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Unformatted text preview: 42 SUBMERGED BODY IN WAVES 174 42 Submerged Body in Waves A fixed, submerged body has a circular cross-section of constant diameter one meter, with length twenty meters. For the calculations below, use the Morison formulation for wave- induced force, with C d = 1 . 2. Fix the wave amplitude at one meter, and consider the frequency range of 0.1 to two radians per second. For each of the first four items below, in addition to making a plot please answer: What is the maximum magnitude and at what frequency does it occur? What are the physical mechanisms that create the curve you see? 1. Consider the body oriented horizontally and pointing into waves, at a fixed depth of four meters. Calculate and show in a graph the total heave force magnitude as a function of wave frequency . See Figure 1. The maximum magnitude of vertical force is 18.1kN, at about 1.1 rad/s. Since the wave amplitude is taken as constant at all frequencies, the Morison forces are increasing rapidly as the frequency goes up. At about 1.75 rad/s, however, there is a zero net force because the wavelength is the same as the body length. The fact that this plot is made for a unity wave amplitude means that the square of this function could be multiplied by the wave spectrum, to get the spectrum of the force. Beware of the deep-water assumption however, as indicated below. 2. Under the same conditions, calculate and show in a graph the total pitch moment magnitude as a function of wave frequency. Take the moment around the center of the body ( L/ 2). The maximum pitch moment magnitude is 122 kNm at 1.45 rad/s. Explanation is similar to the case of vertical force, except that the zero frequency is now quite high; it is where the wavelength is equal to about sixty percent of the body length (not half!)....
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.
- Spring '05