Phononic crystals and elastic metamaterials have recently received significant attention due to their potential for unconventional wave control. Despite this interest, one outstanding issue is that their band diagram is typically fixed once the structure is designed. To overcome this limitation, periodic structures with adaptive elastic properties have recently been proposed for Bragg- and local resonance-driven structures.

In this context, we report about the effect of an applied external mechanical load on a periodic structure exhibiting band gaps induced by inertial amplification mechanism. If compared to the cases of Bragg scattering and ordinary local resonant metamaterials, we observe here a more remarkable curve shift, modulated through large but fully reversible compression (stretch) of the unit cell, eventually triggering significant (up to two times) enlargement (reduction) of the width of a specific band gap. An important up (down)-shift of some dispersion branches over specific wavenumber values is also observed, showing that this selective variation may lead to negative group velocities over larger (smaller) wavenumber ranges. In addition, the possibility for a non-monotone trend of the lower limit of the first BG under the same type of external applied prestrain is found and explained through an analytical model, which unequivocally proves that this behaviour derives from the different unit cell effective mass and stiffness variations as the prestrain level increases. These peculiarities derive from the hinge-like behaviour of some regions of the unit cell, which is typical of structures exhibiting the inertial amplification mechanism.

The effect of the prestress on the dispersion diagram is investigated through the development of a 2-step calculation method: first, an Updated Lagrangian scheme, including a static geometrically nonlinear analysis of a representative unit cell undergoing the action of an applied external load is derived, and then the Floquet-Bloch decomposition is applied to the linearized equations of the acousto-elasticity for the unit cell in the deformed configuration.

Finally, the most evident consequence on the dispersion curves of the application of an external prestress, i.e. the band gap shift with respect to the unloaded structure, is demonstrated through nonlinear transient numerical simulations, clearly proving the capability of the structure to switch from a pass- to a stop-band behaviour over the same frequency range.

The results presented herein provide insights in the behaviour of band gaps induced by inertial amplification, and suggest new opportunities for real-time tunable wave manipulation.

声子晶体和弹性超材料由于其非常规波控制的潜力，最近受到了广泛的关注。尽管有这种兴趣，但一个突出的问题是，一旦设计了结构，它们的能带图通常就固定了。为了克服该限制，最近已提出具有自适应弹性的周期性结构用于布拉格和局部共振驱动的结构。

在这种情况下，我们报告了施加的外部机械载荷对周期性结构的影响，该周期性结构表现出由惯性放大机制引起的带隙。如果与布拉格散射和普通的局部共振超材料的情况相比，我们在这里观察到了更显着的曲线位移，该位移通过晶胞的大但完全可逆的压缩（拉伸）进行调制，最终触发了显着的（最多两倍）的增大（减小）。 ）特定带隙的宽度。还观察到一些分散分支在特定波数值上的重要的上移（下移），表明该选择性变化可能导致较大（较小）波数范围内的负群速度。此外，通过分析模型发现并解释了在相同类型的外部施加的预应力下第一个BG下限的非单调趋势的可能性，并明确地证明了这种行为源自不同的晶胞有效质量和刚度变化随着预应力水平的提高。这些特性来自于晶胞某些区域的铰链状行为，这是表现出惯性放大机制的结构的典型特征。

通过开发一种两步计算方法来研究预应力对色散图的影响：首先，得出一种更新的拉格朗日方案，其中包括对承受外加载荷作用的代表性晶胞进行静态几何非线性分析。 ，然后将Floquet-Bloch分解应用于变形构型中晶胞的声弹性线性方程。

最后，通过非线性瞬态数值模拟证明了施加外部预应力时色散曲线的最明显结果，即带隙相对于未加载结构的位移，清楚地证明了结构从通过转换的能力-在相同频率范围内的阻带行为。

本文介绍的结果提供了对由惯性放大引起的带隙行为的见解，并为实时可调波操纵提出了新的机会。