Free Vibration of a Cantilever Euler-Bernoulli Beam Carrying a Point Mass by Using SEM

Abstract

The objective of this research is to study the free vibration of a cantilever Euler-Bernoulli beam carrying a point mass with moment of inertia at the free end using the spectral element method (SEM). Typically, the shape (or interpolation) functions used in the Spectral element method are derived from exact solutions of the governing differential equations of motion in the frequency domain. The beam was discretized by a single spectral element which was connected by a point mass at the free end. The dynamic stiffness matrix of the beam is formulated in frequency domain by considering compatibility conditions at the additional mass position. Then, the first three natural frequencies of the cantilever beam are determined. After the validation of the spectral element method, the influence of the non-dimensional mass parameter and the non-dimensional mass moment of inertia on the first three natural frequencies and shape mode are examined.