A) \[a\cos \frac{\pi x}{2L}\cos \frac{\pi y}{2L}\]
B) \[a\sin \frac{\pi x}{L}\sin \frac{\pi y}{L}\]
C) \[a\sin \frac{\pi x}{L}\sin \frac{2\pi y}{L}\]
D) \[a\cos \frac{2\pi x}{L}\cos \frac{\pi y}{L}\]
Correct Answer: B
Solution :
Since the edges are clamped, displacement of the edges \[u(x,y)=0\]for line ? OA i.e. \[y=0\], \[0\le x\le L\] AB i.e.\[x=L\], \[0\le y\le L\] BC i.e.\[y=L\], \[0\le x\le L\] OC i.e.\[x=0\], \[0\le y\le L\] The above conditions are satisfied only in alternatives (b) and (c). Note that \[u(x,y)=0\], for all four values e.g. in alternative (d), \[u(x,y)=0\]for \[y=0,y=L\] but it is not zero for \[x=0\] or \[x=L\]. Similarly in option A. \[u(x,y)=0\] at \[x=L,y=L\] but it is not zero for \[x=0\] or\[y=0\], while in options (b) and (c), \[u(x,y)=0\]for \[x=0,y=0,x=L\] and \[y=L\]You need to login to perform this action.
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