Vibration analysis of a bi-directional functionally graded nano beams with various boundary conditions using Ritz method

Vibration analysis of functionally graded nano beams with different boundary conditions is presented in this paper. The first-order shear deformation theory and nonlocal elasticity theory are used to incorporate size small effect of functionally graded nano beams. Ritz-type analytical solution is used to solve the characteristic equations of motion for different boundary conditions.