Analyzing free vibration of a beam-type liquid micro-pump with free boundary approach

Abstract

The purpose of this article is the comprehensive analysis of free vibration of beam-type liquid micro-pump with a free boundary approach. Besides the liquid loading on the micro-beam, the kinematic compatibility between liquid and micro-beam is modeled according to the free boundaries. Galerkin and separation of variables methods are employed to solve these equations. Based on the nonlinear nature of the equations, the Newmark method is applied to obtain the normal frequencies, mode shapes, and the fluid oscillation of the coupled system. The aim of this model is to achieve the exact results for the small oscillations of micro-beam in the liquid container. Comparing the free and fixed boundary method reveals that for small oscillation of Euler–Bernoulli micro-beam, there is a slight deviation on the natural frequency, which can be negligible.