On the Vibration of a Square Clamped Plate

By MILTON ABRAMOWITZ and WILLIAM F. CAHILL I National Bureau of Standards, Washington, D.C. 1 The present paper i s concerned with the problem of vibrations of a square plate clamped on all four edges. We shall employ the method of f ini te differences and invest igate the possibi l i ty of improving the accuracy of the numerical results. Th i s problem has been treated by various 1 authors (e/. R E F E R E N C E S 1, 4 to 9) and we shall u se their resul ts as a means of test ing the techniques suggested here. Since Aronszajn, using the Rayleigh-Ritz and Weinstein methods, has computed very c lose upper 1