Document Type : Article

**Authors**

School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

**Abstract**

In the current study, an analytical solution based on the modified couple stress theory for a nonlinear model describing the couple 3D motion of a functionally graded tapered micro-bridge is presented. The small scale effects and the nonlinearity arising from the mid-plane stretching are taken into consideration. Governing equations of motions are derived utilizing the modified couple stress theory and applying Hamilton principle. Dynamic and static analyses to determine the effects of lateral distributed forces and mid-plane stretching are investigated. To this aim, analytical Homotopy-pade technique is employed to capture the nonlinear natural frequencies in high amplitude vibrations of tapered micro-bridges with different types of geometries and material compositions. The obtained results of frequencies propose that there is a good agreement between the present analytical results and the numerical ones in opposed to well-known multiple-scale method. Furthermore, comparing the results in 2D and 3D analyses shows that in 2D analysis, the stiffness and natural frequency of the micro-beam is underestimated and it is found that increasing the tapered ratio has different impacts on natural frequencies for micro-beams with different slender ratios.

**Keywords**

**Main Subjects**

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