Geometrically Nonlinear Vibration Analysis of Functionally Graded Porous Plates and Shells

Abstract

Functionally graded materials (FGM) are typically a mixture of two or more distinguished materials with a smooth and continuous variation of constituent material properties in one or more directions. FGM shows a heterogeneous characteristic that permits the structures to avoid and eliminate the stress concentration and delamination phenomena commonly observed in laminated composites. However, FGM is susceptible to developing pores due to manufacturing constraints which decreases the strength of FGM. Also, vibrations caused in functionally graded (FG) structures exhibit large amplitudes due to the structures' flexibility. Therefore, it is crucial to investigate the effect of porosities on the geometrically nonlinear behavior of porous FG plates and shells. In this dissertation, the effect of porosities and their distributions on porous FG plates and shells subjected to different geometrical non-uniformities, temperature, two- directional gradation, and saturated porosities are considered for the analysis. The effects of nonlinear temperature distribution and geometrical non-uniformities such as different types of variable thickness and skew angle are considered for the analysis. A nonlinear finite element model is developed by employing the first-order shear deformation theory in conjunction with von Kármán's geometric nonlinearity relations. The governing equations are derived using Hamilton's principle. Then, the direct iterative approach and Newmark's time integration method are utilized to extract the numerical results. Effective material characteristics of the porous FG plate constantly change in the thickness direction. The influence of porosity and its distributions on the nonlinear vibration and dynamic behavior of the geometrically non- uniform porous FG plates are investigated. Generally, FGM has been limited to altering material properties in a single direction. However, this approach may be ineffective for designing components frequently subjected to considerable temperature changes in different directions. Therefore, the numerical evaluation is extended to analyze two-directional functionally graded porous (TDFGP) plates and shells with four different materials. The influence of porosities and two-directional gradation profiles for four distinct materials with longitudinal and transverse gradation are considered for the analysis. The vibration and dynamic viii responses of TDFGP plates and shells are evaluated for various shell forms such as spherical, hyperboloid, ellipsoid, and cylindrical shells. It is inevitable to produce flawless FGM devoid of the entrapment of fluids in pores using contemporary production procedures, which drastically vary the performance of FGM. Thus, the influence of fluid-filled pores on the nonlinear vibration and supersonic flutter analysis of FG saturated porous materials (FGSPM) plates in the thermal environment has been studied. The effects of pore fluid pressure and temperature- dependent elastic stiffness coefficients on the nonlinear flutter behavior of FGSPM plates are evaluated using poroelasticity theory and Piston theory. The results reveal that the porosity nature and its distributions significantly affect the nonlinear behavior of the geometrically non-uniform FG porous plates under thermal load. In addition, the nonlinear behaviors can be changed and controlled considerably by altering the volume fraction gradation profiles in the required direction for each material with an appropriate combination of materials. The FGSPM plates exhibit enhanced stiffness without increasing weight compared to the FG plates with void porosity. It is believed that the research work presented in this dissertation may considerably help in the usability of porous FG plates and shells in the advanced engineering domains of aerospace, bio-medical, electronics, nuclear energy, and smart structures.