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Unformatted text preview: MAE 472, Spring 2010 Homework #3 Due 2/18/09 Problem 1 The helicopter rotor blade shown below is subjected to the uniform line load of 50 lb/in. in the —z
direction and pressure of 2.5 psi in the +y direction as shown below. The section properties are Iyy = 724.69 in4 and IZZ = 43.77 in“. Note that the coordinate system is different.
Use the Rayleigh-Ritz method to determine the bending deflections v0(x) and w0(x) assuming:
v0 (x) = b] + bzx + [73x2 wO (x) 2 01+ 02x + c3x2 Problem 2 The cantilevered beam shown below is supported on the left end with a rotational spring and a roller.
The beam has constant rigidity E]. (a) Of the four shape functions below, which two are appropriate for the beam? Explain why. . . z7r z7r
./, (z) = 2(2—L) f2 (2) = 22 (z—L) f3 (2) = zs1n(Tj f4 (2) Wood?)
(b) Using one of the shape functions that you chose in part (a), find the deflection of the beam, u0(Z).
X rotational spring
M = K 9 Problem 3 Using the Rayleigh—Ritz method, determine the approximate transverse displacement of the beam
(u0(z)), using the shape function, 10m f.(2)=sin(3‘—] and E = 200,000 MPa. ' a!" -«'-’n q: r H M, _ ‘ ‘
diu‘qu .aruuﬂtés“ ‘ ‘ ...
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- Spring '08