Publications

Extending SMAC to multiple reference FRFs

Hensley, Daniel P.; Mayes, R.L.

Multiple references are often used to excite a structure in modal testing programs. This is necessary to excite all the modes and to extract accurate mode shapes when closely spaced roots are present. An algorithm known as SMAC (Synthesize Modes And Correlate), based on principles of modal filtering, has been in development for several years. This extraction technique calculates reciprocal modal vectors based on frequency response function (FRF) measurements. SMAC was developed to accurately extract modes from structures with moderately damped modes and/or high modal density. In the past SMAC has only worked with single reference data. This paper presents an extension of SMAC to work with multiple reference data. If roots are truly perfectly repeated, the mode shapes extracted by any method will be a linear combination of the "true" shapes. However, most closely spaced roots are not perfectly repeated but have some small difference in frequency and/or damping. SMAC exploits these very small differences. The multi-reference capability of SMAC begins with an evaluation of the MMIF (Multivariate Mode Indicator Function) or CMIF (Complex Mode Indicator Function) from the starting frequency list to determine which roots are likely repeated. Several seed roots are scattered in the region of the suspected multiple roots and convergence is obtained. Mode shapes are then created from each of the references individually. The final set of mode shapes are selected based on one of three different selection techniques. Each of these is presented in this paper. SMAC has long included synthesis of FRFs and MIFs from the roots and residues to check extraction quality against the original data, but the capability to include residual effects has been minimal. Its capabilities for including residual vectors to account for out-of-band modes have now been greatly enhanced. The ability to resynthesize FRFs and mode indicator functions from the final mode shapes and residual information has also been developed. Examples are provided utilizing the SMAC package on multi-reference experimental data from two different systems.