Study Of Vibration Characteristics For Moderately Thick Plates And Shells Of Revolution And Coupled Structures Subjected To General Boundary Conditions

The composite moderately thick plates and shells of revolution,as the elementary structural components,have been widely used in various engineering fields such as aerospace industry,marine engineering,petrochemical container industry,aircraft industry,civil engineering,rocket and railroad transportation industry and so on.The study of the vibration characteristics for such structures is also one of the important research branches in the engineering fields.In the actual engineering,the perfect classical boundary conditions are unrealistic,while the elastic boundary and point boundary are more universal.As for the existing solution methods,they have the drawback that when dealing with different boundary conditions the constant modifications should be made in the solution procedures and corresponding computation codes to adapt the variation,which results in very tedious and inefficient work.However,even for the simplest structure,the types of the classical boundary condition they encountered are abundant and it will bring big trouble inevitably.So it's of great theoretical significance and has practical engineering value to develop a unified formulation to analyze the vibration characteristics of the composite moderately thick plates and shells of revolution and their coupled structures with arbitrary boundary conditions and to conduct the parametric study for such the engineering structures.In this paper,the following research contents are carried out:The basic theory of the improved Fourier series is introduced in detail and its characteristic and superiority are presented by the comparison with other existing methods.The application range of the first-order shear deformation theory applied to the vibration characteristic analysis of the moderately structures is discussed by the applicability analysis of the commonly used elastic theories.On this basis,the basic procedure of vibration characteristic analysis for composite structures with arbitrary boundary conditions is presented;and taken the composite laminated straight beam as an example,the effectiveness and correctness of the present method is validated by numerical examples.A unified theoretical analysis model for the vibration characteristic of composite plates of revolution with arbitrary boundary conditions is built.All the displacement field functions of the plate are expressed in the product form of a two-dimensional standard Fourier cosine series supplemented with four polynomial functions and a one-dimensional Fourier cosine series,where the auxiliary functions are introduced to eliminate the potential discontinuities of the boundary.At the boundary,the artificial virtual boundary technique,which is composed of three groups of linear displacement springs and two groups of rotation springs,isintroduced to simulate the boundary force,and by adjusting these elastic stiffness values,the arbitrary boundary conditions can be simulated furthermore.Moreover,when the angle of sectors equals to 2?,the artificial virtual coupling technique is introduced in the coupling boundary conditions to meet the corresponding continuous conditions,by which the circular and circle model can be obtained.The vibration behavior can be obtained by solving a simple standard linear equation group.By a great many numerical examples,the good convergence of the constructed unified analysis model is validated,and it also can be seen that the present model can be used to make prediction of vibration characteristics for the annular sector plate,circular sector plate,annular plate and circular plate.In addition,some new results for the composite laminated and functionally graded annular sector plate,circular sector plate,annular plate and circular plate are presented.These results can be treated as benchmark data for future research methods for there are no published results in the reported literature.Then,the unified analysis model of vibration characteristics for the composite cone/column/sphere and doubly-curved shell of revolution with arbitrary boundary conditions is built based on the first-order shear deformation theory.The 2-D improved Fourier series is adopted to express the displacement functions of the structure,and the artificial virtual boundary technique and the artificial virtual coupling technique are used to separately simulate the continuous conditions of arbitrary boundary conditions and coupling positions.The vibration characteristics of the structure with arbitrary boundary conditions can be all acquired by solving for a standard eigenvalue problem.In actual applications,different from other methods,the present model doesn't need any hypotheses applied to the boundary condition and other parameters,which contributes to the future parametrization study.By numerical results,it's shown that the presented model has good convergence and accuracy.Compared to other existing methods,the present method has the advantage that when the geometry parameters or boundary conditions change,only the initial parameters without the core solution codes need modifying.On this basis,the modal frequency parameters for the composite doubly-curved shells with different geometry parameters and boundary conditions are given.These results can serve as benchmark solutions for future researches and also enrich the research results.Besides,the parametrization study of vibration characteristics for shells of revolution is conducted and the results show that the effects of the boundary constraint conditions,geometry parameters and material parameters on the vibration characteristics are interrelated.On the basis of the study of the single structure,the unified analysis model of vibration characteristics for composite-material coupling structures of revolution with arbitraryboundary and coupling conditions is built.The linear and rotation displacement field functions of all the substructures are expressed using the improved 2-D Fourier series and all the boundary conditions are realized by the arbitrary elastic stiffness coefficients,which can efficiently avoid the limit of boundary conditions.At the coupling positions of the substructures,adopt the uniformly distributed elastic coupler consisting of three groups of linear displacement springs and two groups of rotary constraint coupling springs to meet the coupling effects of five forces: torque,moment,transverse shear force,in-plane shear stress and in-plane longitudinal force.By assigning different values to the coupling springs,the arbitrary elastic coupling conditions can be simulated.All the unknown expanded coefficients of the displacement field function are treated as generalized variables,and combined with the Ritz method which is based on the energy-variational principle to conduct the partial derivation,the vibration characteristic equations of the coupling structures can be obtained.By conducting analysis of the vibration characteristic for coupling structures with different material types and taking the FEM results as reference data,the rapid convergence,good stability and accuracy of the present model is validated.As mentioned before,there is still no need to make any corrections to the kernel of the solution process when the boundary or coupling conditions change.Since there are no published results for the parametrization study of composite-material coupling structures of revolution,the present results can be regarded as benchmark data for other future approximate numerical methods and also provide the theoretical support for the design of such coupling structures.