Accelerated dynamic modeling of bolted flanges in aero-engine casings


Often, in the field of structural dynamics, engineers use predictive models to verify a structure’s dynamic response to external excitations, specifically when designing new structures that implement bolted connections. This can be attributed to the fact that modeling of bolted flanges has remained an appalling challenge. One notorious case is with bolted flanges employed in aero-engine castings. These flanges have been shown to exhibit a non-linear response when subjected to forced vibrations. As of now, models in use for structural dynamic analysis of such flanges are accurate, nonetheless, they are cumbersome when it comes to the design of new structures.

To date, three types of model have been reported, namely: thin layer elements, distributed contact elements and lump models, as potential solutions to the problem of aero-engine flange modeling. Each of these approaches has their own pros and cons. Regardless, the lump models have yielded promising results, however, currently in use lump models do not account for spigot connections. Generally, the models used either require model updating from modal testing, or they require a large number of nonlinear elements.

In this view, Professor Kamran Behdinan and his student Marc-Antoine Beaudoin at University of Toronto, Toronto, Canada, presented a study where they proposed a novel lump model for the nonlinear dynamic analysis of bolted flanges. To be precise, their novel approach could account for the nonlinear phenomena of partial clearance and friction, and had analytical parameters related to the flange geometry. Their work is currently published in the research journal, Mechanical Systems and Signal Processing.

The study commenced with the design of a test structure, i.e. a simplified and reduced scale version of a typical aero-engine connection. The section was composed of two pipes connected by a bolted flange. The researchers focused on the structure’s first bending mode because it was most influenced by the joint nonlinearities. Altogether, the model was implemented in finite element analysis and compared with an experiment where a test structure was excited by an electromechanical shaker.

The authors observed that the novel lump model was able to predict the structural response better than a traditional linear method; yet it did not require model updating, and it used a very limited number of nonlinear elements. Additionally, the team highlighted that inclusion of spigots increased the natural frequency of the first bending mode. Moreover, by observing the variations of contact status in a distributed contact element model, it was found that the approximation of bi-linear stiffness was valid for higher excitation levels, while being over simplifying for smaller excitations.

In summary, a new lump model was built for the nonlinear dynamic analysis of aero-engine bolted flanges. Ideally, the model’s constitutive equations were formulated to include the effect of partial clearance, friction, and a spigot connection. As a result, the lump model demonstrated promising results for aero-engine bolted flange modeling. Overall, based on facts enlisted, the researchers concluded that the model was well suited for the early design phase of new aero-engine casings.

About the author

Marc-Antoine Beaudoin received the MASc degree in mechanical engineering from the University of Toronto in 2018 under the supervision of Prof. Kamran Behdinan. He then worked as a powertrain engineer and a project manager at Nordresa, now a part of Dana Inc. In 2019, Marc-Antoine began his doctoral studies at McGill University.

His research interests are the modelling and control of dynamical systems with a current focus on the machine learning control of powertrains for electric vehicles  

About the author

Dr. Kamran Behdinan, earned his Ph.D in Mechanical Engineering from the University of Victoria in British Columbia in 1996, and has a considerable experience in both academic and industrial settings. Kamran was appointed to the academic staff of Ryerson University in 1998, tenured and promoted to the level of associate professor in 2002 and subsequently to the level of Professor in 2007 and served as the director of the aerospace engineering program (02-03), and the founding Chair of the newly established Department of Aerospace Engineering (07/2003 – 07/2011).  Kamran was a founding member and the Executive Director of the Ryerson Institute for Aerospace Design and Innovation (2003-2011). He was also a founding member and the coordinator of the Canadian-European Graduate Student Exchange Program in Aerospace Engineering at Ryerson University. Dr. Behdinan held the NSERC Design Chair in “Engineering Design and Innovation”, 2010-2012, sponsored by Bombardier Aerospace and Pratt and Whitney Canada. Dr. Behdinan joined the Department of Mechanical and Industrial Engineering, University of Toronto, in the rank of Full Professor in September 2011.

He is the NSERC Design Chair in “Multidisciplinary Design and Innovation – UT IMDI”, sponsored by NSERC, University of Toronto, and thirteen companies including Bombardier Aerospace, Pratt and Whitney Canada, United Technology Aerospace Systems, Magna International, Honeywell, SPP Canada Aircraft, Ford, and DRDC Toronto. He is the founding director of the “University of Toronto Institute for Multidisciplinary Design and Innovation”, an industry-centred project-based learning institute in partnership with major aerospace and automotive companies.

Dr. Behdinan is the past President of the Canadian Society of Mechanical Engineering (CSME), served as a member of the technical and scholarship committees of the High Performance Computing Virtual Laboratory (HPCVL) and a member of the Design Division of the Canadian Aeronautics and Space Institute (CASI). He is the founding director and principal investigator of the University of Toronto, Department of Mechanical and Industrial Engineering “Advanced Research Laboratory for Multifunctional Lightweight Structures”, funded by the Canadian Foundation for Innovation (Leader’s Opportunity Fund) and Ontario Research Fund. His research interests include Design and Development of Light-Weight Structures for aerospace, automotive, and nuclear applications, Multidisciplinary Design Optimization of Aerospace and Automotive systems, Multi-scale Simulation of Nano-structured Materials and Composites.

He has supervised 28 PhDs, 110 Masters’, and 34 Post-Doctoral Fellows and Scholars. He has also published more than 330 peer-reviewed Journal and Conference papers, and 9 book chapters. He has been the recipient of many prestigious awards and recognitions such as the Research Fellow of Pratt and Whitney Canada and Fellows of the CSME, ASME, the Canadian Academy of Engineering, EIC, AAAS, as well as Associate Fellow of AIAA.


Marc-Antoine Beaudoin, Kamran Behdinan. Analytical lump model for the nonlinear dynamic response of bolted flanges in aero-engine casings. Mechanical Systems and Signal Processing, volume 115 (2019) page 14–28.

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