| Abstract: | When damping in a system is both significantly high and its distribution is non-classical the solution of dynamical problems by conventional modal analysis is complicated by the presence of coupling between the normal co-ordinates. Further, the convergence of a solution may be erratic with successive modal additions, leading to the need to include a larger number of modes than would otherwise be expected. In this paper methods of modal analysis in structural dynamics are discussed and their derivations briefly given. These include the conventional mode displacement method and the force summation method, employing normal modes, and the analogous procedures with damped modes. In the latter, dynamic response equations are not coupled. Dynamic loading solutions by the four approaches, each taking account of the non-classical damping distribution, are demonstrated with a simple model representing a structure on a compliant foundation. The results strongly suggest that the use of damped modes with force summation could be the most effective procedure when damping is non-classical. |
