In this paper, a new beam element based on third-order Reddy beam theory and modified couple stress theory is introduced for static and dynamic analyses of microbeams. The beam is resting on Kelvin–Voigt-type viscoelastic foundation. Equilibrium equations are derived by using Hamilton’s principle. Galerkin finite element method is applied to the governing equations, and shape functions of the new beam element have been derived. As a result, applying only six elements are suitable for assessing beam behavior precisely, and it is beneficial due to the reduction in computation time. The proposed element is a two-node element with 4 degrees of freedom at each node. The effect of different stiffness and damping of viscoelastic foundation, boundary condition and length parameters on natural frequency and transient response of the microbeam is investigated.

中文翻译：

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基于修正耦合应力和三阶梁理论的粘弹性基础微梁静态、自由和受迫振动响应的新梁单元

在本文中，基于三阶 Reddy 梁理论和修正的偶应力理论引入了一种新的梁单元，用于微梁的静态和动态分析。梁位于 Kelvin-Voigt 型粘弹性基础上。平衡方程是利用哈密顿原理推导出来的。将伽辽金有限元方法应用于控制方程，推导出新梁单元的形函数。因此，仅应用六个元素适合精确评估梁的行为，并且由于减少了计算时间而有益。建议的单元是一个双节点单元，每个节点有 4 个自由度。粘弹性地基不同刚度和阻尼的影响，