Vibration Modeling And Analysis Of Plates And Shells With Passive Constrained Damping Layer

Passive constrained layer damping(PCLD)plates and shells have the advantages of low cost,great efficiency,high reliability and strong robustness,which are widely used in vibration control of the ship structures.Scholars have made a systematic study of PCLD structures.The finite element method has the disadvantages of the low computational accuracy and efficiency.The traditional analytical method are applied to classical boundaries and simple structures,and the theoretical calculation is very complex.In this paper,taken PCLD plates and shells as the research object,based on the classical theory and the shear deformation theory,adopt the method of Rayleigh-Ritz method and used improved Fourier series to establish a vibration model which meets arbitrary boundary conditions and rapidly converges.The main research contents are as follows:The elastic shell model in the curvilinear coordinate system is established.The basic mechanical relations of the curved shell are established based on the three-dimensional elastic theory.Using the improved Fourier series to construct the allowable equation of the curved shell.The Rayleigh-Ritz method is used to solve the structure frequency and mode.Defined the Lamé constant of the plate and shell structure to convert the elastic shell model in the curvilinear coordinate system into the plate and shell model in the corresponding coordinate system.Classical boundary conditions and elastic boundary conditions are further defined and established.On the basis of the curved shell model,established the PCLD thin plate model and medium thick plate model which based on the classical theory and the shear deformation theory,respectively.In some engineering applications of PCLD structures which have thick viscoelastic damping layer,the former is no longer applicable,while the latter is more applicable due to the consideration of bending effect caused by transverse shear stress.Firstly,the accuracy of the model is confirmed by comparing the literature data,and the vibration and damping characteristics of the structure are further discussed in detail.The effects of classical and elastic boundary conditions,thickness of damping layer and constraint layer,different width-thickness ratio,material parameters and fiber angle of composite material on structural vibration are considered.On the basis of curved shell model,established the PCLD thin cylindrical shell model and thick cylindrical shell model which based on classical theory and shear deformation theory,respectively.The correctness of this model is verified by comparing the literature data,and then the influence of boundary conditions,structural characteristics and material parameters on the vibration of PCLD cylindrical shell is explored.Through a large number of examples,the effects of various boundary conditions,arbitrary boundary spring stiffness,the thickness of damping layer and constraint layer,shear parameters and the lamination mode of the structure on the vibration and damping characteristics of the structure are analyzed.