIMO) control do not offer flexibility to account for limitations in experimental test setups or tailor the control to specific test objectives. The work presented in this paper introduces a method to leverage global optimization approaches to define a MIMO control input to match a data set representing field data. This contrasts with traditional MIMO input estimation methods which rely on direct inverse methods. Efficacy of the iterative optimization method depends on the objective function and optimization method used as well as the definition of the format of the input cross-power spectral density (CPSD) matrix for the optimization routine. Various objective functions are explored in this work through sampling as well as implementation within the iterative optimization process and their impact on the resulting output CPSD. Performance of iterative optimization is assessed against the traditional, direct pseudoinverse method of obtaining the input CPSD as well as the buzz method and weighted least squares (LS). Constraints can be used within the optimization process to control the magnitude and other aspects of the input CPSD, which allows for shaker limitations to be accounted for, among other considerations. Iterative optimization can provide the best input CPSD possible for a test setup while accounting for any shortcomings the setup may have, including force and voltage constraints, which is not possible with traditional methods.
Flight testing provides an opportunity to characterize a system under realistic, combined environments. Unfortunately, the prospect of characterizing flight environments is often accompanied by restrictive instrumentation budgets, thereby limiting the information collected during flight testing. Instrumentation selection is often a result of bargaining to characterize environments at key locations/sub-systems, but may be inadequate to characterize the overall environments or performance of a system. This work seeks to provide an improved method for flight environment characterization through a hybrid experimental-analytical method, modal response extraction, and model expansion. Topics of discussion will include hardware design, assessment of hardware under flight environments, instrumentation planning, and data acquisition challenges. Ground testing and model updating to provide accurate models for expansion will also be presented.
The ability to extrapolate response data to unmeasured locations has obvious benefits for a range of lab and field experiments. This is typically done using an expansion process utilizing some type of transformation matrix, which typically comes from mode shapes of a finite element model. While methods exist to perform expansion, it is still not commonplace, perhaps due to a lack of experience using expansion tools or a lack of understanding of the sensitivities of the problem setup on results. To assess the applicability of expansion in a variety of real-world test scenarios, it is necessary to determine the level of perturbation or error the finite element model can sustain while maintaining accuracy in the expanded results. To this end, the structure model’s boundary conditions, joint stiffness, and material properties were altered to determine the range of discrepancies allowable before the expanded results differed significantly from the measurements. The effect of improper implementations of the expansion procedure on accuracy is also explored. This study allows for better insights on prospective use cases and possible pitfalls when implementing the expansion procedure.
Aerospace systems and components are designed and qualified against several operational environments. Some of these environments are climatic, mechanical, and electrical in nature. Traditionally, mechanical test specifications are derived with the goal of qualifying a system or component to a suite of independent mechanical environments in series. True operational environments, however, are composed of complex, combined events. This work examines the effect of combined mechanical shock and vibration environments on response of a dynamic system. Responses under combined environments are compared to those under single environments, and the adequacy/limitations of conventional, single environment test approaches (shock only or vibration only) will be assessed. Test integration strategies for combined shock and vibration environments are also discussed.