This article examines the free size-dependent vibration behaviour of an Euler–Bernoulli type double-microbeam system, made of two microbeams elastically connected, with simply supported, clamped–clamped and clamped–pinned boundary conditions using an assumed-mode expansion technique (AMET) along with finite-element verifications; effects of altering the couple-stress-tensor-related parameter and the stiffness coefficient of the elastic connection are studied. The double-microbeam problem is formulated nonlinearly utilising Hamilton’s principle, alongside the modified couple stress theory (MCST), and energy terms. Employing the AMET, the free vibration characteristics were obtained through solving motion equations. For the double-microbeam system and the elastic connection, a finite-element method (FEM) based model and simulations are developed which enabled us in a partial verification of our results; the agreement is excellent. Moreover, another set of partial verifications is performed with available data in the literature by neglecting one of the microbeams and the spring connection. The study revealed increasing either the couple-stress-tensor-related parameter or stiffness coefficient of the elastic connection increases the natural frequencies of the double-microbeam system. It is also found that both the microbeams vibrate in the same manner in the first mode expansion and out of phase by 180° in the second mode expansion. Altering the boundary effect from pinned–pinned to clamped–pinned, and again to clamped–clamped was found to increase the natural frequencies of the double-microbeam system accordingly.

本文研究了由欧拉–伯努利类型的双微束系统的自由尺寸相关的振动行为，该系统由两个微束弹性连接而成，并采用假定模式展开技术（AMET）简单地支撑，夹紧-夹紧和夹紧-钉扎边界条件）以及有限元验证；研究了改变耦合应力-张量相关参数和弹性连接的刚度系数的影响。利用汉密尔顿原理，改进的耦合应力理论（MCST）和能量项，非线性地解决了双微束问题。使用AMET，通过求解运动方程获得自由振动特性。对于双微束系统和弹性连接，开发了基于有限元方法（FEM）的模型和仿真，这使我们能够部分验证我们的结果；协议很棒。此外，通过忽略微梁和弹簧连接中的一个，利用文献中的可用数据执行另一组部分验证。研究表明，增加与耦合应力张量相关的参数或增加弹性连接的刚度系数都会增加双微梁系统的固有频率。还发现，两个微束在第一模式扩展中以相同的方式振动并且在第二模式扩展中异相180°。发现将边界效应从“钉扎”变为“钉扎”，再到“钉扎”，会相应地增加双微束系统的固有频率。