Research On Dynamic Similarity Design Method For Thin-walled Conical Shell Structures

Thin-walled conical shell structure is widely used in engineering practice because of its advantages of large rigidity,strong bearing capacity and less consumables.Taking aeroengine as an example,there are a lot of thin-walled conical shell structures in its structure.In order to avoid resonance,many scholars have studied the dynamic characteristics of thin-walled conical shell structure.For the dynamic analysis of thin-walled conical shell with large size,complex processing technology and high cost of manufacturing materials,the finite element simulation analysis method,analytical method and prototype test method are usually used.These methods usually have inevitable defects.The first two methods solve the theoretical results,which usually have deviation from the actual results.The prototype structure is tested and studied,Not only the test cycle is long,the test is difficult and the test cost is high.Therefore,in order to make up for the disadvantages of prototype test,model test is needed to predict the dynamic characteristics of prototype.The model test not only reduces the test difficulty,shortens the test period,but also greatly reduces the test cost,thus promoting the development of the research on the dynamic characteristics of thin-walled conical shell structure.In this paper,three typical conical shell structures,thin-walled conical shell,concave conical shell and cone column composite shell,are taken as examples to study the dynamic similarity design(1)The dynamic equilibrium equations of thin-walled conical shell,side concave conical shell and cone column composite shell are established by using the theory of plate and shell,elastic mechanics and other relevant theoretical knowledge,which provides the basis and basis for the analysis of vibration characteristics of thin-walled conical shell and the establishment of similar models.(2)Based on the equation analysis method,the complete geometric similarity of thin-walled conical shell is established.In order to establish the geometric similarity of distortion,a design method of dynamic similarity model based on the least square method is proposed.Then,the geometric similarity relation of distortion is established,and the applicable range of geometric dimension of distortion model is deduced.On this basis,the geometric similarity error function of distortion is established,and its feasibility is verified.Finally,the influence of geometric parameters on natural frequency is analyzed,which provides a reference for similar model design of conical shell.(3)Based on dimensional analysis and least square method,the dynamic similarity of conical shell with concave side wall is established.Because of the complex structure,the parameters in the dynamic balance equation are more and more complex,and the equation analysis method is difficult to solve,so based on the dimension analysis method and the least square method,the dynamic similarity relationship of the conical shell with concave side wall is established,and the applicable range of the geometric dimension of the distortion model is deduced.On this basis,the geometric similarity of distortion is modified and verified by the finite element simulation analysis.(4)On the basis of the above design method of conical shell similar model,the dynamic similar relationship of conical cylindrical composite shell is established,and the applicable range of geometric dimension of its distortion model is obtained.On this basis,the geometric similar relationship of distortion is modified,and finally verified by finite element simulation analysis.(5)The accuracy of the geometric similarity relation of the thin-walled conical shell is verified by the experimental research,and the influence of the geometric parameters on the natural frequency of the conical shell is also obtained,which provides a reference for the dynamic similarity model test of the conical shell.