Vibration and Critical Speed of Orthogonally Stiffened Rotating FG Cylindrical Shell Under Thermo-Mechanical Loads Using Differential Quadrature Method

In this article, an approximate solution using differential quadrature method is presented to investigate the effects of thermo-mechanical loads and stiffeners on the natural frequency and critical speed of stiffened rotating functionally graded cylindrical shells. Transverse shear deformation and rotary inertia, based on first-order shear deformation shell theory (FSDT), are taken into consideration. The equations of motion are derived by the Hamilton's principle while the stiffeners are treated as discrete elements. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of the constituents. The temperature field is assumed to be varied in the thickness direction. The equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations applying the DQM. The results obtained include the relationship between frequency characteristics of different power-law index, rotating velocities, thermal loading and amplitude of axial load. To validate the present analysis, the comparison is made with a number of particular cases in literature. Excellent agreement is observed and a new range of results are presented for stiffened rotating FG cylindrical shell under thermo-mechanical loads which can be used as a benchmark to approximate solutions.