Constrained Green’s Function for a Beam with Arbitrary Spring and Nonlinear Spring Foundation

As an important structure of micro-robots, micro-beams play an increasingly important role in daily production and life, especially in the biological and medical fields. During the use of micro-beam instruments, vibrations occur due to the unevenness of the skin, which affect the accuracy and stability of precision instruments. To analyze this problem, this chapter studies the free vibration of beams with spring at arbitrary positions and nonlinear spring foundations. Through the Laplace transform and the principle of linear superposition, the constrained Green’s function is obtained. Numerical calculations are performed to validate the present solutions and the effects of various important physical parameters are investigated. It was found that the mode and deflection of the beams were changed by the springs and foundations.