Free Vibration Analysis of a Stepped Cantilever Beam with a Mass and a Spring at the End

끝단에 스프링과 질량을 가진 단진보의 자유진동해석

  • Published : 1996.09.01


A cantilever beam with a mass and a spring at the end can be use to model a miniature flexible arm. It is necessary to know the natural frequencies and mode shapes to discuss its free vibration, especially when modal analysis is employed. A beam is clamped-free. In this paper we look at the lateral vibration of beams that have step changes in the properties of their cross sections. The frequency equation is derived by Bernoulli-Euler formulation and is sloved by the separation of variable. The parameters of the beam, 'mass and spring stiffness' are defined as nondimensionalized parameters for wide application of the results. According to the change of eigenvalues and mode shape are presented for this beam. The results presented are the eigenvalues and the natural frequencies for the first three modes of vibration. Results show that the parameters have a significant effect on the natural frequency.


Frequency;Mode Shape;Bernoulli-Euler Formulation;Piezoelectric Bimorph Cells