Relationships between Existence of Negative Group Velocity and Physical Parameters of Materials for Lamb-Type Waves in Solid/Liquid/Solid Structure

We considered the negative group velocity of plate-mode waves. Lamb waves are a typical example of existence of negative group velocity. However, if we try to apply the negative group velocity of Lamb waves to some applications such as acoustical flat lenses, there is a problem about the existence of negative group velocity of Lamb waves. Its existence depends only on Poisson's ratio. That is, the negative group velocities of Lamb waves depend only on physical parameters of materials. Consequently, we considered to control a negative group velocity. The negative group velocity of Lamb-type waves in a solid/liquid/solid structure can be controlled by changing the thickness of a liquid layer. In this research, we considered the relationships between the existence of negative group velocities and the parameters of each layer material with respect to Lamb-type waves in a solid/liquid/solid structure by numerical calculation. As a result, it was confirmed that the negative group velocity of Lamb-type waves depended not only on Poisson's ratio but also on the density of each layer and the longitudinal wave velocity of the liquid layer. This result is useful when the negative group velocity of Lamb-type waves is applied to acoustical flat lenses, which require the negative group velocity.