A new approach to the mechanical response of micro-mechanic problems is presented using the modified couple stress theory. This model captured micro-turns due to micro-particles' rotations which could be essential for microstructural materials and/or at small scales. In a micro media based on the small rotations, sub-particles can also turn except the whole domain rotation. However, this framework is competent for a static medium. In terms of dynamic investigations of micro materials, it is required to involve micro-rotations' mass inertias. This fact persuades us to pay particular attention to the micro mechanics' samples and directed us to re-derive the modified couple stress model to propose and represent a new micro-mechanic approach which is well-deserved, especially for dynamic studies of microstructures. In carrying out this job, the classical beam has provided the basic form of formulation procedure. The continuum medium has been limited to a square flat non-porous beam deducing a homogeneous isotropic micromaterial. As long as the time-dependent results are concerned due to studying micro-mass inertia in time history, there would be two solution steps. The Galerkin decomposition technique is imposed in accord with an analytical postulate to issue the algebraic problem distributing time-dependent equations. The latter, the Homotopy perturbation method delivers time-dependent outcomes. The solution methods have been validated by building numerical models in Abaqus software. On the new achievements of this study, one can declare that both static and dynamic length scale parameters are very effective in order to study vibrations of microstructures. If the values of these characteristic lengths are considerable, the nonlinear frequency analysis will be essential. Furthermore, the stiffness of the structure will be higher if the values of both length scale parameters increase.

使用修正的耦合应力理论提出了一种解决微机械问题的机械响应的新方法。该模型捕获了由于微粒的旋转而产生的微转，这对于微观结构材料和/或小尺度来说可能是必不可少的。在基于小旋转的微介质中，除了全域旋转外，子粒子也可以旋转。然而，这个框架适用于静态媒体。在微观材料的动力学研究中，需要涉及微观旋转的质量惯性。这一事实促使我们特别关注微观力学样本，并指导我们重新推导修改后的耦合应力模型，以提出并代表一种当之无愧的新微观力学方法，尤其是对于微观结构的动态研究。在开展这项工作时，经典梁提供了制定程序的基本形式。连续介质仅限于方形扁平无孔梁，推导出均匀各向同性微材料。只要研究时间历程中的微质量惯性，只要关注随时间变化的结果，就会有两个求解步骤。伽辽金分解技术是根据分析假设施加的，以发布代数问题分布的时间相关方程。后者，同伦微扰方法提供时间相关的结果。求解方法已通过在 Abaqus 软件中建立数值模型得到验证。根据这项研究的新成果，可以说静态和动态长度尺度参数对于研究微结构的振动都非常有效。如果这些特征长度的值相当大，则非线性频率分析将是必不可少的。此外，如果两个长度尺度参数的值都增加，则结构的刚度会更高。