Nonlinear free vibration analysis of functionally graded third-order shear deformable microbeams based on the modified strain gradient elasticity theory

作者：Sahmani S; Bahrami M^*; Ansari R

来源：Composite Structures, 2014, 110: 219-230.

DOI：10.1016/j.compstruct.2013.12.004

• Micromechanics
• Functionally graded materials
• Nonlinear vibration
• Strain gradient elasticity theory
• Third-order shear deformation theory

In the present investigation, a numerical analysis is conducted to predict size-dependent nonlinear free vibration characteristics of third-order shear deformable microbeams made of functionally graded materials (FGMs). For this purpose, the modified strain gradient elasticity theory and von Karman geometric nonlinearity are implemented into the classical third-order shear deformation beam theory to develop a nonclassical higher-order beam model including three additional length scale parameters to capture size effect efficiently. It is assumed that the material properties of the FGM microbeams are evaluated by the Mod-Tanaka homogenization technique. On the basis of the Hamilton%26apos;s principle, the size-dependent nonlinear governing differential equations of motion and associated boundary conditions are derived and then discretized along various end supports by employing generalized differential quadrature (GDQ) method. A direct iterative process corresponding to both positive and negative deflection cycles is adopted. Secondly, a parametric study is performed to demonstrate the influences of the values of dimensionless length scale parameter, material property gradient index and length to thickness aspect ratio on the linear and nonlinear natural frequencies of FGM microbeams.

• 出版日期2014-4