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Unformatted text preview: Homework assignment 4 * Due date: Monday December 3, 2007 1. Buckling of a tower See figure 8 . 16 on p. 501 in the text. Consider the following CauchyEuler equation 1 which describes the deflection y ( x ) from the vertical in terms of the height x measured from the top of the untruncated tower: x 2 y 00 + Pa 2 EI y = , x ∈ ( a, a + L ) y ( a ) = y ( a + L ) = The top of the tower corresponds to x = a ( a is the part of the tower that is truncated) and the ground corresponds to x = a + L , so the height of the tower is L . The positive parameters are as follows: P for the vertical load, I for the moment of inertia, E for the modulus of elasticity. Under certain conditions in particular when the load is high enough the tower may buckle and the purpose of this problem is to determine when this will happen. By definition, buckling occurs if the above boundary value problem has a nontrivial solution ( y ( x ) 6 = 0)....
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 Summer '06
 DeLeenheer
 Boundary value problem, nontrivial solution, boundary condition, nontrivial periodic solution, untruncated tower

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