It is shown that the continuum limit of the metamaterial mass-in-mass model with additional attached mass describes not only the appearance of the additional band gap but also variations in the width and the position of the band gaps. These variations are governed by the key parameter—the stiffness ratio of the attached masses. Numerical study of periodic boundary excitation of the harmonic waves reveals suppression of the harmonic waves for the frequencies lying inside the both band gap areas. Also it is found that harmonic waves recover differently for the frequencies below and above the band gap values. The control mechanism is developed based on the abrupt variation of the stiffness ratio. It gives rise to the arising of phase shift of the wave, its suppression or recovery of the previously suppressed harmonic wave. Nonlinear long wavelength generalization of the model results in obtaining the model equation whose coefficients differ from those of the usual nonlinear mass-in-mass model. It gives rise to propagation of the localized wave with another amplitude and velocity.

结果表明，具有附加附加质量的超材料质量质量模型的连续极限不仅描述了附加带隙的出现，还描述了带隙宽度和位置的变化。这些变化由关键参数——附着质量的刚度比决定。谐波周期性边界激励的数值研究揭示了对位于两个带隙区域内的频率的谐波的抑制。还发现对于低于和高于带隙值的频率，谐波恢复不同。该控制机制是基于刚度比的突变而开发的。它引起波的相移、其抑制或先前抑制的谐波的恢复。模型的非线性长波长推广导致获得的模型方程的系数不同于通常的非线性质中质量模型的系数。它引起局域波以另一种振幅和速度传播。