The 2017 Nonlinear Mechanics and Dynamics (NOMAD) Research Institute was successfully held from June 19 to July 28, 2017. NOMAD seeks to bring together participants with diverse technical backgrounds to work in small teams to utilize an interactive approach to cultivate new ideas and approaches in engineering . 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 17 students from around the world came to Albuquerque, New Mexico to participate in the six - week long program held at the University of New Mexico campus. The students collaborated on one of six research projects that were developed by various mentors from Sandia National Laboratories, academia, and other government laboratories. In addition to the research activities, the students attended weekly technical seminars, toured the National Museum of Nuclear Science & History, 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 o n their research findings that was broadcast via Skype. Many of the research discoveries made at NOMAD are published as proceedings at technical conference s and have direct alignment with the critical mission work performed at Sandia.
Proceedings of ISMA 2018 - International Conference on Noise and Vibration Engineering and USD 2018 - International Conference on Uncertainty in Structural Dynamics
Structural dynamic models of mechanical, aerospace, and civil structures often involve connections of multiple subcomponents with rivets, bolts, press fits, or other joining processes. Recent model order reduction advances have been made for jointed structures using appropriately defined whole joint models in combination with linear substructuring techniques. A whole joint model condenses the interface nodes onto a single node with multi-point constraints resulting in drastic increases in computational speeds to predict transient responses. One drawback to this strategy is that the whole joint models are empirical and require calibration with test or high-fidelity model data. A new framework is proposed to calibrate whole joint models by computing global responses from high-fidelity finite element models and utilizing global optimization to determine the optimal joint parameters. The method matches the amplitude dependent damping and natural frequencies predicted for each vibration mode using quasi-static modal analysis.
An assessment of two methodologies used at Sandia National Laboratories to model mechanical interfaces is performed on the Ministack finite element model. One method uses solid mechanics models to model contacting surfaces with Coulomb frictional contact to capture the physics. The other, termed the structural dynamics reduced order model, models the interface with a simplified whole joint model using four-parameter Iwan elements. The solid mechanics model resolves local kinematics at the interface while the simplified structural dynamics model is significantly faster to simulate. One of the current challenges to using the whole joint model is that it requires calibration to data. A novel approach is developed to calibrate the reduced structural dynamics model using data from the solid mechanics model to match the global dynamics of the system. This is achieved by calibrating to amplitude dependent frequency and damping of the system modes, which are estimated using three different approaches.
The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.
Thin beams and panels subjected to large loadings will behave nonlinearly due to membrane stretch effects as they approach deflections on the order of their thickness; this behavior can be efficiently and accurately modeled using nonlinear reduced order models based on the structure’s linear normal modes. However, the complexity of such reduced order models grows cubically with the number of linear modes in the basis set, making complicated geometries prohibitively expensive to compute. Component mode synthesis techniques may be used to reduce this cost by assembling a set of smaller nonlinear subcomponent models, each of which can be more quickly computed than a nonlinear model of the entire structure. Since geometric nonlinearity is heavily dependent on each structure’s boundary conditions, however, subcomponents of an assembly which are constrained only at their interfaces – such as panels mounted to an underlying frame – prove difficult to treat using existing nonlinear modeling techniques. This work uses Craig-Bampton dynamic substructuring combined with characteristic constraint modes for interface reduction to examine the challenges associated with panel and frame assemblies, with a simple example motivating a discussion of current solutions and future challenges.
Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low-order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large-scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low-order set of nonlinear equations using a truncated set of fixed-interface and characteristic constraint modes. The method used to extract the coefficients of the nonlinear reduced-order model is nonintrusive, in that it does not require any modification to the commercial finite element code but computes the reduced-order model from the results of several nonlinear static analyses. The nonlinear reduced-order models are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees of freedom, and the nonlinear normal modes of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861-degree-of-freedom model down to only 23 degrees of freedom while still accurately reproducing the nonlinear normal modes.
The Craig-Bampton approach for component mode synthesis in structural dynamics has been widely used to reduce the order of large, detailed finite element models made from linear elastic materials. This methodology separates the full order model into smaller subcomponents and reduces the equations of motion with a truncated set of fixed-interface modes and static constraint modes. A drawback of this approach is that the model has one constraint mode for every interface degree-of-freedom, which may result in a large and prohibitively costly superelement. Previous work has addressed this issue via characteristic constraint modes, which reduces the number of interface degrees-of-freedom by performing a secondary modal analysis on the interface partition. The current work extends the Craig-Bampton approach with interface reduction to include subcomponents with linear viscoelastic materials modeled using a Prony series. For substructures containing materials such as foams or polymers, the viscoelastic constitutive law more accurately represents the material energy dissipation compared to traditional viscous or modal damping. The new approach will be demonstrated on the assembly of two composite plates with fixed boundary conditions along one edge.
Structural dynamics models with localized nonlinearities can be reduced using Hurty/Craig-Bampton component mode synthesis methods. The interior degrees-of-freedom of the linear subcomponents are reduced with a set of dynamic fixedinterface modes while the static constraint modes preserve the physical coordinates at which the nonlinear restoring forces are applied. For finite element models with a highly refined mesh at the boundary, a secondary modal analysis can be performed to reduce the interface down to a truncated set of local-level characteristic constraint modes. In this research, the cost savings and accuracy of the interface reduction technique are evaluated on a simple example problem involving two elastic blocks coming into contact.