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

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 1. Technical Staff Member, Associate Member ASME, [email protected], (505) 667-6950 2. Associate Professor, Senior Member ASME, [email protected], (303) 492-1743 3. Senior Member of Technical Staff, [email protected], (505) 844-9329 Experimental Determination of Local Structural Stiffness by Disassembly of Measured Flexibility Matrices Scott W. Doebling, Lee D. Peterson, Kenneth F. Alvin 11/24/98 Page 2 of 38 example problems. NOMENCLATURE Stiffness connectivity matrix d Node-to-sensor offset distance EI Beam cross-sectional bending stiffness parameter Applied force vector GJ Beam cross-sectional torsional stiffness parameter Structural flexibility matrix Identity matrix of size Structural stiffness matrix Transformations between sensor and global degrees of freedom L Length of structural finite element Structural mass matrix Number of finite elements or superelements in model Number of global degrees of freedom in model Number of measurement sensor degrees of freedom Number of stiffness eigenvalues for entire structure or superelement Number of elemental degrees of freedom in finite element Diagonal matrix of elemental stiffness eigenvalues Diagonal matrix of assembled stiffness eigenvalues for entire structure or superelement A [ ]