Spectral finite elements combined with energy flow techniques: Hybrid approach for the energy flow parameters evaluation

Abstract

Energy flow parameters involved in many energy flow techniques (statistical energy analysis, or its local formats) are mainly deduced from pure analytical basic theories. However, in practice, application of SEA or alternatives to complex realistic structures suffers from the choice of subsystems and needed relevant inputs. This paper proposes a procedure which reuses existing reduced finite element modeling of the structural component in view of energy flow parameters identification. Precisely, extraction and analysis of dispersion curves for typical structures, wave numbers, and energy velocities, are first concerns in this contribution. The dispersion curves extraction is based on a spectral problem and uses a reduced finite element model. Properties of eigensolutions of the posed spectral problem are first demonstrated and some remarkable aspects in term of energy flow parameters are discussed. Definitions of energy velocity, needed for modal densities expressions associated with the spectral finite element model, are presented in depth. Ultimately, extension of the proposed formulation, in order to deal with coupled complex structural components is given. This leads to the numerical evaluation of diffusion matrix (reflection and transmission parameters), often needed in order to define coupling loss factor or equivalent energy transfer quantities. Some numerical applications are finally presented.