Analysis Of Vibration Characteristics Of A Thermoelastic Coupling Rotating Circular Plate

In practical engineering,the circular plate is an important component of many systems and has a very wide range of applications,especially the vibration characteristics of the sports plate in thermal environment is very broad in engineering and aerospace,mechanical,instrumentation and civil engineering the application,but also brought a lot of problems.Such as machinery in the roulette,turbo engine,computer hard drive,building the foundation and so on.Moreover,these structures and temperatures are all coupled.Temperature affects the stress distribution of the structure,which in turn affects the temperature distribution of the structure.Therefore,it is necessary to study this issue.At present,most scholars mainly focus on quasi-static thermo-elastic coupling or static thermo-elastic coupling and some dynamic characteristics of the plate under thermal environment.In this paper,the vibration characteristics and stability of the thermo-elastic coupled rotating disk are studied.Based on the theory of Kirchhoff thin plate and the heat conduction equation considering the influence of deformation,a differential equation of motion for a thermo-elastic coupled rotating disk is established.The eigenvalue of the system is obtained,and the numerical solution is based on the differential transformation method.The thermo-elastic coupling circular plate was also verified by finite element simulation.The influence of thermo-elastic coupling factor and angular velocity on the complex frequency of rotating disk under various boundary conditions is analyzed.The mainly research includes:(1)The mechanical model adopted in this paper is a rotating disk under the action of temperature field.The disk rotates around the central axis at a constant angular velocity.The variation of temperature along the thickness direction is far greater than that along the radial and circumferential directions.Based on the theory of Kirchhoff thin plate and the principle of force balance,the differential equations of motion of a thermo-elastic coupled rotating disk with lateral deflection are deduced and the boundary conditions are given.The resulting differential equations and boundary conditions are properly simplified,and then non-dimensional,and then based on the differential transformation of the equation discretization,and then organize the system to solve the characteristic equation MATLAB programming.Finally,the finite element simulation analysis of this model is also carried out.(2)Aiming at the obtained transverse vibration differential equation of rotating disk,if the influence of temperature field and angular velocity is neglected,the problem degenerates to the problem of free vibration of solid disk.Then,the equations are transformed by using the differential transformation method,and then the equations are solved to obtain the natural frequencies of the free vibration of the circular plate.Compared with the existing literature,the feasibility and accuracy of this method are verified.(3)Considering the rotating circular plate under the influence of temperature,the uniform rotating of the circular plate is set,and the vibration characteristics of the thermo-elastic coupled rotating circular plate are analyzed.If the thermal elastic coupling coefficient of the equation is zero,then the equation will degenerate into the problem of rotating disc.The variation of each order of the rotating disc with the dimensionless angular velocity and the critical divergence and instability angular velocity of the disc are analyzed.Finally,considering the effect of thermo-elastic coupling coefficient,the effect of thermo-elastic coupling coefficient on each order of frequency and the influence on the critical velocity of the divergent instability of the rotating disk,we find that the critical velocity is larger than that of non-coupling case.