Nonlinear eigenfrequency prediction of functionally graded porous structure with different grading patterns

The effect of full-scale geometrical nonlinearity on the eigenfrequencies of the porous graded curved panel structure is examined in this current work, considering the configurational variation due to curvature (single/doubly). A nonlinear isoparametric finite element formulation has been derived using the Green-Lagrange nonlinear strain and the higher-order deformation kinematics. Additionally, each mid-plane strain is incorporated within the model to count the exact structural flexure due to the large deformation. Further, the equation of motion has been converted to a set of algebraic forms through a nine-noded quadrilateral element and solved computationally (via MATLAB code) in association with the direct iterative method. The comparison and convergence tests are carried out to check the accuracy of the mathematical model by solving different sets of examples as same as the references. Afterwards, the model has been used to compute the nonlinear frequency (NLF) data to examine the influence of various structural input parameters, i.e. porosity, grading pattern, amplitude ratio, power-law exponent, curvature ratio, end-support conditions, geometrical shapes, thickness ratio and aspect ratio.

Automated summary

This study examines the effect of full-scale geometrical nonlinearity on the eigenfrequencies of porous graded curved panel structures, using a nonlinear isoparametric finite element formulation and computational methods to analyze and compare the results.