Advancements in hybrid dynamic models combining experimental and finite element substructures

This paper presents very practical enhancements to the transmission simulator method (TSM); also known as the Modal Constraints for Fixtures and Subsystems (MCFS). The enhancements allow this method to be implemented directly in finite element software, instead of having to extract the reduced finite element model from its software and implement the substructure coupling in another code. The transmission simulator method is useful for coupling substructures where one substructure is derived experimentally and the other is generated from a finite element model. This approach uses a flexible fixture in the experimental substructure to improve the modal basis of the substructure; thus, providing a higher quality substructure. The flexible fixture substructure needs to be removed (decoupled) from the experimental substructure to obtain the true system characteristics. A modified method for this removal and coupling of the experimental and analytical substructures is provided. An additional improvement guarantees that the experimental substructure matrices are positive definite, a requirement for many finite element codes. Guidelines for designing robust transmission simulator hardware are provided. The concepts are applied to two sample cases. The first case consists of a cylinder connected by eight bolts to a plate with a beam. The second example is an outer shell structure that is connected through a bolted flange to a complex internal payload structure.

► A method is given to couple experimental and analytical substructures in a FE code.
► The transmission simulator method accounts for the joint stiffness and damping.
► Guidelines for designing a robust flexible fixture are provided.
► Algorithms to select sensor and forcing measurement degrees of freedom are provided.
► A method for guaranteeing positive definite stiffness and mass matrices is provided.