An underwater sensor is mounted below the keel of the fast patrol boat shown in Figure 10.29. The supporting bracket is of cylindrical cross-section (diameter 0.04 m), and so is subject to an oscillating side-force due to vortex shedding. The bracket is of negligible mass compared with the sensor itself, which has a mass of 4 kg. The bracket has a tip displacement stiffness of 25 000Nm^–1. The frequency of the oscillating side-force is SU/d, where U is the speed of the vessel through the water, d is the diameter of the supporting bracket and S is the Strouhal number for vortex shedding from a circular cylinder. S has the value 0.20 approximately. At what speed will the frequency of the side-force coincide with the natural frequency of the sensor and mounting?

Transcribed Image Text:

Figure 10.29 An underwater sensor mounting.