Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams

作者：Ghayesh Mergen H; Farokhi Hamed; Gholipour Alireza; Tavallaeinejad Mohammad

来源：International Journal of Engineering Science, 2017, 120: 51-62.

DOI：10.1016/j.ijengsci.2017.03.010

• Axially functionally graded material
• Tapered microbeam
• Bending
• Forced nonlinear vibration
• Modified couple stress theory (MCST)

The forced nonlinear size-dependent vibrations and bending of axially functionally graded (AFG) tapered microbeams are examined incorporating extensibility. Employing the modified version of the couple stress-based theory, the nonlinear partial differential equations for the transverse and longitudinal motions for a clamped-clamped AFG tapered microbeam are obtained via Hamilton's principle. The variation of the mechanical properties and the cross-section of the AFG microbeam along the length are included in the equations of motion based on exponential distributions of the moduli of elasticity, mass density, Poisson's ratio, and cross-sectional area. The Galerkin method is utilised to obtain a set of discretised nonlinear differential equations of ordinary type; this set of equation is solved with the help of Houbolt's finite difference technique together with the Newton-Raphson method. The effects of the small-scale parameter, the gradient index, material properties variation, and the taper ratio on the nonlinear vibrations of the microsystem are investigated.

• 出版日期2017-11
• 单位McGill