Investigation of nonlinear free vibration of FG-CNTRC cylindrical panels resting on elastic foundation

Non-linear vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) cylindrical shell panel on elastic foundation have not been sufficiently examined. In this situation, this study aims at the profound numerical investigation of the non-linear vibration response of FG-CNTRC cylindrical panels on Winkler -Pasternak foundation by introducing an accurate and effective 2-D meshfree-based non-linear numerical method. The large -amplitude free vibration problem is formulated according to the first -order shear deformation theory (FSDT) with the von Karman non -linearity, and it is approximated by Laplace interpolation functions in 2-D natural element method (NEM) and a non-linear partial derivative operator H-NL. The complex and painstaking numerical derivation on the curved surface and the crucial shear locking are overcome by adopting the geometry transformation and the MITC3+ shell elements. The derived nonlinear modal equations are iteratively solved by introducing a three -step iterative solving technique which is combined with Lanczos transformation and Jacobi iteration. The developed non-linear numerical method is estimated through the benchmark test, and the effects of foundation stiffness, CNT volume fraction and functionally graded pattern, panel dimensions and boundary condition on the non-linear vibration of FG-CNTRC cylindrical panels on elastic foundation are parametrically investigated.