| 摘 要： | In this paper,we obtain the analytic solution of free vibra-tion frequency and mode shapes of rectangle,circle and ellip-tic membranes.The approximate solution of membrane with arbi-trary boundary is also obtained.All of these membranes areacted on by unequal tension in two directions.For the rectangle membrane,in this paper we transform itsvibration equation into one of usual membranes by trnasformingthe coordinate,thus it is easy to get the solution.For thecircle membrane,first we transform the coordinate in the sameway we deal with the rectangle membrane.Next we transform thevibration equation into the Mathieu equation,then we get a for-mula of frequeney of that membrane with some Mathieu function’sproperty.In the solution the elliptic membrane is similar tothat of the circle membrane.Finally,some examples are given.
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