Nonlinear Dynamic Modeling And Numerical Simulatioan Of Rotating Circular Cylindrical Shells

As main components of aeroengine’s compressor, studying the dynamiccharacteristics of rotating circular cylindrical shell, to make the work frequency faraway from resonant frequency and avoid resonance fatigue and structural damage,has a significant meaning for fault diagnosis and the structure design of thecompressor.Considering the effect of centrifugal force、 Coriolis force and circumferentialprestress，we use Hamilton principle to get the equilibrium equation of Donnellnonlinear rotating cylindrical shell. Using the beam function to simulate axialvibration model, for the simply supported boundary conditions spread the vibrationdisplacement as triangle series, Galerkin method are used to discrete partialdifferential equation to ordinary differential equation. Removing the nonlinearterms in the equilibrium equation we can get linear shell’s equilibrium equation,through the Meirovitch method we can Obtain the forward wave frequency and thebackward wave frequency of the Gyro system. For different geometric models andmode number, we discussed the relationship of the forward and backward wavefrequency and axial half wave number, the circumferential wave number, length andthickness of the cylindrical shell and the rotation speed. Considering the radialharmonic excitation, we get the amplitude-frequency characteristic of the system,and found that the forward and backward wave frequency in dynamic and staticcoordinate system meet the law of travelling wave.For the elastic vibration, we mainly focused on the radial vibration andneglected the in-plane inertial and velocity terms, which can reduce the degree offreedom of the system and simplify the problem. Many works have done with thissimplification, but no one pointed out that how this kind of simplification how affect the forward wave and back wave frequency. So we compared the forwardwave and back wave frequency under different modal combinations and rotatingspeed in this paper.Consider the nonlinear terms to study the nonlinear vibration of rotatingcylindrical shells, we can get amplitude frequency characteristic of different modalcombinations, and discussed how the geometric parameters effect it, found a hardcharacteristic phenomenon，super harmonic resonance and subharmonic resonance.