Strain replication using modal decomposition and expansion in acceleration-based MIMO

The goal of dynamic testing is to replicate loads and stresses that a system undergoes in its field environment in a laboratory setting. It is common practice to match acceleration specifications in a vibration test and assume that by doing so the component is properly tested. Multi-Input Multi-Output (MIMO) testing was developed to more representatively match the field environment by simultaneously controlling multiple acceleration locations on a system. However, variations in field vs. laboratory boundary conditions can make it difficult to accurately replicate strains or stresses in a laboratory environment even when accelerations are closely matched at multiple locations. However, direct measurement of strain using strain gauges is unfavorable because they require extensive surface preparation, provide localized measurements, and have a low signal-to-noise ratio. Therefore, determination of strain from acceleration measurements in tests is important. Currently, there is no technique available to conduct acceleration-based MIMO to achieve strain matching at critical locations. MIMO tests are conducted to match accelerations even though strain is better correlated to damage. This paper provides a technical basis for conducting MIMO tests to match strains at various locations of a test article. Experiment on a cantilever beam subject to single input free vibration was conducted to investigate the influence of dominant modes over less dominant modes and the results were analyzed using applicable theory. This allowed the inaccuracies associated with both experimental and theoretical processes to be quantified. The methodology was then used on a more realistic 3-storie structure where the strains at various locations were matched using a MIMO control scheme implemented with acceleration-based control. In this paper, the authors first propose a multimode strain estimation method that accounts for the contribution of different modes to the strain responses using curvature mode shapes. The accuracy of the method is quantified on a cantilever beam via forced and free vibrations tests and FEM analyses. Subsequently, this paper presents a novel acceleration-based MIMO testing technique that uses a forward and backward Modal Decomposition and Expansion (MDE) methodology to account for impedance differences between the field and laboratory environment. This method was shown to accurately replicate strains corresponding to the first three significant modes at several critical locations in a model 3-story structure.