Analysis of fluid-structure interaction vibration based on the detection principle of SI-FLAT flatness measurement systems

In order to reveal the mechanical essence of the detecting principle of SI-FLAT flatness measurement systems, the mathematical model of the relationship between amplitude and residual stress was established, based on the theory of fluid-structure interaction vibration of thin plates. The terms of inertia and fluid pressure were introduced to the equilibrium equation in incompatible Föppl-von Kármán equations. The time variables were separated out from the velocity function of fluid, pressure function of fluid, deflection function of thin plates and stress potential function of thin plates with consideration of periodic aerodynamic load. Therefore, the partial differential equations aiming at steady state of SI-FLAT flatness measurement systems was obtained. Solving the equations by using the method of separation of variables, the mathematical relationship between amplitude and residual stress was established. Combined with measured residual stress, the distribution of actual amplitude of thin plates could be calculated by the Siemens'amplitude-residual stress model, which coincided with the amplitude calculated by the fluid-structure interaction vibration model. The influences of fluid velocity at air pump's inlet, detecting distance and excitation frequency on amplitude were analyzed by using the fluid-structure interaction vibration model, which provides a theoretical basis for application of SI-FLAT flatness measurement systems.