Optimal Input Design for the Dynamic Testing of Mechanical Systems

Abstract

A technique to synthesize optimal excitations for dynamic testing is presented. A quadratic function of the frequency response at modeled degrees of freedom of the test object is employed as the test severity measure, subject to an energy constraint on forcing excitation. The optimal test excitation is generated by successively solving a matrix-eigenvalue problem, off line, at all discrete spectral points of interest and then inverse Fourier transforming the optimal spectrum. The technique provides the worst excitation vector, which is the optimal test excitation, as well as the best excitation vector, which corresponds to the best operating environment. Two numerical examples are provided to illustrate the technique. In both cases the worst severity is found to be one or more orders of magnitude higher than the best severity, for the same level of input excitation energy. These results support the practical experience that serious undertesting and severe overtesting can result for comparable levels of forcing input, unless the spectral content of test excitation is carefully chosen by taking the dynamic characteristics of the test object into consideration. The concepts presented in this paper can lead to improved design approaches for disturbance isolators.