The present paper deals with the solution of the title problem applying Lord Rayleigh’s optimization concept when solving integral equations by means of the Ritz method. Polynomial expressions containing a power‐law term with an undetermined exponent ‘‘γ’’ are used. Since the calculated eigenvalue constitutes an upper bound, by minimizing it with respect to γ, one is able to improve the value of the frequency coefficient. A lower bound is then determined using the method of traces. It is shown that both sets of results, upper and lower bounds, are quite close and are also in agreement with the numerical results obtained by means of a finite element algorithm.