Abstract
The problem of the bending and free vibrations of a clamped and edge-supported plate is considered. The proposed algorithm is the algorithm described in /1/, made specific for the case of the biharmonic equation. It does not have saturation /2/, i.e., its accuracy will be the higher, the smoother the solution. The program is constructed in such a manner that if the plate boundary is sufficiently smooth and given parametrically, then several of the first eigenvalues can be calculated and the bending problem can be solved. An illustration is presented of the eigenfrequency computation for an edge-supported plate whose boundary (an epitrochoid) has a curvature of the order of 10 3 at twelve points (the curvatures enter explicitly in the appropriate boundary condition). The first eigenfrequencies are calculated with 7–8 places after the decimal point. The solution is obtained because of the accurate method of discretization and the study of the structure of the appropriate finitedimensional problem. This would permit execution of computations with a large number of points (up to 1230). A comparison is given with the results of computations of other authors for a circle and an ellipse /3–5/.
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