Mode shape expansions for the dynamic testing of cable domes considering random pretension deviations

Cable domes maintain their structural stability and deformation resistance substantially depending on the geometrical stiffness contributed by pretension. Dynamic testing can be employed to monitor the possible stiffness degeneration caused by pretension deviations in existing cable domes. The measured incomplete mode shapes should be expanded for effectively evaluating the actual structural stiffness. However, conventional methods lose effectiveness for expanding mode shapes of cable domes whose modes are sensitive to the pretension deviations. A novel method is developed in this paper to expand the incomplete mode shapes of existing cable domes with random pretension deviations. For a monitored target mode of the existing structure, its mode shape can be approximately expressed as a linear combination of a few mode shapes of the ideal structure. Once their combinational coefficients are determined based on the measured incomplete mode shape, the expansion of this target mode is achieved. Two key steps are included: the determination of these so-called contribution modes and the estimation of their combinational coefficients. For the prescribed limit values of equivalent member length errors adopted to simulate random pretension deviations, contribution modes can be determined by considering the mode shape variations and mode jumpings. A proposed contribution mode effective independence (CMEI) method is further put forward to obtain the best estimate of combinational coefficients and the optimal layout of sensors. The numerical example of a cable dome illustrates the invalidation of the conventional expansion methods when random pretension deviations are considered. In contrast, the method proposed in this paper is validated to be effective and reliable even in the cases of severe modal variations and high noise levels.