Effects of residual stresses on mechanical properties of segmented micro deformable mirrors

Effects of residual stresses on mechanical properties such as voltage vs. displacement response, pull-in voltage and structural resonant frequency of segmented micro deformable mirrors were investigated with both finite element method (FEM) and analytical method. A simplified model was adopted to study the structural spring constant on the existence of residual stress and two methods for imposing residual stress on structures were utilized for the purpose. Both results of analytical method and FEM show that larger structural spring constant can be obtained by introducing tensile residual stress. Consequently, mechanical properties relevant to spring constant are also greatly affected. The higher the tensile residual stress is, the stronger the structural stiffness will be. That means in order to induce the same structural displacement of mirror plate as stress-free state, higher voltage is demanded. Meanwhile, with higher tensile residual stress, larger pull-in voltage and greater structural resonant frequency are achieved. For the situation of compressive residual stress, totally the opposite influences can be observed. In conclusion, residual stress (no matter tensile or compressive) can greatly affect the mechanical properties of segmented micro deformable mirrors. Accurate control of it is needed for optimizing the structural design and improving the performance of devices.