Analysis of Linear Nonconservative Vibrations

The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to linear nonconservative systems. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the extended modal analysis can offer substantial reduction in computational effort and ample physical insight. Many numerical techniques, for example the collocation method, involve discretized equations resembling those of linear nonconservative vibrations. These numerical techniques can be greatly streamlined if the method of equivalence transformations is incorporated.