Dynamic interaction between bi-directional functionally graded materials and magneto-electro-elastic fields: A nano-structure analysis

摘要

In the paper, a novel model of bi-directional (2D) functionally graded materials (FGMs) nanobeams resting on the Pasternak foundation under the magneto-electro-elastic (MEE) fields based on the Timoshenko beam theory is presented to investigate the dynamic interaction behavior. Taking the interaction between the 2D FGMs and MEE fields as well as the nonlocal elastic theory into account, the governing equations of the nanobeams resting on the Pasternak foundation are established by made use of the Hamilton's principle. The generalized differential quadrature method (GDQM) is put forward to discretize the dynamic model of the nanobeams and carried out the calculations of the natural frequencies and associated mode shapes. We can find that the asymmetric modes in the MEE nanobeams are dependent on the 2D FGMs, which is significantly different from the former research. Numerical examples reveal the influences of the foundation coefficients, length-thickness ratio, magneto-electro-mechanical loadings and material distributions on the dynamic characteristics in details. It is notable that the analytical results are beneficial for designing accurately the smart nanostructures constructed from multi-ferroic composites.