Experimental Determination of Local Structural Stiffness by Disassembly of Measured Flexibility Matrices

Abstract

A new method is presented for identifying the local stiffness of a structure from vibration test data. The method is based on a projection of the experimentally measured flexibility matrix onto the strain energy distribution in local elements or regional superelements. Using both a presumed connectivity and a presumed strain energy distribution pattern, the method forms a well-determined linear least squares problem for elemental stiffness matrix eigenvalues. These eigenvalues are directly proportional to the stiffnesses of individual elements or superelements, including the cross-sectional bending stiffnesses of beams, plates, and shells, for example. An important part of the methodology is the formulation of nodal degrees of freedom as functions of the measured sensor degrees of freedom to account for the location offsets which are present in physical sensor measurements. Numerical and experimental results are presented which show the application of the approach to example problems.

Design and Analysis of Advanced Materials in a Thermal/Acoustic Environment. Delivery Order 0007: Volume 1 - Structural Health Monitoring

“…The measured flexibility has been decomposed into elemental stiffness parameters for an assumed structural connectivity. The flexibility matrix is decomposed by projecting it onto an assemblage of the element-level static structural eigenvectors [103]. Curvature changes in the deformed shape of the structure when subjected to a uniform load (called the uniform load surface) can be calculated using the uniform load flexibilities to indicate damage.…”

A Coupled Approach for Structural Damage Detection with Incomplete Measurements

“…It is important to note that the first vector is equivalent to the full mode shape calculated with the EV approach given in equation (12). The coefficients γ li in equation (18) are determined by partitioning equation (18) into the active and omitted sets and then solving a least-squares problem involving only the active set.…”

“…Matrix disassembly is a process that decomposes a structural matrix into a matrix representation of the connectivity between DOFs and a matrix containing the magnitude information [12][13][14][15]. This formulation has the following form for the stiffness matrix:…”

“…A primary contribution of this work is to provide an approach to retain these capabilities by first estimating the full dynamic residual {b i }. The procedure suggested to perform this estimation begins by performing a matrix disassembly on the stiffness matrix [12][13][14][15]. This will produce a set of basis vectors used to estimate the full dynamic residual.…”

“…It has been suggested that reduction/damage identification/expansion should be handled as coupled problems [6]. This work describes the development of such an integrated procedure that is initiated by first disassembling the structural stiffness matrix [12][13][14][15] into a connected set of springs. The columns of the spring connectivity matrix are then used as a set of candidate basis vectors for estimating the full dynamic residual.…”