An Improved Unified Solution for a Vibration Equation of Tension-Stiffening Beam Using Extended Rayleigh Energy Method

The tension-stiffening effect is very important for physical science, which has been widely used in MEMS, sensors and micro-motion stages. The analytical solutions of the tension-stiffening beam are extremely significant, in consideration of the inefficiency of finite element analysis (FEA) for the design and optimization. Commonly, there are three typical types of boundary conditions for tension-stiffening (or stress-induced) beams, i.e., clamped-clamped, clamped-hinged, and hinged-hinged. But only the hinged-hinged beam has an analytical solution. Therefore, a method based on extended Rayleigh energy method is proposed in this paper to deduce the analytical solutions of three boundary conditions. The predictions are verified to be in good agreement with FEA and experiment results.