Collaborative Research: New Nonlinear Modal Analysis Framework for Multi-Scale Modeling of Structures with Bolted Interfaces

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Engineers in many industries use the finite element method to divide structures into small elements so that the equations governing each can be found and solved by computers. This allows one to compute the stresses and deformation of structures with complicated shapes such as airplanes, machines, biomedical implants, etc. and to predict whether the structure can survive the loads it will experience in operation. While this method has proven very effective in many scenarios, even modern computers are not powerful enough to model the interfaces between parts accurately. As a result, billions of dollars are spent annually testing structures to determine the stiffness of interfaces, such as bolted connections, in order to adjust the simulation models so that they better capture the real behavior of the structure. This makes new machines much more expensive and often leads to designs that break prematurely, potentially endangering lives. Prediction is particularly difficult when a structure, such as an aircraft, experiences dynamic loads due to turbulence in the air passing over the wings. This work will explore a new means of simulating the motion of structures with bolted interfaces and will perform experiments to seek to understand how to model friction and microscopic slip in the joints and its effect on vibration damping. The methodology can be easily integrated in existing finite element software, to facilitate its transition and broad adoption. The research will be complemented by outreach activities at the PIs institutions and a short course exposing students and researchers to the technique formulated as part of the project.The physics that are responsible for energy dissipation in mechanical joints are complicated and span the full range of length scales. While much has been learned in recent years about the nature of nano- and meso-scale contact interfaces, friction is exceedingly complicated and may be influenced by local elasticity, chemistry, plasticity, surface roughness and lubrication provided by oxides or thin layers of wear particles. This work posits a new reduced order modeling framework that allows one to connect the physics of small scale contacts to the global motion of the assembly. An extension to modal analysis that can then be used to obtain a wealth of insight into the response of the structure under a variety of loading conditions. The methodology will be validated through simulations on various structures and through experiments on assemblies with bolted interfaces, providing new insights into the role of interfaces on a structure's response. Simulations will be performed to understand how the features/parameters of various friction laws manifest themselves in the damping and nonlinearity of the global dynamic response.