Frecuencias propias de vigas Euler-Bernoulli no uniformes

this paper has studied the problem of natural frequencies for euler-bernoulli beams having non-uniform crosssection. the numerically-obtained solutions were compared to asymptotic solutions obtained by the wentzel-kramers-brillouin (wkb) method. it was established that wkb formula precision was higher than 3% for high frequencies (≥ 4 mode).