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Multiple modes in the vibration of cantilevered shells

Journal of Sound and Vibration
Publication Date
DOI: 10.1016/0022-460x(87)90473-1
  • Mathematics


Abstract The term multiple modes describes pairs of modes which are similar in shape but occur at different frequencies. This phenomenon has been observed in holographic vibration test results for a turbine blade. Pairs of modes were found, such as two modes which both resembled first torsional modes. In this investigation holographic interferometry was used to verify the earlier results for the turbine blade and to investigate three shell segments simulating blades. The shells ranged in size from moderately to very thick with length to thickness ratios of 16, 8 and 5·6. The blade geometry is characterized by a circumferential angle of 142° and a ratio of length to inner radii arc length near 1·0. In addition, a NASTRAN finite element analysis was performed on these simulated blades. Both mode shapes and frequencies were found to be in good agreement with the results from the experiment. The multiple mode phenomenon was found to be an artifact of the holographic experiment. Pairs of modes were found in the NASTRAN results for the simulated blades in which the out-of-plane displacements (those seen in the hologram) were very similar, but for which the displacements in the plane of the hologram differed significantly. Thus, the two modes which appeared in the experimental results as first torsional modes were seen to include quite different in-plane displacements. The two modes are therefore quite different and do not contradict the normal result, which may be justified from such elementary considerations as a Rayleigh quotient, that similar modes must produce similar frequencies.

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