A rigid multibody method for free vibration analysis of beams with variable axial parameters

Abstract

This paper presents a new approach to the problem of determining the frequencies and mode shapes of Euler-Bernoulli tapered cantilever beams with a tip mass and a spring at the free end. The approach is based on the replacement of the flexible beam by a rigid multibody system. Beams with constant thickness and exponentially and linearly tapered width, as well as double-tapered cantilever beams are considered. The influence of the tip mass, stiffness of the spring, and taper on the frequencies of the free transverse vibrations of tapered cantilever beams are examined. Numerical examples with results confirming the convergence and accuracy of the approach are given.

Free vibration analysis of axial-loaded beams with variable cross sections and multiple concentrated elements

“…However, only concentrated mass was considered. Nikolić and Šalinić (2016) used a rigid multibody method to study the free vibration of beams with variable axial parameters, and the influence of linear spring and concentrated mass are considered. By including the linear spring, rotational spring, and concentrated mass, Wu and Chen (2008) used the transfer matrix method to assess the free vibration characteristics of uniform or multistep uniform beams, after which Boiangiu et al (2014) used the transfer matrix method to evaluate the natural frequency of conical beams and a multistep variable-section beam.…”