In the present paper, for the first time, theoretical analysis for static, dynamic, and transient responses of micro-plates made of different materials were comprehensively performed. The constitutive relations of analyzed materials satisfy assumptions of the modified couple stress theory. Additionally, values of length scale parameters of studied materials are taken from well-established experimental results presented in the literature. A generalized model of micro-plates made from Cu, Ni, Ti, and Epoxy satisfies assumptions of Reissner–Mindlin plate theory. The formulated generalized boundary value problem is solved by analytical and the radial basis function finite difference (RBF-FD) methods. A convergence study is performed to show the advantages and correctness of the obtained numerical solution. The meshless numerical method is easy to implement and it provides accurate results that are in excellent agreement with analytical solutions. Effects of material parameters, boundary conditions, and assumptions of classical and the modified couple stress theory on the static bending, free vibration and transient responses of micro-plates are presented and discussed.

本文首次对不同材料微板的静态、动态和瞬态响应进行了综合理论分析。分析材料的本构关系满足修正偶应力理论的假设。此外，所研究材料的长度尺度参数值取自文献中提出的成熟的实验结果。由 Cu、Ni、Ti 和环氧树脂制成的微板的广义模型满足 Reissner-Mindlin 板理论的假设。通过解析和径向基函数有限差分（RBF-FD）方法解决了公式化的广义边值问题。进行收敛性研究以显示所获得数值解的优点和正确性。无网格数值方法易于实施，它提供了与解析解非常一致的准确结果。介绍和讨论了材料参数、边界条件以及经典和修正耦合应力理论对微板静态弯曲、自由振动和瞬态响应的假设的影响。