Fundamental Transverse Vibration Circular Frequency of a Cantilever Beam with an Intermediate Elastic Support

The problem of analyzing the dynamic vibration of a uniform beam was widely investigated in the scientific literature where various numerical methods were considered. The objective of the present study is to investigate the fundamental transverse vibration circular frequency ω1 of a cantilever beam with an intermediate elastic support of variable abscissa a. The analysis is based on the Euler–Bernoulli assumptions and carried out by using the finite element method (FEM). The validation concerned the fixed-free and fixed-pinned ends conditions of the beam. After this, the investigation was conducted by varying both the spring stiffness value from zero to infinite and the abscissa a from 0 to L. Different values of the fundamental circular frequency ω1 are determined for describing the dynamic behavior of the current vibrating beam system. The plotted curves show the variations of the transverse vibration circular frequency ω1 depending on the beam intermediate support location and stiffness.