7. F4 O string 1. 0402xl0 15 EI 2 a ll XTot u 2 . 0805xl0 15 EI 2 stringTot all For the deformed plate, .!_ ; 0 /0 D{ [ 32w + 3 2 2 a 2 w a 2 w a2w 2 u plate = wl 2 (1-v) [a7 oy2 - (a"xay)) } dx dy 2 0 0 ax 2 ~ The integral of the second term in brackets is equal to zero for any w deflection shape if the plate is either simply supported or clamped at the edges. Thus, 1 20 20 3 2w + 3 2w 1 2 2:: D [a7 ay2 dx dy 1 20 20 2 2 4 - f f D[a 11 (12x -12ax + 2a )(y 2 0 0 Introduce two new variables. F and G: F (12y 2 - 12ay + 2a 2 ) Integrate over x first:
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