Non-uniform Euler-Bernoulli beams’ natural frequencies

Abstract

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 WentzelKramers-Brillouin (WKB) method. It was established that WKB formula precision was higher than 3% for high frequencies (≥ 4 mode).

En el presente trabajo se estudia el problema de frecuencias propias de la viga Euler-Bernoulli de sección no uniforme; se comparan las soluciones del problema obtenidas numéricamente con la solución asintótica lograda mediante el método Wentzel-Kramers-Brillouin (WKB). Se establece que la precisión de las fórmulas WKB es mayor del 3% para frecuencias altas (número de modo ≥ 4).