Publications

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Years of work by 1350 and others has shown that the phenomenology behind EM penetration of joints and seams is a major driver in the shielding effectiveness of ND systems. Via analysis of a canonical cylindrical geometry and comparison against experimental data, we will provide evidence supporting the theory that proper treatment of contact phenomenology including joint deformation, asperity-induced contact impedance, and appropriate treatment of machining tolerance values is required to match electromagnetics modeling and simulation results to experimental data.

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Bolted interfaces are a major source of uncertainty in the dynamic behavior of built-up assemblies. Contact pressure distribution from a bolt’s preload governs the stiffness of the interface. These quantities are sensitive to the true curvature, or flatness, of the surface geometries and thus limit the predictive capability of models based on nominal drawing tolerances. Fabricated components inevitably deviate from their idealized geometry; nominally flat surfaces, for example, exhibit measurable variation about the desired level plane. This study aims to develop a predictive, high-fidelity finite element model of a bolted beam assembly to determine the modal characteristics of the preloaded assembly designed with nominally flat surfaces. The surface geometries of the beam interface are measured with an optical interferometer to reveal the amount of deviation from the nominally flat surface. These measurements are used to perturb the interface nodes in the finite element mesh to account for the true interface geometry. A nonlinear quasi-static preload analysis determines the contact area when the bolts are preloaded, and the model is linearized about this equilibrium state to estimate the modal characteristics of the assembly. The linearization assumes that nodes/faces in contact do not move relative to each other and are enforced through multi-point constraints. The structure’s natural frequencies and mode shapes predicted by the model are validated by experimental measurements of the actual structure.

Lacayo et al. (Mechanical Systems and Signal Processing, 118: 133–157, 2019) recently proposed a fast model updating approach for finite element models that include Iwan models to represent mechanical joints. The joints are defined by using RBE3 averaging constraints or RBAR rigid constraints to tie the contact surface nodes to a single node on each side, and these nodes are then connected with discrete Iwan elements to capture tangential frictional forces that contribute to the nonlinear behavior of the mechanical interfaces between bolted joints. Linear spring elements are used in the remaining directions to capture the joint stiffness. The finite element model is reduced using a Hurty/Craig-Bampton approach such that the physical interface nodes are preserved, and the Quasi-Static Modal Analysis approach is used to quickly predict the effective natural frequency and damping ratio as a function of vibration amplitude for each mode of interest. Model updating is then used to iteratively update the model such that it reproduces the correct natural frequency and damping at each amplitude level of interest. In this paper, Lacayo’s updating approach is applied to the S4 Beam (Singh et al., IMAC XXXVI, 2018) giving special attention to the size and type of the multi-point constraints used to connect the structures, and their effect on the linear and nonlinear modal characteristics.

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Structural dynamic finite element models typically use multipoint constraints (MPC) to condense the degrees of freedom (DOF) near bolted joints down to a single node, which can then be joined to neighboring structures with linear springs or nonlinear elements. Scalability becomes an issue when multiple joints are present in a system, because each requires its own model to capture the nonlinear behavior. While this increases the computational cost, the larger problem is that the parameters of the joint models are not known, and so one must solve a nonlinear model updating problem with potentially hundreds of unknown variables to fit the model to measurements. Furthermore, traditional MPC approaches are limited in how the flexibility of the interface is treated (i.e. with rigid bar elements the interface has no flexibility). To resolve this shortcoming, this work presents an alternative approach where the contact interface is reduced to a set of modal DOF which retain the flexibility of the interface and are capable of modeling multiple joints simultaneously. Specifically, system-level characteristic constraint (S-CC) reduction is used to reduce the motion at the contact interface to a small number of shapes. To capture the hysteresis and energy dissipation that is present during microslip of joints, a hysteretic element is applied to a small number of the S-CC Shapes. This method is compared against a traditional MPC method (using rigid bar elements) on a two-dimensional finite element model of a cantilever beam with a single joint near the free end. For all methods, a four-parameter Iwan element is applied to the interface DOF to capture how the amplitude dependent modal frequency and damping change with vibration amplitude.

The 2019 Nonlinear Mechanics and Dynamics (NOMAD) Research Institute was successfully held from June 17 to August 1, 2019. NOMAD brings together participants with diverse technical backgrounds to work in small teams to cultivate new ideas and approaches in engineering mechanics and dynamics research. NOMAD provides an opportunity for researchers especially early career researchers - to develop lasting collaborations that go beyond what can be established from the limited interactions at their institutions or at annual conferences. A total of 20 students came to Albuquerque, New Mexico to participate in the seven-week long program held at the Mechanical Engineering building on the University of New Mexico campus. The students collaborated on one of seven research projects that were developed by various mentors from Sandia National Laboratories, the University of New Mexico, and academic institutions. In addition to the research activities, the students attended weekly technical seminars, various tours, and socialized at various off-hour events including an Albuquerque Isotopes baseball game. At the end of the summer, the students gave a final technical presentation on their research findings. Many of the research discoveries made at NOMAD are published as proceedings at technical conferences and have direct alignment with the critical mission work performed at Sandia.

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Transient simulations of linear viscoelastically damped structures require excessive computational resources to directly integrate the full-order finite element model with time-stepping algorithms. Traditional modal reduction techniques are not directly applicable to these systems since viscoelastic materials depend on time and frequency. A more appropriate reduction basis is obtained from the nonlinear, complex eigenvalue problem, whose eigenvectors capture the appropriate kinematics and enable frequency-based mode selection; unfortunately, the computational cost is prohibitive for computing these modes from large-scale engineering models. To address this shortcoming, this work proposes a novel two-tier reduction procedure to reduce the upfront cost of solving the complex, nonlinear eigenvalue problem. The first reduction step reduces the full-order model with real mode shapes linearized about various centering frequencies to capture the kinematics over a full range of viscoelastic material behavior (glassy, rubbery, and glass-transition zones). This tier-one reduction preserves time-temperature superposition and allows the equations to depend parametrically on operating temperature. The second-level reduction then solves the complex, nonlinear eigenmode solutions in the tier-one reduced space about a fixed temperature to further reduce the equations-of-motion. The method is demonstrated on a cantilevered sandwich plate to showcase its accuracy and efficiency in comparison to full-order model predictions.

Experiments, modeling and simulation were used to study the nonlinear dynamics of a jointed-structure in a shock tube. The structure was a full-span square cylinder with internal bolted connections excited by fluid loading. The width-based Reynolds number was ≈10⁵. The cylinder was exposed to an impulsive force associated with the incident shock followed by transverse loading imposed by vortex shedding. In the experiment, aerodynamic loading was characterized with high-speed pressure sensitive paint (PSP). Digital image correlation (DIC) concurrently measured the structural response. The maximum displacement occurred when the vortex shedding frequency most closely matched the structural mode of the beam associated with a rocking motion at the joint. A finite element model was developed using Abaqus, where the nonlinear contact dynamics of the joint were simulated using Coulomb friction. The PSP data loaded the model and the interaction was treated as one-way coupled. The simulations well-matched the trends observed in the experiment. Overall, the root-mean-square values of the transverse displacement agreed to within 24% of the experiment. The modeling showed rocking about the joint during vortex shedding was critical to the nonlinear damping and energy dissipation in the structure. We conclude this campaign highlights the importance of jointed-connections to energy dissipation in structures under aerodynamic loading.