A Semi-Analytical Method to Design Distributed Dynamic Vibration Absorber of Beam Under General Elastic Edge Constraints

Abstract

In engineering practice, dynamic vibration absorber is an effective method to control vibration of beam structure. The mathematical model of beam coupled with spring–mass systems under elastic edge constraints is established in this paper. In addition to Fourier cosine series, supplementary sine functions are introduced to represent the displacement function of the beam. The spring–mass system is considered by increasing degrees of freedom when constructing the mass matrix and stiffness matrix. The efficiency of solving equivalent mass is greatly improved in the comparison with FEM, which is important when designing dynamic vibration absorber. Subsequently, we conduct parametric analysis of the control effect about the dynamic vibration absorber based on the current mathematical model. The procedure of designing distributed dynamic vibration absorber of beam structure under various boundary condition is also presented. To verify the validity of the current mathematical model and design procedure, a cantilever beam experiment was conducted. The findings presented in the current research may be useful for researchers in the process of multi-line spectrum vibration control of beam structure.