Free Vibration of Compliant Mechanisms Based on Euler-Bernoulli-Beams

This paper presents an analytical approach for computing the natural frequencies of planar compliant mechanisms consisting of any number of beam segments. The approach is based on the Euler-Bernoulli Beam theory and the transfer matrix method (TMM), which means there is no need for a global dynamics equation, but instead low-order matrices are used which result in high computational efficiency. Each beam segment is elastic, thin, has a different rectangular cross-section or a different orientation and is treated as an Euler-Bernoulli beam. The approach in principle does not differentiate between the flexure hinges, and the more rigid beam sections, both are treated as beams. The difference in stiffness solely results from the changes in the cross sections and length. A finite element analysis (FEA), as often used in practical applications, has been carried out for various geometries to serve as state-of-the-art reference models to which the results obtained by the presented analytical method could be compared. Various test specimens (TS) consisting of concentrated and distributed compliance in various degrees of complexity were produced and measured in free- and forced vibration testing. The results from experiments and the FEA compared to those of the proposed method are in very good correlation with an average deviation of 1.42%. Furthermore, the analytical method is implemented into a readily accessible computer-based calculation tool which allows to calculate the natural frequencies efficiently and to easily vary different parameters.