A computational homogenization framework is presented to study the dynamics of locally resonant acoustic metamaterial structures. Modelling the resonant units at the microscale as representative volume elements and building on well-established scale transition relations, the framework brings as a main novelty a reduced-order macroscopic homogenized continuum whose governing equations involve no additional variables to describe the microscale dynamics unlike micromorphic homogenized continua obtained by alternative computational homogenization approaches. This model-order reduction is obtained by formulating the governing equations of the micro- and macroscale problems in the frequency domain, introducing a finite-element discretization of the two problems and performing an exact dynamic condensation of all the degrees of freedom at the microscale. An appropriate inverse Fourier transform approach is implemented on the frequency-domain equations to capture transient dynamics as well; notably, the implementation involves the Exponential Window Method, here applied for the first time to calculate the time-domain response of undamped locally resonant acoustic metamaterial structures. The framework may handle arbitrary geometries of micro- and macro-structures, any transient excitations and any boundary conditions on the macroscopic domain.

提出了计算均质化框架来研究局部谐振声学超材料结构的动力学。该框架将微尺度上的谐振单元建模为代表性体积元素，并建立在完善的尺度转换关系的基础上，带来了一个主要的新颖性，即降阶宏观均质连续体，其控制方程不涉及额外的变量来描述微尺度动力学，这与微形态均质化不同。通过替代计算均质化方法获得的连续体。这种模型降阶是通过在频域中制定微观和宏观问题的控制方程、引入两个问题的有限元离散化以及在微观尺度上对所有自由度进行精确的动态压缩来获得的。在频域方程上实施适当的傅里叶逆变换方法来捕获瞬态动态；值得注意的是，该实现涉及指数窗法，该方法首次应用于计算无阻尼局部谐振声学超材料结构的时域响应。该框架可以处理微观和宏观结构的任意几何形状、任何瞬态激励以及宏观域上的任何边界条件。