A SYMMETRICAL INVERSE VIBRATION PROBLEM WITH OVERDAMPED MODES

Several previously published results have addressed the inverse eigenv alue problem for lumped parameter non-conservative systems. These inve rse results give conditions which allow the construction of mass norma lized, velocity and position coefficient matrices based I on given eig envalues and eigenvectors. Previous theories have examined the constru ction of symmetric coefficients given complex and zero eigenvalues (ri gid bodies). Here, the theory of real symmetric inverse eigenvalue pro blems is extended to include the possibility of specifying real eigenv alues, corresponding to overdamped modes. Specifically, conditions are given that allow the construction of real, symmetric, mass normalized damping and stiffness matrices given specified eigenvalues and eigenv ectors, some of which may correspond to overdamped modes.