Vibration Analysis of Engineering Structures with Frictional Contact Using a Novel Equality-Based Framework

Many critical engineering systems, ranging from aircraft engines and power turbines to robotic devices and precision instruments, contain components that interact through friction and contact. These interactions are difficult to model, yet they play a vital role in determining the reliability, efficiency, and durability of such systems. Inaccurate vibration predictions can lead to fatigue, wear, or even failure, with significant safety and economic consequences. The research funded by this award aims to provide new mathematical tools and computational methods to more accurately simulate the complex dynamic behavior of structures with frictional contact. By reformulating how these interactions are represented, this research aims to eliminate longstanding simplifications and approximations that limit current analysis techniques. These advances will help engineers better understand and predict the performance of engineering systems, enabling safer and more efficient designs and longer-lasting technologies. The outcomes are expected to benefit multiple industries and support broader national goals related to economic prosperity, energy efficiency, and security. The project also supports the training of graduate and undergraduate students and will be integrated into engineering curricula. Outreach activities will introduce engineering topics to high school students through hands-on demonstrations and mentoring, thus fostering interest in STEM careers. The research objective of this project is to create a novel equality-based framework for modeling and analyzing the vibrations of large-scale structural systems with nonlinearities arising from friction and unilateral contact. Unlike traditional methods that handle non-smooth behavior by introducing penalization, regularization, massless interface, or time-domain approximations, the approach in this project reformulates friction and unilateral contact laws as exact non-smooth equalities. This allows the application of established frequency-domain techniques, such as weighted residual and harmonic balance methods, to compute periodic responses, assess stability, and perform nonlinear modal analysis. The methodology will be extended to handle a variety of contact and friction laws, two- and three-dimensional frictional contact, interfaces with multiple contact points, and finite element discretizations. In addition, reduced-order models for the vibration of large-scale structures will be constructed by defining invariant manifolds for systems with frictional contact constraints, enabling highly efficient simulations of complex dynamics. Non-smooth modal analysis will also be generalized to systems under periodic excitation, yielding compact models for forced response prediction. The new formulations will be benchmarked against conventional techniques and applied to large-scale engineering assemblies, such as bladed disks with shrouds, friction dampers, and blade root interfaces, demonstrating the effectiveness and versatility of the approach. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.