Multiphysics model reduction of thermomechanical vibration in a state-space formulation

The aim of this work is to propose a new multiphysics mode synthesis (MMS) for the thermomechanical vibration problem. The present thermomechanical model is based on a state-space formulation, which consists of displacement, velocity, and temperature shift. The state-space based thermomechanical formulation is symmetric unlike a conventional non-symmetric formulation for the displacement and temperature shift. In the proposed MMS, the structural variables, the displacement and velocity, are first reduced, which is then applied to the coupling term in the thermal parts. A term of the thermal domain is then reduced while preserving the multiphysics coupling effects, resulting in improved accuracy. The proposed two-step MMS with the thermal physics domain update can be implemented with the coupling term derived using the residual flexibility. The proposed MMS strategy can be also applied to accelerate the computational speed using independent parallel solvers. The performance of the proposed MMS method is evaluated through numerical examples.