Approximate analytical solution of equivalent stiffness and natural frequency for prestressed beams
Abstract
Prestressed beams are widely used in micro-sensors and actuators, the relationship between the stiffness, natural frequency and prestress is an important physical relationship. It is easy to obtain static deformation for pure bending, and vibration frequency for pure tension. In this paper, based on assumption that the tension force does not affect the bending deformation, and mode shape does not affect the frequency of tension, we proposed a new approximate solution, and find the solution for three different boundary conditions including clamped-clamped, hinged-hinged and clamped-hinged. Compared with the finite element analysis results, the relative error is less than 2.21%. The presented method is simplify but efficient for estimate the equivalent stiffness and natural frequency of prestressed beams.
