Research On Dynamic Uncertainty Of Rotating Thin-walled Cylindrical Shell Based On Interval Method

The cylindrical shell has the advantages of high structural strength,large stiffness and light weight,and has been widely used in aerospace,ocean engineering,pipelines,large dams and cooling towers.With the increasing use of cylindrical shells in large industrial systems such as aero-engines and gas turbines,especially for rotating cylindrical shells,the vibration characteristics become more complicated due to the rotational speed.With the changes of environment,working time,working conditions and other conditions,the model parameters have uncertain characteristics,such as the stiffness and damping of the bolt connection,which makes it difficult to predict system dynamics through deterministic models.Therefore,it is of great significance to study its dynamic uncertainty.Considering the influence of centrifugal force,rotational softening,Coriolis force and initial stress on the structure of bolted rotating cylindrical shell,based on the energy method and finite element theory,the dynamic model of bolted cylindrical shell structure is established,and the influence of the rotational speed on the natural characteristics of the system is analyzed.Then,considering the uncertainty of the parameters of the rotating cylindrical shell,the natural characteristics and steady-state response of the cylindrical shell are analyzed.Finally,the dynamic model of rubbing between the rotating cylindrical shell and the stator blade is established,and the uncertainty of the vibration response of the system is analyzed with parameter uncertainty.The main research contents of this paper are as follows:(1)Based on the finite element method and the hyperparametric 8-node shell element,the finite element dynamics model of two typical flanged cylindrical shell structures with bolted joints is established.The natural frequencies of the two kinds of cylindrical shell structures under the elastic boundary conditions are calculated.The mode shape is compared with the modal experiment and the commercial finite element software to verify the validity of the model built in this chapter.On this basis,considering the centrifugal force,rotational softening,Coriolis force and initial stress of the cylindrical shell,the dynamic model of the system is established,and the influence law of the rotational speed on the inherent characteristics of the bolted flanged cylindrical shell structure is analyzed.(2)Based on the established dynamic model of deterministic rotating cylindrical shell,the influence of bounded but uncertain parameters on the inherent characteristics of the system is analyzed.Based on the interval analysis method,considering the uncertainty parameter as the interval distribution,the solution model of the natural frequency interval of the rotating cylindrical shell is established by using the interval Taylor method and the Chebyshev polynomial surrogate model respectively.The uncertainty parameters are analyzed based on the two methods.Influence and verify the efficiency and accuracy of the two methods by Monte Carlo simulation.Finally,the influence of the boundary connection stiffness and the bolting stiffness between the cylindrical shells on the system’s natural frequency uncertainty is analyzed for the two cylindrical shell connections.(3)The formula for solving the steady-state response of a deterministic rotating cylindrical shell is derived.Considering the rotational speed,Young’s modulus,modal damping coefficient,external excitation amplitude,geometric size and boundary connection stiffness uncertainty of the cylindrical shell,the Chebyshev polynomial interval is used.The range of the steady-state response of the system is analyzed,and the efficiency and accuracy of the method are verified by scanning method under single parameter uncertainty.At the same time,the range of steady-state response of multi-parameter uncertainty is solved and the parameters are analyzed.The effect of uncertainty on the vibration response of the system.Finally,for the connection structure of two cylindrical shells,the influence law of the joint stiffness between the boundary and the stiffness of the cylindrical shell on the steady-state response uncertainty is analyzed.(4)Based on the dynamic model of the rotating cylindrical shell,considering the eccentric rubbing due to the installation of the cylindrical shell or other reasons,the deterministic dynamics of the rotating cylindrical shell excited by nonlinear rubbing under the aerodynamic force is established.On this basis,considering the rubbing stiffness,eccentricity and the gap between the cylindrical shell and the stator of the cylindrical shell as uncertain parameters,the Chebyshev polynomial surrogate model was used to analyze the response characteristics of single parameter and multi-source uncertain parameters to system vibration.