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A square membrane of side lengths L, which is initially at rest on the xy-plane has...

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Advance Math

A square membrane of side lengths L, which is initially at reston the xy-plane has its edges fixed on the xy-plane. A periodicforce per unit area, given by A?cos?(??t) for t > 0,andA=constant, acts at every point in the membrane. Apply appropriatefinite Fourier transforms to show that the displacements in themembrane.

Answer & Explanation Solved by verified expert
4.0 Ratings (616 Votes)
A basic problem in free vibration of the membrane is to solve Eq 161 subject to proper boundary conditions To this end express the membrane displacement as 165wxytwxycost which when substituted into Eq 161 yields 1662x22y2wxy2Twxy0 Equation 166 along with the boundary conditions defines an eigenvalue    See Answer
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