Research On Vibration Characteristics Of Panel Structures Subjected To Complex Boundary Conditions

Panel structures of rectangular plates and panels with curvature including cylindrical panels and spherical panels are widely used in major engineering fields,such as vehicle manufacturing,machine,ship,architecture,major engineering field,etc.Therefore,the vibration analysis for panel structures has an important significance and practical application value.Now most of panel structure vibration research focus on the specific boundary conditions,especially for specific classical boundary conditions.Different displacement functions are usually changed to adapt to the various boundary conditions,which greatly increases the workload of calculation.In this paper,the displacement function of the panel structures is described by Spectro-Geometry Method and Rayleigh-Ritz method is used to obtain the unknown coefficients of the displacement function,which adapts to the complex boundary condition including the classical boundary,elastic boundary and partial boundary condition.Firstly,introduce the Spectro-Geometry Method simply.And then based on the first-order shear deformation theory,Spectro-Geometry Method is used to establish vibration analysis model of rectangular plates subjected to complex boundary conditions.The displacement function of rectangular plates is composed of Fourier cosine function and the sine auxiliary function.Five groups of spring(three groups of linear spring and two groups of rotational spring)are adopted to simulate the boundary conditions.The convergence and accuracy of the present method are validated by the vibration analysis of rectangular plates subjected to complex boundary condition.Secondly,vibration analysis model of the composite laminated rectangular plate and functionally graded rectangular plate are established,respectively.And the convergence and accuracy of the present analysis model are checked.On the basis,the effects on structural vibration characteristics of the geometrical parameters,material parameters and the boundary spring stiffness values are analyzed,which is of great significance for practical application.In this paper,vibration analysis of the panel structures with the point supported and non-uniform boundary conditions are given and the calculated data are compared with the results obtained by finite element software.Moreover,some new results are also given to enrich the vibration characteristic analysis of the laminatedmaterial and functionally graded rectangular panel,which can be served as a comparison benchmarking.Finally,the rectangular panel structure is extended to the cylindrical panel with single curvature and the spherical panel with double curvature.Based on the first-order shear deformation theory,the vibration analysis model of the panel structures is established by Spectro-Geometry Method.The accuracy and convergence of the cylindrical panel and spherical panel models with the composite laminated material and functionally graded material are verified through several comparisons,and the structural parameters are also analyzed.Through the research on the vibration of the panel structures,the displacement function of the panel structures described by the Spectro-Geometry Method can obtain the vibration characteristics of the panel structures with complex boundary conditions.And the vibration analysis results of the panel structures with point supported and non-uniform boundary conditions are also enriched.