Semi-analytical vibration analysis of FGM cylindrical shells surrounded by elastic foundations in a thermal environment

The natural frequency and transient response of FGM cylindrical shells under arbitrary boundary conditions are performed in present work. A novel semi-analytical method, which integrates Durbin's inverse Laplace transform and the differential quadrature method, is developed to analyze the dynamical behavior of cylindrical shells. Durbin's numerical inversion method is selected to gain time domain solutions. The trigonometric series expansion is used in the circumferential direction whereas the use of differential quadrature method provides numerical solutions in terms of axial direction. Comparisons show that the calculated natural frequencies are in good agreement with results in the literature. Convergence study illustrates that the developed method is rapidly convergent with the increase of sampling points, and the calculated transient response of the cylindrical shell is validated by comparing with Navier's solution. The influences of boundary conditions, material graded indexes, temperature changes, elastic foundation coefficients and geometric parameters on transient response are analyzed. Numerical results indicate that the peak displacement of cylindrical shells increases with the increase of temperature changes and length-radius ratios or the decrease of elastic foundation coefficients and thickness-radius ratios.