Experimental modal substructuring to estimate fixed-base modes from tests on a flexible fixture

Fixed boundary conditions are often difficult if not impossible to simulate experimentally, but they are important to consider in many applications. In principle, modal substructuring or impedance coupling approaches can be used to predict the fixed base modes of a system from tests where the system has some other boundary condition if the motion at the connection point can be measured, but this approach can be highly sensitive to imperfections in the experimental measurements. This work presents two alternatives that reduce the sensitivity to experimental errors, capitalizing on recent works where additional degrees of freedom are used to improve the robustness of substructure uncoupling. The system of interest is tested while mounted on a stiff fixture, where some modes of the fixture inevitably interact with those of the system of interest. The modes of the system–fixture assembly are extracted using a modal test and then a modal substructuring approach is used to apply constraints to eliminate the motion of the fixture. Two types of constraints are proposed, one based on the modes of the fixture and the other on a singular value decomposition of the fixture motion that was observed during the test. Neither approach requires an estimate of the displacements or rotations at the points where the system of interest is connected to the fixture. The methods are validated by applying them to experimental measurements from a simple test system meant to mimic a flexible satellite on a stiff shaker table. A finite element model of the subcomponents was also created and the method is applied to its modes in order to separate the effects of measurement errors and modal truncation. The proposed method produces excellent predictions of the first several modes of the fixed-base structure, so long as modal truncation is minimized. The proposed approach is also applied to experimental measurements from a wind turbine blade mounted in a stiff frame and found to produce reasonable results.