Measurement of Residual Flexibility for Substructures Having Prominent Flexible Interfaces
Verification of a dynamic model of a constrained structure requires a modal survey test of the physical structure and subsequent modification of the model to obtain the best agreement possible with test data. Constrained-boundary or fixed-base testing has historically been the most common approach for verifying constrained mathematical models, since the boundary conditions of the test article are designed to match the actual constraints in service. However, there are difficulties involved with fixed-base testing, in some cases making the approach impractical. It is not possible to conduct a truly fixed-base test due to coupling between the test article and the fixture. In addition, it is often difficult to accurately simulate the actual boundary constraints, and the cost of designing and constructing the fixture may be prohibitive. For use when fixed-base testing proves impractical or undesirable, alternate free-boundary test methods have been investigated, including the residual flexibility technique. The residual flexibility approach has been treated analytically in considerable detail and has had limited frequency response measurements for the method. This concern is well-justified for a number of reasons. First, residual flexibilities are very small numbers, typically on the order of 1.0E-6 in/lb for translational diagonal terms, and orders of magnitude smaller for off-diagonal values. This poses difficulty in obtaining accurate and noise-free measurements, especially for points removed from the excitation source. A second difficulty encountered in residual measurements lies in obtaining a clean residual function in the process of subtracting synthesized modal data from a measured response function. Inaccuracies occur since modes are not subtracted exactly, but only to the accuracy of the curve fits for each mode; these errors are compounded with increasing distance from the excitation point. In this paper, the residual flexibility method is applied to a simple structure in both test and analysis. Measured and predicted residual functions are compared, and regions of poor data in the measured curves are described. It is found that for accurate residual measurements, frequency response functions having prominent stiffness lines in the acceleration/force format are needed. The lack of such stiffness lines increases measurement errors. Interface drive point frequency respose functions for shuttle orbiter payloads exhibit dominant stiffness lines, making the residual test approach a good candidate for payload modal tests when constrained tests are inappropriate. Difficulties in extracting a residual flexibility value from noisy test data are discussed. It is shown that use of a weighted second order least-squares curve fit of the measured residual function allows identification of residual flexibility that compares very well with predictions for the simple structure. This approach also provides an estimate of second order residual mass effects.