Analytical Method Of Free Vibration Of Sandwich Plates And Shells With Functionally Graded Flexible Core

Functionally graded materials (FGMs) are usually made from a mixture of metals and ceramics which vary continuously and gradually over volume in composition and microstructure. In spite of microscopically inhomogeneous, FGMs are macroscopically homogeneous composites. These advantages help to reduce mechanically and thermally induced stresses caused by the material property mismatch and to improve the bonding strength. Therefore, FGMs are usually applied in the sandwich plates and shells to improve the bonding strength between the core and the face sheets and to reduce mechanically and thermally induced stresses caused by the material property mismatch between the core and the face sheets. Because the vibration behavior is an important indictor to characterize the structure performance, the research on the vibration of FGM sandwich plates and shells has significant theoretical value and practical value.This thesis studies the free vibration of several novel types of FGM sandwich plates and shells with flexible core by using high order sandwich plane theory (HSAPT), including:sandwich plate with both functionally graded face sheets and functionally graded flexible core, sandwich plate with bilinearly graded flexible core, grid stiffened sandwich plate with flexible functionally graded material filled, submerged composite sandwich cylindrical shell with functionally graded flexible core and grid stiffened sandwich cylindrical shell with flexible functionally graded material filled. The main works presented in the thesis are as follows:(1) Free vibration of sandwich plate with both functionally graded face sheets and functionally graded flexible core is studied by using refined high order sandwich plane theory. The properties of FGM follow a power-law function. The first order shear deformation theory is used for the face sheets and a3D-elasticity solution of weak core is employed for the core. The core layer has transverse normal and shear resistance only. On the basis of continuities of the displacements and transverse stresses at the interfaces of the face sheets and the core, equations of motion are obtained by using Hamilton’s principle. The accuracy of the present approach is validated by comparing the analytical results obtained for a degradation model-sandwich plate with functionally graded face sheets and homogeneous flexible core with ones published in the literatures, as well as the numerical results obtained by finite element method and good agreements are reached. Then, parametric study is conducted to investigate the effect of distribution of functionally graded material properties, thickness to side ratio on the vibration frequencies.(2) Free vibration of sandwich plate with bilinearly graded flexible core is studied by using refined high order sandwich plane theory. The bilinearly graded flexible core is considered as two monotonically graded flexible core layers. As a result, the laminated two-layered core is analyzed and formulated by the mixed layer-wise theory. Then the sandwich plate is analyzed by combining the refined high order sandwich plane theory and the mixed layer-wise theory. In this way, the continuities of the displacements and stresses at the interfaces of face sheets and core, upper core layer and lower core layer are achieved. Meanwhile, the computation of this method is effectively reduced compared with the one by three dimensional theory and mixed layer-wise theory for the sandwich plate.(3) Free vibration of grid stiffened sandwich plate with flexible functionally graded material filled is studied. Due to the discontinuity between the materials of the ribs and the filler, the smear or homogenous method is usually used to study grid stiffened sandwich plate with filler in previous literature. This thesis introduces the discrete method to deal with the ribs. In addition, the material of the ribs is steel or other hard material so that the3D-elasticity solution of weak core cannot be used because the in-plane stresses cannot be neglected. Therefore, the both in-plane stresses and vertical stresses of the core are considered when using the high order sandwich plane theory. The classic thin plate theory is used for the face sheets. On the basis of continuities of the displacements at the interfaces of the face sheets and the core, Lagrange’s equations of motion are obtained by using Hamilton’s principle. Then the Chebyshev polynomials are adopted for the shape function and the frequency is solved by Ritz method.(4) Free vibration of submerged composite sandwich cylindrical shell with functionally graded flexible core is studied. The refined high order sandwich plane theory is employed for the structure while the wave propagation method is used to study the fluid-structure interaction. Assuming the wave travelling in the axial direction of the shell is approximately obtained by studying the wave travelling in a similar beam. Then the fluid loading can be obtained by the wave equation. Base on the continuity of the displacements at the interface of the outer face of the cylindrical shell and the fluid, equations of motion are obtained by using Hamilton’s principle.(5) Free vibration of grid stiffened sandwich cylindrical shell filling flexible functionally graded material is studied. The method employed for the structure is the same as the one for grid stiffened sandwich plate with flexible functionally graded material filled and the Lagrange’s equations of motion are derived. By using the Navier’s solution, the natural frequency of the grid stiffened sandwich cylindrical shell filling flexible functionally graded material is obtained.The thesis studies the free vibration of several novel FGM sandwich plates and shells with flexible core analytically. Different method is adopted depending on the type of the structure. New thoughts and methods are provided for studying the free vibration of novel FGM sandwich plates and shells with flexible core, which has a certain reference value for the further research and engineering design.