Research of Vibration Behavior of Porous FGM Panels by the Ritz Method

In this paper, free vibration analysis of the porous functionally graded shallow shells with a complex form of the plan and supported to elasticity foundation is conducted. A mathematical model of the problem is fulfilled by using the first shear deformation theory (FSDT). It is assumed that material properties vary continuously through the thickness of the shell according to a power law (P-FGM). Two types of models describing porosity distribution (even and uneven) are considered. The variational Ritz method combined with the R-functions theory is applied to analyze the free vibrations of the porous shallow shells with the complex plan form. A comparison of the obtained numerical results for the natural frequencies with known results has been done, and a good agreement is obtained. The investigation of the shallow shells with a complex geometric form of the plan is fulfilled to demonstrate the possibilities of the proposed approach. The influence of different geometric and mechanical parameters on the natural frequencies is studied.