Parallel harmonic balance method for analysis of nonlinear mechanical systems

Mechanical vibration analysis and modelling are essential tools used in the design of various mechanical components and structures. In the case of turbine engine design specifically, the ability to accurately predict vibration of various parts is crucial to ensure their safe operation while maintaining efficiency. As the designs become increasingly complex and margins for errors get smaller, high fidelity numerical vibration models are necessary for their analysis. Research of parallel algorithms has progressed significantly in the last decades, thanks to the exponential growth of the world's available computational resources. This work explores the possibilities for parallel implementations for solving large scale nonlinear vibration problems. A C++ code using MPI was developed to validate these implementations in practice. The harmonic balance method is used in combination with finite elements discretisation and applied to an elastic body with the Green-Lagrange nonlinear model for large deformations. A parameter continuation scheme using a predictor-corrector approach is included to compute frequency response functions. A Newton-Raphson solver is used to solve the bordered nonlinear system of equations in the frequency domain. Three different parallel algorithms for solving the linearised problem in each Newton iteration are analysed - a sparse direct solver (using MUMPS library), GMRES (using PETSc library) and an inhouse implementation of FETI. The performance of the solvers is analysed using beam testcases and a fan blade geometry. Scalability of MUMPS and the FETI solver is assessed. Full nonlinear frequency response functions with turning points are also computed. Use of artificial coarse space and preconditioning in FETI is discussed as it greatly impacts convergence properties of the solver. The presented parallel linear solvers show promising scalability results and an ability to solve nonlinear systems of several million degrees of freedom.Open Acces

Surface expression of metabotropic glutamate receptor variants mGluR1a and mGluR1b in transfected HEK293 cells.

International audienceClass C G-protein coupled receptors form obligatory dimers. Metabotropic glutamate receptors (mGluRs) are found commonly as homodimers. Alternative splicing of mGluR1 gene results in vivo in the expression of a long variant mGluR1a and at least two short variants mGluR1b and d. The amino acid sequences diverge within their carboxyl-termini six amino acid residues following RRKK motif. This four basic residue sequence was shown to have pronounced impact on function and trafficking of the short variants, while for mGluR1a the long C-terminus reduces the effects caused by presence of the RRKK motif. Here we investigated consequences of interactions between long mGluR1a and short mGluR1b variants. Our results show that mGluR1a interferes with mGluR1b trafficking to the cell surface in HEK293 transfected cells. Expression of a mGlu1a mutant incapable of activating G-proteins with mGluR1b mutated in the glutamate binding site led to the formation of a functional heterodimer. Moreover, we show that swapping long mGluR1a and/or short mGluR1b C-termini with corresponding regions in chimerical GB1 and GB2 gamma-amino butyric acid b (GABAb) receptor subunits do not exclude heterodimerization. These data reveal that the C-terminal ends of mGluR1 do not control subunit association, such that mGluR1 dimers with two distinct C-termini can form and function properly