PLEASE READ: --> This is a Dynamics-Offshore Structures Problem: Please only ans

Question

PLEASE READ: --> This is a Dynamics-Offshore Structures Problem: Please only answer if you are very good at Dynamics (offshore strucutres). I have limited questions left, and do not want a wrong answer (I also do not want to give a bad rating). So PLEASE, ONLY, answer if you are sure how to solve this problem and that you are 100% right. It is not easy and requires many steps. If not answered by 12am CST (Central Standard Time-USA Chicago time) on 9/19/18, please disregard and DON'T answer anymore. Thank you very much for all the help.

PLEASE READ: --> This is a Dynamics-Offshore Structures Problem: Please only answer if you are very good at Dynamics (offshore strucutres). I have limited questions left, and do not want a wrong answer (I also do not want to give a bad rating). So PLEASE, ONLY, answer if you are sure how to solve this problem and that you are 100% right. It is not easy and requires many steps. If not answered by 12am CST (Central Standard Time-USA Chicago time) on 9/19/18, please disregard and DON'T answer anymore. Thank you very much for all the help.

There is a cylinder floating in the water. The cylinder has radius "r", height "h", and density "p". When the cylinder has rotational motion with respect to the center of coordinate system on the mean water level, Find horizontal acceleration at an infinitesimal circular plate (colored by blue below) with dz (thickness) in terms of z and 0 (horizontal displacement can be approximated to arc length measured at the plate after the small angle rotation) What is corresponding inertia loading at the infinitesimal plate? Is this loading force or moment? If it's force, what is resultant inertia moment at the infinitesimal plate? Assume the cylinder density is half of the water,find total inertia moment on the cylinder. a. b. c. d. Arc lengthi After rotation

Explanation / Answer

given cylinder in water

radius = r

height = h

density = rho

a. for the colored strip

tangential acceleration = z*theta"

radial acceleration = (z*theta')^2/z = z*theta'^2

hence horizontal acecleration = z*theta"

b. inertia loading = dm*g*sin(theta)

for small theta

momemnt dM = g*theta*rho*pi*r^2*dz

c. dM = I*alpha = I*theta" = dm*z^2*(theta") = rho*pi*r^2*z^2*theta"*dz

d. total moment = M

M = moment due to weight of top and bottom halves cancels out

hence moment is due to buoyant force

length of cylinder L

then

rho*pi*r^2*Lg = 2*rho*pi*r^2*h*g

h = L/2 ( submerged length of cylinder)

hence

M = mg*l*sin(theta)/4

M = rho*pi*r^2*h*sin(theta)/4

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