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Wave-induced accelerations of cargo and equipment in Java Create qr bidimensional barcode in Java Wave-induced accelerations of cargo and equipment

Wave-induced accelerations of cargo and equipment generate, create qr code jis x 0510 none in java projects Bar code to 2D Code We want to stress that j2se QR Code 2d barcode the coordinate system xyz in Figure 7.11 is not xed relative to the instantaneous position of the ship. This is, for instance, important when we want to study the effect of wave-induced ship oscillations on objects (cargo or equipment) on the deck of the vessel.

We might want to nd out when the object loses grip or to design foundations or other lashing devices. Consider a head sea condition in which the vessel is oscillating in surge, heave, and pitch. There is then a linear component g 5 along the ship- xed x-axis.

Here g is gravitational acceleration.. 7.2 Linear wave-induced motions in regular waves 233 Fz Eq. (7.29) shows that t he derived response variable (relative acceleration).

1 + zc 5 ax = 1 + zc 5 g 5 (7.32). (xc,yc,zc). Fx is important in evaluat ing whether an object on the deck will lose grip or in designing foundations or other lashing devices for the object. If we consider oblique sea, eq. (7.

32) can be generalized to ax = 1 + zc 5 yc 6 g 5 . (7.33).

Figure 7.12. Object wit Denso QR Bar Code for Java h mass M on the deck in head sea conditions.

Center of gravity coordinates (xc , yc , zc ) in the global (x, y, z) coordinate system. The (x, y, z) coor dinate system is body xed. A force with components Fx and Fz acts from the deck on the object.

. There is, then, also a relative acceleration component a y = 2 zc 4 + xc 6 + g 4 (7.34). Let us consider the con QR Code ISO/IEC18004 for Java sequences of that. We consider an object with mass M on the deck (Figure 7.12).

The deck is assumed horizontal in the mean oscillatory position of the vessel. The center of gravity of the object has coordinates (xc , yc , zc ) in the (x, y, z) coordinate system de ned in Figure 7.11.

The longitudinal wave-induced acceleration component at the center of gravity of the object is consistent with linear theory equal to 1 + zc 5 if we refer to either the x- or x-axis. Here dot means time derivative. We now consider equilibrium conditions of the object along the body xed coordinate axes x and z.

Consistent with lin ear theory and using Newton s second law in the x-direction, we have M ( 1 + zc 5 ) = Mg 5 + Fx . (7.29).

along the y-axis to be considered. We note that the signs of the g-terms in eqs. (7.

33) and (7.34) are different. We have already explained the sign in eq.

(7.33). If we look at Figure 7.

11, we see that positive roll 4 means a gravity acceleration component g 4 along the negative y-axis. We also emphasize that eqs. (7.

33) and (7.34) are the accelerations needed to estimate the dynamic forces on the object while the forces on the deck/seafastening have opposite directions..

7.2.1 The equations of awt qr barcode motions When the hydrodynamic forces have been found, we can set up the equations of rigid-body motions.

This follows by using the equations of linear and angular momentum. For steady-state sinusoidal motions, we may write. 6 k=1. Here Fx is the force co swing QR Code mponent in the x-direction acting on the object as a result of sea fastening and/or friction forces from the deck. If the object is not fastened, we write Fx = Fz, (7.30).

[(Mjk + Ajk) k + B jk k + C jk k] = F j ei e t ( j = 1, . . .

, 6) , (7.35). where is a friction c Quick Response Code for Java oef cient and Fz is the force component in the z-direction acting from the deck on the object. Consistent with linear theory and by using Newton s second law in the z-direction gives M ( 3 xc 5 ) = Mg + Fz. (7.

31). We see from eq. (7.31) that it is necessary that Fz is positive.

Otherwise, the object will leave the deck.. where Mjk, Ajk, Bjk, an qrcode for Java d C jk are, respectively, the components of the generalized mass, added mass, damping, and restoring matrices of the ship. For example, the subscripts in Ajk k refer to the force (moment) component in j-direction because of motion in k-direction. F j are the complex amplitudes of the exciting force and moment components.

Obtaining the hydrodynamic forces is by no means trivial. The equations for j = 1, 2, 3 follows from Newton s second law, which assumes an inertial system like the (x, y, z) system. For instance, let.

234 Semi-displacement Vessels us consider j = 1. For a structure that has lateral symmetry (symmetric about the xz-plane) and with center of gravity at (0, 0, zG) in its static equilibrium position, we can write the linearized acceleration of the center of gravity in the x-direction as d2 1 d 2 5 + zG 2 . dt 2 dt From this, the components of the mass matrix Mjk follow as M11 = M, M14 = 0, M12 = 0, M15 = MzG, M13 = 0 M16 = 0.

sidering where the vertical position of the center of gravity is. The added mass and damping loads are steadystate hydrodynamic forces and moments due to forced harmonic rigid-body motions. There are no incident waves; however, the forced motion of the structure generates outgoing waves.

The forced motion results in oscillating uid pressure on the body surface. If the linearized pressure is expressed as in eq. (3.

6), and no interaction with local steady ow is considered, then it is the pressure part p1 = U t x (7.38). Here M is the ship mass tomcat qr-codes . We have similar results for the other translatory directions, that is, j = 2, 3. For j = 4, 5, 6, we have to use the equations derived from the angular momentum.

We can then set up the following mass matrix M 0 0 0 MzG 0 0 M 0 MzG 0 0 0 0 M 0 0 0 Mjk = , MzG 0 I44 0 I46 0 0 0 0 I55 0 MzG 0 0 0 I46 0 I66 (7.36) where I j j is the moment of inertia in the jth mode and I jk is the product of inertia with respect to the coordinate system (x, y, z) . Explicitly: I44 = I66 = (y + z )dM,.

that is considered in t he equation of added mass and damping loads. The velocity potential is linearly dependent on the forced motion amplitude and is harmonically oscillating with the forcing frequency. Integration of these pressure loads over the mean position of the ship s surface gives resulting forces and moments on the ship.

By de ning the force components in the x-, y-, and z-directions as F1 , F2 , and F3 and the moment components along the same axes as F4 , F5 , and F6 , we can formally write the hydrodynamic added mass and damping loads due to harmonic motion mode j as Fk = Akj d2 j d j Bkj . dt 2 dt (7.39).

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