An isogeometric approach for nonlocal bending and free oscillation of magneto-electro-elastic functionally graded nanobeam with elastic constraints

Abstract

This work uses isogeometric analysis (IGA), which is based on nonlocal hypothesis and higher-order shear beam hypothesis, to investigate the static bending and free oscillation of a magneto-electro-elastic functionally graded (MEE-FG) nanobeam subject to elastic boundary constraints (BCs). The magneto-electric boundary condition and the Maxwell equation are used to calculate the variation of electric and magnetic potentials along the thickness direction of the nanobeam. This study is innovative since it does not use the conventional boundary conditions. Rather, an elastic system of straight and torsion springs with controllable stiffness is used to support nanobeams’ beginning and end positions, creating customizable BCs. The governing equations of motion of nanobeams are established by applying Hamilton’s principle and IGA is used to determine deflections and natural frequency values. Verification studies were performed to evaluate the convergence and accuracy of the proposed method. Aside from this, the impact of the input parameters on the static bending and free oscillation of the MEE-FG nanobeam is examined in detail. These findings could be valuable for analyzing and designing innovative structures constructed of functionally graded MEE materials.

Graphical abstract

Keywords

elastic boundary conditions / isogeometric analysis / nanobeam via nonlocal theory / grading of magneto-electro-elastic functions

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