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We report the results of the calculation of negative effective density and negative effective compliance for a layered composite. We show that the frequency-dependent effective properties remain positive for cases which lack the possibility of localized resonances (a 2-phase composite) whereas they may become negative for cases where there exists a possibility of local resonance below the length-scale of the wavelength (a 3-phase composite). We also show that the introduction of damping in the system considerably affects the effective properties in the frequency region close to the resonance. It is envisaged that this demonstration of doubly negative material characteristics for 1-D wave propagation would pave the way for the design and synthesis of doubly negative material response for full 3-D elastic wave propagation

Negative effective dynamic mass-density and stiffness: Micro-architecture and phononic transport in periodic composites