Non-linear dynamic characteristic of a relief valve controlled by a thin annular plate

In current research, the transverse motion of a thin annular plate is studied, thus determining the static and dynamic opening of a relief valve. Using the geometrically non-linear theory of thin plates, the governing equations in cylindrical coordinates are systematically deduced for obtaining the transient behavior. An equivalent method for replacing the concentrated force is innovatively proposed so that all of the loads of the plates can be given by a unified expression, which reduces the number of the governing equations and intermediate boundary conditions. Combining harmonic differential quadrature (HDQ) and method of solving ordinary differential equations, the governing equations are rapidly solved out. The results of the numerical method are verified with those of finite element analysis (FEA). Applying step loads, all of the theoretical values and FEA results give us insight into the attenuate vibration response of the relief valve, showing great ability of keeping steady positions and rapid dynamics.