Numerical modal responses of damaged functionally graded porous structures - a finite element approach

Abstract The present work investigates the modal responses of functionally graded porous panels (FGPPs) with the inclusion of damage. The finite element (FE) model has been developed for the FGPP considering a single equivalent layer (SEL) approximation based on higher order shear deformation theory (HSDT). The eigen value characteristic equation of the FGPP is derived using the principle of minimum potential energy and a MATLAB FE code for estimating the frequencies of the same has been derived in the present work. The FE model’s accuracy is initially validated by using the same for computing the numerical solutions of earlier works available in the open literature. The developed FE model is hence used to predict the eigen frequencies of the FGPP. Several functionally graded panels with even and uneven porosity distributions are taken in for evaluation of the eigen frequencies. Also, the numerical results are produced considering various geometrical forms (double/single) and damages in the form of cracks. The parametric study and analysis carried out in this article using the derived model integrated with both the damage and intact shell effects could serve as reference for future works in the similar areas of research. Also, the influence of various parameters like, porosity distribution (even/uneven), the length to the width ratio ( a/b ), and the thickness/aspect ratio ( a/h ), the shell geometry, and the curvature ratios ( R/a ) of the both the damaged and intact shells on the frequency responses of the same has been reported. The influences of porosity and damage on frequency responses of FGPP are examined numerically, since these parameters play a vital role and influence the frequency values thereby effecting the modal responses. Moreover, the porosity and the presence of damage in the graded structure influences its specific strength property. The study is significant as many of the applications of such material structures are subjected to vibration induced failures.