Abstract
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.
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