Free vibrations of microplates with non‐classical shape are considered in the paper. Governing equations are based on the modified couple stress theory and Kirchhoff–Love plate theory. It is assumed that the plate is isotropic or orthotropic and satisfy various boundary conditions. An analysis is performed by the variational‐structural method which is based on R‐functions theory and Ritz method. The testing of the proposed method is carried out by comparison with known in literature results and analytical solutions. The developed method is applied to the study of the influence of the material length scale parameter, boundary conditions, shape parameters, material characteristics on vibration frequencies. Also, size‐dependent analysis for buckling of the isotropic and orthotropic microplate subjected to uniaxial load is performed by the proposed approach. Critical loads for a plate with complex shape, different types of boundary conditions and material are calculated in order to study their effect on buckling.

中文翻译：

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基于修正耦合应力理论的形状复杂的正交异性小尺寸板的振动与屈曲

本文考虑了非经典形状的微孔板的自由振动。控制方程基于改进的耦合应力理论和基尔霍夫-洛夫板理论。假定板是各向同性或正交各向异性的，并且满足各种边界条件。通过基于R的变分结构方法进行分析功能理论和Ritz方法。通过与文献结果和分析解决方案进行比较，对提出的方法进行了测试。该方法用于研究材料长度尺度参数，边界条件，形状参数，材料特性对振动频率的影响。同样，通过提出的方法对各向同性和正交各向异性微板在单轴载荷下的屈曲进行了尺寸依赖性分析。计算具有复杂形状，不同类型的边界条件和材料的板的临界载荷，以研究其对屈曲的影响。