Active Meta Materials and the Change of the Path of Elastic Waves and Blast Waves

The concept of a negative refractive index stimulated research activity in 1960s. One researcher showed that it is possible to realize negative refractive index if we have a material that can have simultaneous negative electric permeability and negative magnetic permittivity, at the same frequency. At that time, no such material was available. After three decades, several physicists started to explore the possibility of using meta materials to achieve the objective. Meta materials are materials with specially designed internal structure. They extended the research further to design a coordinate transformation technique, with distributed permeability and permittivity to steer the optical wave in any desired path. It was difficult to achieve these objectives because the optical wave lengths are very small. Then, the interest shifted to impacting elastic waves where the wave lengths are large. However, the goal of steering the wave required a new distribution of the elastic modulus and a new distribution of density, in the material after active meta material control. In this paper, a method of achieving such a distribution by using active meta materials and the associated control procedures is presented. Three basic structures are considered. They are the structures that resist flexural vibrations, longitudinal waves and torsional waves. All three cases result in identical active meta material control equations and control procedures with different natural frequencies that are functions of both the density and elastic constants.