Reduction Techniques of Vibration in Curved Beams Using Negative Group Velocity

Abstract

The dispersion curve of an extensional wave of a curved beam has negative slope at a restricted frequency region. A wave packet which is synthesized by more than two extensional waves at the region of negative slope has negative group velocity. This paper addresses an issue of engineering application of the negative group velocity. Firstly, the horizontal axis of dispersion curve was normalized as a dimensionless frequency to specify the frequency region of negative slope. Then, a structure to allow negative group velocity was designed as a U-shaped beam based on the normalized dispersion curve, and waves on the beam was verified using transient response analysis of a finite element model. Validation was carried out from the standpoint of both negative group velocity and backward movement of structural intensity. The results show that wave energy in a curved beam does not propagate in the positive direction along the axial direction.