Frequency response smoothing, matrix assembly and structural paths: A new approach for structural dynamics up to high frequencies

Abstract

Frequency response smoothing by geometric mean values, in conjunction with a solution written in terms of structural paths, provides a new approach for estimating the mean frequency responses of complex structures subjected to mechanical excitation from low to high frequencies. A theoretical formulation is derived for continuous structures with discrete connections between components. This formulation is based on the assembly of the smoothed dynamic stiffnesses of each component in a classical way, followed by a manipulation in terms of structural paths to provide the smoothed frequency responses of the whole structure. The results can be easily interpreted due to the physical meaning of the structural paths. This approach is applied to trusses for illustration; however, it can be extended to any structure provided that the formulation of each component is established, as in a finite element approach. Computer time efficiency for large structures will depend on the selection of the “shortest” paths (similar to modal truncation for modal superposition approach). Finally, the application to dynamic substructuring with component dynamic stiffnesses or flexibilities is presented, showing promising capabilities for analysis and testing of complex structures up to high frequencies.