Publications

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This work extends recent methods to calculate dynamic substructuring predictions of a weakly nonlinear structure using nonlinear pseudo-modal models. In previous works, constitutive joint models (such as the modal Iwan element) were used to capture the nonlinearity of each subcomponent on a mode-by-mode basis. This work uses simpler polynomial stiffness and damping elements to capture nonlinear dynamics from more diverse jointed connections including large continuous interfaces. The proposed method requires that the modes of the system remain distinct and uncoupled in the amplitude range of interest. A windowed sinusoidal loading is used to excite each experimental subcomponent mode in order to identify the nonlinear pseudo-modal models. This allows for a higher modal amplitude to be achieved when fitting these models and extends the applicable amplitude range of this method. Once subcomponent modal models have been experimentally extracted for each mode, the Transmission Simulator method is implemented to assemble the subcomponent models into a nonlinear assembled prediction. Numerical integration methods are used to evaluate this prediction compared to a truth test of the nonlinear assembly.

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One of the more common forms of passive vibration isolation in mechanical systems has been the use of elastomeric or foam pads. Cellular silicone foam is one such example which has been used for vibration isolation and mitigating the effects of mechanical shock. There are many desirable properties of cellular silicone, including its resilience and relative insensitivity to environmental extremes. However, there is very little test data that is useful for understanding its dynamic characteristics or for the development of a predictive finite element model. The problem becomes increasingly difficult since foam materials typically exhibit nonlinear damping and stiffness characteristics. In this paper we present a test fixture design and method for extraction of a few dynamic properties of one type of cellular silicone foam pad. The nonlinear damping characteristics derived from the experimental testing are then used to attempt to improve the predictive capability of a linear finite element model of the system. Difficulties and lessons learned are also presented.

A phenomenon in which structural and internal acoustic modes couple is occasionally observed during modal testing. If the structural and acoustic modes are compatible (similar frequencies and shapes), the structural mode can split into two separate modes with the same shape but different frequencies; where one mode is expected, two are observed in the structural response. For a modal test that will inform updates to an analytical model (e.g. finite element), the test and model conditions should closely match. This implies that a system exhibiting strongly coupled structural-acoustic modes in test should have a corresponding analytical model that captures that coupling. However, developing and running a coupled structural-acoustic finite element model can be challenging and may not be necessary for the end use of the model. In this scenario, it may be advantageous to alter the test conditions to match the in-vacuo structural model by de-coupling the structural and acoustic modes. Here, acoustic absorption material was used to decouple the modes and attempt to measure the in-vacuo structural response. It was found that the split peak could be eliminated by applying sufficient acoustic absorbing material to the air cavity. However, it was also observed that the amount of acoustic absorbing material had an effect on the apparent structural damping of a second, separate mode. Analytical and numerical methods were used to demonstrate how coupled systems interact with changes to damping and mode frequency proximity while drawing parallels to the phenomena observed during modal tests.

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Jointed interfaces are sources of the greatest amount of uncertainty in the dynamics of a structural assembly. In practice, jointed connections introduce nonlinearity into a system, which is often manifested as a softening response in frequency response, exhibiting amplitude dependent damping and stiffness. Additionally, standard joints are highly susceptible to unrepeatability and variability that make meaningful prediction of the performance of a system prohibitively difficult. This high degree of uncertainty in joint structure predictions is partly due to the physical design of the interface. This paper experimentally assesses the influence of the interface geometry on both the nonlinear and uncertain aspects of jointed connections. The considered structure is the Brake-Reuß beam, which possesses a lap joint with three bolted connections, and can exhibit several different interface configurations. Five configurations with different contact areas are tested, identified, and compared, namely joints with complete contact in the interface, contact only under the pressure cones, contact under an area twice that of the pressure cones, contact only away from the pressure cones and Hertzian contact. The contact only under the pressure cone and Hertzian contact are found to behave linearly in the range of excitation used in this work. The contact area twice that of the pressure cone behaves between the complete contact and contact only under the pressure cone cases.

Classical structural analysis techniques have proven time and time again to be remarkably accurate for systems consisting of a single, continuous piece of material. Unfortunately, nearly all real engineering structures are assembled from multiple parts, joined by bolts, rivets, or other fasteners, and these joints introduce nonlinearities and uncertainties into systems’ structural stiffness and damping. Nonlinear damping due to jointed connections in particular is critical to limiting the resonant response of a structure, yet it remains poorly understood. This work seeks to understand the degree to which joint properties are dependent on the rest of the structure. The testable hypothesis is that the boundary conditions and the far-field structure itself (i.e. distribution of the stiffness and mass) change the way in which the interface is loaded, thus altering the perceived or deduced nonlinear properties of the mechanical joint. This hypothesis is investigated using experimental impact hammer testing methods in order to understand the extent to which alteration in the boundary conditions and far-field structure change the interface properties as well as the underlying mechanics during loading. Numerical tools are also employed to investigate and complement the experimental results, focusing on two fronts: replicating the experimental results with discrete joint models, and investigating joint loading for different modes using numerical modal analysis.

Linear structural dynamic models are often used to support system design and qualification. Overall, linear models provide an efficient means for conducting design studies and augmenting test data by recovering un-instrumented or unmeasurable quantities (e.g. stress). Nevertheless, the use of linear models often adds significant conservatism in design and qualification programs by failing to capture critical mechanisms for energy dissipation. Unfortunately, the use of explicit nonlinear models can require unacceptably large efforts in model development and experimental characterization to account for common nonlinearities such as frictional interfaces, macro-slip, and other complex material behavior. The computational requirements are also greater by orders of magnitude. Conversely, modal models are much more computationally efficient and experimentally have shown the ability to capture typical structural nonlinearity. Thus, this work will seek to use modal nonlinear identification techniques to improve the predictive capability of a finite element structural dynamics model. Part I of this paper discusses the experimental aspects of this work. Linear natural frequencies, damping values, and mode shapes are extracted from low excitation level testing. Subsequently, the structure is excited with high level user-defined shaker inputs. The corresponding response data are modally filtered and fit with nonlinear elements to create the nonlinear pseudo-modal model. This is then used to simulate the measured response from a high level excitation experiment which utilized a different type of input. The nonlinear model is then employed in a reduced order, generalized structural dynamics model as discussed in Part II.

Linear structural dynamic models are often used to support system design and qualification. Overall, linear models provide an efficient means for conducting design studies and augmenting test data by recovering un-instrumented or unmeasurable quantities (e.g. stress). Nevertheless, the use of linear models often adds significant conservatism in design and qualification programs by failing to capture critical mechanisms for energy dissipation. Unfortunately, the use of explicit nonlinear models can require unacceptably large efforts in model development and experimental characterization to account for common nonlinearities such as frictional interfaces, macro-slip, and other complex material behavior. The computational requirements are also greater by orders of magnitude. Conversely, modal models are much more computationally efficient and experimentally have shown the ability to capture typical structural nonlinearity. Thus, this work will seek to use modal nonlinear identification techniques to improve the predictive capability of a finite element structural dynamics model. Part I of this paper discussed experimental aspects of this work. Part II will consider use of nonlinear modal models in finite element modeling. First, the basic theory and numerical implementation is discussed. Next, the linear structural dynamic model of a configuration of interest is presented and model updating procedures are discussed. Finally, verification exercises are presented for a high level excitation using test data and simulated predictions from a structural dynamics model augmented with models obtained in nonlinear identification efforts.

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