Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory

Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method

Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges

In this paper a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to impact internal pressure is considered. The axisymmetric conditions are assumed for the 2D-FG cylinder. The finite element method with graded material properties within each element is used to model the structure, and the Newmark direct integration method is implemented to solve the time dependent equations. The time histories of displacements, stresses and 2D wave propagation are investigated for various values of volume fraction exponents. Also the effects of mechanical properties distribution in radial and axial direction on the time responses of the FG cylinder as well as the stress distribution are studied and compared with a cylinder made of 1D-FGM. The achieved results show that using 2D-FGM leads to a more flexible design. To verify the presented method and data, the results are compared to published data.

Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading

The nonlinear forced vibration of infinitely long functionally graded cylindrical shells is studied using the Lagrangian theory and multiple scale method. The equivalent properties of functionally graded materials are described as a power-law distribution in the thickness direction. The energy approach is applied to derive the reduced low-dimensional nonlinear ordinary differential equations of motion. Using the multiple scale method, a special case is investigated when there is a 1:2 internal resonance between two modes and the excitation frequency is close to the higher natural frequency. The amplitude–frequency curves and the bifurcation behavior of the system are analyzed using numerical continuation method, and the path leading the system to chaos is revealed. The evolution of symmetry is depicted by both the perturbation method and the numerical Poincare maps. The effect of power-law exponent on the amplitude response of the system is also discussed.

S.M. Hoseini

Papers

Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder