In the current work, we study the role of higher-order and micro-inertia contributions on the mechanical behavior of composite structures. To that scope, we compute the complete set of the effective static and dynamic properties of composite beam structures using a higher-order dynamic homogenization method which incorporates micro-inertia effects. We consider different inner composite element designs, with material constituents that are of relevance for current engineering practice. Thereupon, we compute the effective static longitudinal higher-gradient response, quantifying the relative difference with respect to the commonly employed, Cauchy-mechanics formulation. We observe that within the static analysis range, higher-order effects require high internal length values and highly non-linear strain profile distributions for non-negligible higher-order effects to appear. We subsequently analyze the longitudinal, higher-gradient eigenfrequency properties of composite structural members, accounting for the role of micro-inertia contributions. Thereupon, we derive analytical expressions that relate the composite material's effective constitutive parameters with its macroscale vibration characteristics. We provide for the first-time evidence that micro-inertia contributions can counteract the effect of second-gradient properties on the eigenfrequencies of the structure, with their relative significance to depend on the mode of interest. What is more, we show that the internal length plays a crucial role in the significance of micro-inertia contributions, with their effect to be substantial for low, rather than for high internal length values, thus for a wide range of materials used in engineering practice.

在当前的工作中，我们研究了高阶和微惯性对复合结构力学行为的作用。在此范围内，我们使用包含微惯性效应的高阶动态均质化方法来计算复合梁结构的有效静态和动态特性的完整集合。我们考虑不同的内部复合元件设计，并采用与当前工程实践相关的材料成分。随即，我们计算了有效的静态纵向较高梯度响应，从而量化了相对于常用的柯西力学公式的相对差。我们观察到在静态分析范围内，高阶效应需要较高的内部长度值和高度非线性的应变分布，以便出现不可忽略的高阶效应。随后，我们分析了复合结构构件的纵向，较高梯度的本征频率特性，并考虑了微惯性贡献的作用。因此，我们得出了将复合材料的有效本构参数与其宏观振动特性联系起来的解析表达式。我们首次提供了微惯性贡献可以抵消次梯度特性对结构本征频率的影响的证据，其相对重要性取决于感兴趣的模式。而且，我们证明内部长度在微惯性贡献的重要性中起着至关重要的作用，