Modal Analysis of Linear Asymmetric Nonconservative Systems

In this work, classical modal analysis has been extended to treat lumped parameter asymmetric linear dynamic systems. In the presence of general nonconservative forces, the damping matrix is not simultaneously diagonalizable with the mass and stiffness matrices. The proposed method utilizes left and right eigenvectors of the second-order system and does not require conversion of the equations of motion into the first-order form. Left and right eigenvectors of the nonconservative system are derived in terms of the left and right eigenvectors of the corresponding conservative system using a Galerkin error minimization approach in conjunction with a Neumann expansion method. Transfer functions for the asymmetric nonconservative system are derived in terms of the left and right eigenvectors of the nonconservative system. Suitable numerical examples are given to illustrate the proposed method.