Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

Abstract EN

In this paper, the parametric dynamics of bidirectional functionally graded (BDFG) beams subjected to a time-dependent axial force are studied.

The material properties of beam which vary along both thickness and axial directions follow the power law, and four different distribution patterns are considered.

The coupled nonlinear partial differential equations describing the longitudinal-transverse displacements and the shear deformation are derived using Hamilton’s principle based on Timoshenko beam theory.

The Galerkin scheme is employed to discrete the continuous model resulting in a multiple degree-of-freedom system, namely, the reduced order model.

The nonlinear parametric response of the beam is obtained by solving the discrete system numerically, and the frequency- and force-response curves are constructed by tracing the period motion using the pseudoarclength continuation technique.

Numerical results are presented to examine the effects of system parameters, e.g., gradient parameters, magnitude and frequency of external excitation, and damping coefficients.

Cyclic-fold bifurcation and branch points of the period motion are spotted in parametric resonance of the BDFG beam.

Results show that the asymmetrical material distribution in thickness direction of beam leads to the asymmetry of dynamic responses.

Moreover, the gradient of material in axial direction has more significant effect on the dynamic features of BDFG beam than that in the thickness direction.