Aircraft engine manufacturers are increasingly integrating slender blades while aiming to increase their size in order to achieve higher bypass ratios, which are a major factor in the efficiency of these turbomachines. One example is the open fan RISE project led by Safran Aircraft Engines and General Electric. The aim of this thesis proposal is to develop a technique that combines both substructuring and nonlinear normal modes methods to simulate structures exhibiting frictional contact and geometric nonlinearities.
Model reduction techniques are a key element for the predictive calculation of nonlinear structures in engineering, as they allow efficient design prediction at a reasonable computational cost. When dealing with nonlinear problems, numerous reduction methods take advantage of different properties of the considered problem. In this context, two main classes of methods can be distinguished, depending on whether the nonlinearity is spatially localized (as in the case of frictional contact) or distributed (as in the case of geometric nonlinearity). For localized nonlinearities, substructuring methods are well suited and have proven effective in many cases. For distributed nonlinearities, the method of nonlinear normal modes allows for maximum reduction by considering the curvature of invariant subspaces during the calculation.
Within the Digital Sciences & Technologies department of Safran Tech, specifically in the 'Vibration & Impact Structural Analysis' team, in collaboration with the mechanics laboratory of ENSTA, the objective of this thesis is to contribute to the development of a calculation tool that allows for the construction of super-elements taking into account geometric nonlinearities for the purpose of forced response analysis in the presence of frictional contact interfaces. An industrial application on an open slender fan blade including its kinematic connectionsxions will be conducteddone in order to highlight their influence of the environment over the appearance of internal resonances in a forced response context.
The tasks of the PhD student will include the following:
• Conduct a bibliographic study to gain a thorough understanding of the state-of-the-art in dynamic model reduction methods.
• Familiarize themselves with numerical methods for solving dynamic problems.
• Propose a reduction method based on invariant manifolds for constructing nonlinear super-elements with frictional interfaces.
• Implement the method in a scientific computing code.
• Ensure the objectives and the developments are in line with the business units of SAFRAN
• Apply the method to industrial cases.
The thesis is planned to start in September 2024, with a duration of 3 years.
Education: Master's degree in Solid Mechanics or Applied Mathematics.
This thesis requires good knowledge in solid mechanics, particularly in the finite element method, preferably in vibration dynamics. Additionally, proficiency in programming using scientific computing languages such as Matlab, Python, or Julia is necessary. A strong interest in applied mathematics is required. Knowledge of model reduction techniques would be appreciated.
The candidate should demonstrate autonomy, attention to detail, strong analytical and synthesis skills, as well as good interpersonal skills.
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