On the stochastic vibration analysis of the geometrically nonlinear graded cellular curved panels with material stochasticity

Abstract

In this paper, an effort was made to study the free flexural vibration analysis of the geometrically nonlinear graded cellular curved panels in a stochastic domain. The nonlinear finite element formulations were developed using von Karman nonlinearity hypotheses based on higher-order shear deformation theory, including Lame's parameter. The first-order perturbation technique (FOPT) was employed to assess the stochastic vibration behavior of the graded cellular panels considering randomness in the material properties. The graded cellular curved panels are considered to have three distinguished porosity distributions. The properties of the graded cellular curved panels are continuously varying in the thickness direction as a function of porosity coefficient and mass density. The influences of material stochasticity, porosity coefficient, porosity distribution type, and geometric parameters have been included in the formulations. The detailed convergence and comparison studies were conducted to demonstrate the accuracy and efficiency of the present formulation and highlight the importance of the present study in stochastic environments. The various numerical examples for the second-order statistics (i.e., mean and standard deviation) of the linear frequency parameters (λ) and nonlinear frequencies of the graded cellular structures have been presented which may be considered as the guidelines for future studies in this area of research.