Modal energy transfer of a curved beam as a damping mechanism

Abstract

Curved structure is usually used in modern structural design such as airplane and roofs because of its higher transverse stiffness, less aerodynamic resistance and a better architectural appearance than a flat plate. Autoparamteric vibration of a curved beam is initiated when the excitation frequency is near the resonant frequency of the first symmetric mode and the contribution of the first anti-symmetric mode is significant, even though the excitation on the curved beam is symmetrical. The autoparametric phenomenon of curved beam is proposed to suppress the vibration magnitude of first symmetric mode of beam itself. The curved beam is also proposed to be a vibration damping device with controllable bandwidth. The curved beam exposed to periodic and snap-through motion will also be examined. Autoparamteric behaviour of the curved beam is investigated analytically, numerically and verified experimentally. The extensive results in this study can have three significant findings established. The first one is that the non-absorption region of the 1st symmetric mode can be reduced by adding mass onto the curved beam to adjust the resonance frequency of the first anti-symmetric mode (dip point of the transition curve). The second one is that the resonance frequency of the first anti-symmetric mode can be altered to control the operational frequency range. The autoparametric vibration response can be applied to create an energy-dissipative region with a controllable bandwidth. It is also possible to create a non-dissipative region in between two dissipative regions. This is useful for providing damping for a conventional dynamic absorber without adding high damping material. The damping is due to dissipation of energy to the anti-symmetric mode. The third one is that the snap-through motion of a curved beam can also be utilized as a damping device due to the large energy dissipation. The critical load for the snap-through motion of a simply supported curved beam under impulsive loading can be predicted by simple formula using energy balance method in two-mode analysis. For a known excitation loading, there are two important factors to be considered in the design of the curved beam to be a damping device. i) The curvature of the beam cannot be too high so that the excitation force can be above the critical load for the snap-through motion .The critical load can be reduced by 77% for q0=5.657 and if the anti-symmetric mode is excited. ii) There should be large anti-symmetric mode response during the snap-through motion, so that the strain energy due to snap-through will be high enough for energy dissipation. Therefore the curvature of the beam cannot be too low. Combining the above two conditions, there is an optimum curvature for which the snap-through motion can be excited and the strain energy can be maximized.