Low Frequency Longitudinal Vibrations of an Elastic Bar Made of a Dynamic Material and Excited at One End

The dynamic materials, particularly the spatio-temporal composites, have been investigated in a number of recent publications. In the present paper, we examine a dynamic performance of an elastic bar with material parameters specified as an activated (moving at uniform velocity V ) periodic pattern of segments occupied by ordinary materials 1and 2, with density ρ and stiffness k specified as ρ1 k1 and ρ2 k2 , respectively. We particularly consider the low frequency wave propagation arising when the period d of the material pattern is much less than the wavelength λ of a dynamic disturbance. The bar is excited at its left end by a signal g t