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The "complete" Euler-Bernoulli beam considered in this paper is "sharp" ended, of constant depth and of breadth proportional to xs, where x is the axial co-ordinate measured from the "sharp" end.
For a complete beam (sharp ended) it is a necessary condition that the sharp end remain free, and as a result the frequency equations for clamped, pinned, sliding or free boundary conditions at the large end are the determinant of a 2 × 2 matrix equated to zero.
Use tweezer tips, a needle, or a similar sharp ended point to create the hole.
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Don't bite too hard because raw ramen can be sharp-ended.
And being at the sharp end is proving painful.
"He gets the sharp end of my tongue.
The police are left at the sharp end.
There was no change at the sharp end after that.
Frayed a bit as the game reached the sharp end.
The farmers remain at the sharp end of Jamaican history.
Leaked emails from Sony showed that Jennifer Lawrence and Amy Adams were at the sharp end of the pay gap.
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