Averaging Method For Solving The Second-order, Third-order Thin Circular Cylindrical Shell Vibration Differential Equation

The structure of shell is widely used in engineering, and the thin circular cylindrical shell is specially used in defense and military projects, such as aerospace, aviation, submarine, for its valuable feature, such as perfect geographic shapes, high strength, high elastic modulus, facilitate processed. Some shell-shaped components work in rotating condition, such as the high-speed shaft of aero engine and centrifuge, missile in the air, satellite, etc. A simplified model is selected in this paper, witch is a clamped-free thin circular cylindrical shell, subjected to a harmonic load at the free end, whirls on its axis.First, in this article, the modal equation of the paper,'The Wave Vibration of Rotating Circular Cylindrical Shell', be managed to reduce order to one-order, and receive the estate equation under the general coordinates, prepares for an average. Then, focus on modal equation for the average method, to make certain the conversion matrixes, carries on amplitudes-phase angle, then obtains the autonomous standardized equation set. Finally, by the system of harmonic resonance period response corresponding of the steady-state response equation, we will get the frequency response equation, and acts according to the obtained result to engage in the parameter-vibration analysis as well as the stability analyses, moreover, the solutions of the average method and the harmonic balance method be compared with the numerical solutions.Second, the application of'Parameter Vibration of Nonlinearity on the Precession of Vibrating Shape for Rotating Thin Circular Cylindrical Shell'the paper model, with its Coriolis force to study the impact of the resonance the issue. According to another would choose to ride out the relationship between the two modes, using Galerkin methods of discrete fluctuations of the equation, get the third-order differential equations. Similar to the steps of the above, the average third-order differential equations to solve a test study and discuss the problem within the resonance of the reasons can not appear in this chapter.