Response of a vibratory system to imposed-displacement excitation

Abstract

Under force-excitation the response of a system can, with great advantage, be expressed as a series in which each term represents the contribution of a single normal mode of the system. With displacement-excitation, however, response analysis in terms of the normal modes of the original system does not give a corresponding separation of modal contributions, even when the excitation is harmonically varying. This is not surprising as the normal modes of the now constrained system bear little relation to those of the original system. Analysis of response in terms of constrained-system modes appears to be impossible because these cannot sum to an imposed displacement at their point of constraint. The paper shows that such analysis can nevertheless be achieved, and that in the resulting series solution each term again represents the contribution of a single mode. Results obtained for a single-freedom system are in consequence immediately relevant to more complex systems.