This paper focuses on small-size planar beam lattices, where size effects are modelled by the stress-driven nonlocal elasticity theory in conjunction with the Rayleigh beam theory. The purpose is to propose two novel computational approaches for elastic wave propagation analysis. In a first dynamic-stiffness approach, every lattice member is modelled by a unique two-node beam element, the exact dynamic-stiffness matrix of which is built solving, in concise analytical form, the stress-driven differential equations of motion. In a second finite-element approach, every lattice member is discretized by an increasingly refined mesh of two-node beam elements; in this case, the stiffness and mass matrices of the lattice member are obtained from shape functions built based on the exact solutions of the stress-driven differential equations for static equilibrium. Advantages of the two approaches are compared and discussed. Dispersion curves are calculated for a typical planar lattice, highlighting the role of nonlocality.

本文侧重于小尺寸平面梁晶格，其中尺寸效应通过应力驱动的非局部弹性理论结合瑞利梁理论进行建模。目的是为弹性波传播分析提出两种新颖的计算方法。在第一种动态刚度方法中，每个晶格成员都由一个独特的双节点梁单元建模，构建其精确的动态刚度矩阵，以简明的分析形式求解应力驱动的运动微分方程。在第二种有限元方法中，每个晶格成员都通过日益细化的双节点梁单元网格离散化；在这种情况下，晶格构件的刚度和质量矩阵是从基于静态平衡应力驱动微分方程的精确解构建的形状函数中获得的。比较和讨论了这两种方法的优点。色散曲线是针对典型的平面晶格计算的，突出了非局域性的作用。