I want to find the equivalent orthotropic model for a sinusoidal corrugated plate. During this process I need to find the moment of inertia of the sinusoidal cross section. Any one can help me in calculating this moment of inerta?
First take the origin of the cross-section. Then divide the cross-section into small small element (i.e. either rectangular or any other regular shape ) then by using parallel axis theorem find the M.O.I of every elements and sum it up.
I agree with Pankaj. Later you can refine your model by formulating the expression of the sinusoidal shape including its thickness and solving the integral expression of the moment of inertia. See for instance the following examples in the case of an ellipsoid. Regards!
http://scienceworld.wolfram.com/physics/MomentofInertiaEllipsoid.html
https://www.miniphysics.com/uy1-calculation-of-moment-of-inertia-of-thin-spherical-shell.html
I presume that the section is a rolled roofing sheet or similar. You can program it for a computer as above, or by integrating the function y^2 where y=a*sin(x) with respect to x. Note: you only need to integrate for one quarter of the sin wave.
It is unclear from the question whether the cross section is of exact sinusoidal shape or not. If yes, the answer is quite trivial (see, for example, above comments by Gordon). If the section geometry is described by another function or given in terms of discrete data like x and y values, employ a numerical technique. Please remember that the principal moment of inertia should be calculated with respect to the central axis. That is, you have to determine centroid of the cross section.
Regards.
It is unclear from the question whether the cross section is of exact sinusoidal shape or not. If yes, the answer is quite trivial (see, for example, above comments by Gordon). If the section geometry is described by another function or given in terms of discrete data like x and y values, employ a numerical technique. Please remember that the principal moment of inertia should be calculated with respect to the central axis. That is, you have to determine centroid of the cross section.
Regards.
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