Extracting Modes of Constrained Structure with Elastic Supports from Free Test Data

The dynamic flexibility (DF) and improved dynamic flexibility (IDF) methods can be applied to extract constrained structural modes from free-free modal test data. The residual flexibility method is also good for boundaries of constrained structure with rigid supports. Under elastic support boundary conditions both the DF and residual flexibility methods cannot produce accurate results. This paper expands the previously published IDF method to become a more general approach for structural design engineers. A new method called the general dynamic flexibility (GDF) method has been developed in this paper to extract constrained structural modes from free test data. The GDF method can always be applied as follows: (1) when the boundary support stiffness is very stiff, the GDF method can accurately obtain results from rigid support as by Liu et al. in 2001 and Zhang and Wei in 2003; (2) when the support stiffness is soft, the present method can produce results similar to those free-free modal parameters measured by hanging structures using rubber band; (3) when the support stiffness is zero, the method can reproduce true free-free modal parameters; and (4) when the support stiffness has any finite values, the GDF method can also achieve satisfactory results for engineering use. The algorithm included in the GDF method converges rapidly and is numerically stable in the analysis. This feature is very practical for many engineering applications for using the GDF method.