A Study on Vibration Reduction of the Torsional-Vibration Responses of A Uniform Beam Subjected To An Eccentric Moving Force

Jia-Jang Wu

The conventional single degree-of-freedom (dof) vibration absorber is a widely used device for suppressing the (vertical or horizontal) flexural-vibration responses of a structure induced by dynamic loads. Thus, the relating information is abundant. However, because the device for suppressing the torsional-vibration responses of a structure is rare, the relating literature is limited. The objective of this paper is to determine the optimal parameters for a two-dof vibration absorber such that the torsional-vibration responses of a structure due to dynamic loads can be effectively suppressed. To this end, the equations of motion for a two-dof vibration absorber and the generalized main vibration system corresponding to a certain predominant mode shape of the beam will be firstly derived using the theory of Lagrange's equations. Then, based on the dynamic magnification factor for the rotational dof of the last generalized main vibration system, the optimal parameters of the aforementioned two-dof vibration absorber will be determined. Numerical investigations concerning the use of two-dof vibration absorber for suppressing the rotational-vibration responses of the generalized main vibration system due to dynamic loads will then be conducted. Finally, based on the mode superposition principle, the foregoing technique will be extended to suppress the torsional-vibration responses of a uniform beam subjected to an eccentric moving force. Because, in addition to the torsional-vibration responses, the presented two-dof vibration absorber can also suppress the flexural-vibration responses of the structure to some degree, its functions should be greater than those of the conventional single-dof absorber.