Research On Vibration Characteristics Of Plates And Shells Based On Energy Principle

Plate and shell structures are widely used in aviation,aerospace,shipbuilding,civil engineering and other fields.In practice,this kind of structures is often subjected to the intricate environment and external excitation which can result in structural vibration,fatigue damage and even accompanied by severe radiation noise.Thus,it is of adverse impact to the structure and human life.Based on the energy principle,an improved Fourier series method is used to establish the dynamic model of plates,shells and the combinatorial structure with general boundary conditions.The series solution is obtained.There are weak points in the vibration characteristics of the shell structures with the elastic boundary conditions currently.In this paper,an improved Fourier series is used to describe the displacement functions of the shell structures.The constraint springs are introduced at the boundary and the coupling position to simulate the various compatibility conditions,and it is convenient to construct the unified analysis model of structure under arbitrary boundary condition.The unknown series expansion coefficients are determined using the familiar Rayleigh-Ritz procedure.By comparing the numerical examples of free vibration and forced vibration with various boundary conditions,the correctness of the analytical model is verified.On this basis,the vibration characteristics of different plate and shell models are studied.The vibration characteristics of conical shell and spherical shell with arbitrary boundary conditions are solved by the improved Fourier series method,and the convergence and accuracy of the method are verified.The dynamic analysis model of the functional gradient conical shell and the high-speed rotating conical shell are established.The influences of the critical parameters such as the volume distribution constant of the functionally graded material,the rotational speed of the rotating shell and the boundary conditions on the natural vibration of the structure are discussed in detail.The vibration characteristics of the ring-stiffened cylindrical shell and ring-stiffened conical shell are solved respectively while the stiffeners were treated as discrete elements.The effects of the parameters of stiffener eccentricity,cross section dimension,position distribution on the vibration characteristics are analyzed.In addition,the model of cone-cylinder-sphere combined shell with general boundary condition is established,and the influences of the attached structures such as ring ribs,bulkheads and dynamic vibration absorber on the combined structure is discussed.Some laws are obtained.Finally,the experimental bench of cone-cylinder-sphere combined shell is designed and built up.The vibration characteristics of combined shell are studied through the structural modal test and vibration response test.The experimental and theoretical results match well with each other,which further verified the correctness of present method.The possible errors in the experiment are indicated by analyzing experimental results.