Analytical and Experimental Determination of the Coupled Natural Frequencies and Mode Shapes of a Dynamic Model of a Single-Rotor Helicopter

摘要

A combined analytical and experimental determination is made of the coupled natural frequencies and mode shapes in the longitudinal plane of symmetry for a dynamic model of a single-rotor helicopter. The analytical phase is worked out on the basis of a seven-degree-of-freedom system combining elastic deflections of the rotor blades, rotor shaft, pylon, and fuselage. The calculated coupled frequencies are first compared with calculated uncoupled frequencies to show the general effects of coupling and then with measured coupled frequencies to determine the extent to which the coupled frequencies can be calculated. The coupled mode shapes are also calculated and were observed visually with stroboscopic lights during the tests. A comparison of the coupled and uncoupled natural frequencies shows that significant differences exist between these frequencies for some of the modes. Good agreement is obtained between the measured and calculated values for the coupled natural frequencies and mode shapes. The results show that the coupled natural frequencies and mode shapes can be determined by the analytical procedure presented herein with sufficient accuracy if the mass and stiffness distributions of the various components of the helicopter are known.