Flutter Instability of Timoshenko Cantilever Beam Carrying Concentrated Mass on Various Locations

Abstract

This paper presents effects of shear deformation on flutter instability of cantilever beam subject to a concentrated follower force. The discrete form of equation of motion is formulated based on the Lagrange. In the presented formulation, the beam is modeled using Timoshenko beam theory, and constant shear distribution through the thickness of the beam is considered. Consistent interpolation scheme is adopted to avoid the shear locking for thin beams. Consequently, convergence of the finite element simulation is enhanced. The effect of rotary inertial term is considered in the flutter study, which has significant influence on the beam behavior as the beam thickness increases. The axial degrees of freedom are taken into account in energy expressions, to improve the accuracy of the results. Results presented for different beam geometries. The numerical results show high efficiency and good convergence characteristic. The effect of concentrated mass on the flutter instability of beam is considered and results are presented for various locations and values of concentrated masses. Furthermore, the shear effects are highlighted in this study by comparing the results obtained from the Euler-Bernoulli with those obtained from the Timoshenko beam model.

Biohybrid generators based on living plants and artificial leaves: influence of leaf motion and real wind outdoor energy harvesting

“…Changing the position of the concentrated mass on the artificial leaf is also expected to have an influence on the outcome. A concentrated mass has been shown to increase or decrease the critical flutter force of a beam depending on its location on the beam [30]. We have also observed that not only vertical but also torsional oscillations can occur that are caused by the combination of the blade and thin petiole in the natural leaf and the current design of the artificial leaf.…”