Dynamic system characterization and design using mechanical impedance representations

Vibration testing is a critical aspect in the qualification of fieldable hardware as dynamic environments are typically design drivers, especially in the case of airborne and space-borne systems. However, when testing components or small subassemblies, it is challenging to match the boundary conditions presented by the true installation interface, which can greatly influence the outcome and inferences of a vibration test campaign. Strategically designed test fixtures, which emulate the impedance of the next level of assembly, can more effectively emulate the boundary conditions present in the fielded system. The objective of this paper is to present an approach to impedance matched fixture design, which requires matching both the transfer and output impedances of the true system. The analyses presented within this paper focus on techniques for matching the drive point impedance, which requires correct solutions for both the transfer and output impedances. The impedance matching approach will utilize undamped lumped parameter systems and highlight the advantages of characterizing the high and low frequency behavior. Additionally, closed form representations of these high and low frequency characteristics will be presented for easily realizable 1D lumped parameter systems.