Technique for Estimating Natural Frequencies

The so-called Rayleigh-Ritz direct variational method for the determination of constant coefficients of assumed shape functions has been generalized by the introduction of arbitrary parameters in the shape functions and then illustrated by means of several simple examples of freely vibrating beams and a plate. The arbitrary parameters are determined by minimizing the natural frequency by the rules of differential calculus or by a number of trial calculations, in difficult problems. Although the calculational labor is greater in the applications of the proposed technique than in the common Rayleigh-Ritz method, the technique offers some advantages in regard to accuracy and flexibility. The proposed technique can also be used for estimating Saint-Venant's torques, bifurcation loads on columns and plates, and other eigenvalues.