TY - JOUR
T1 - Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams
AU - Ghayesh, Mergen H.
AU - Farokhi, Hamed
AU - Gholipour, Alireza
AU - Tavallaeinejad, Mohammad
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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.
AB - 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.
KW - Axially functionally graded material
KW - Bending
KW - Forced nonlinear vibration
KW - Modified couple stress theory (MCST)
KW - Tapered microbeam
U2 - 10.1016/j.ijengsci.2017.03.010
DO - 10.1016/j.ijengsci.2017.03.010
M3 - Article
AN - SCOPUS:85021431566
VL - 120
SP - 51
EP - 62
JO - International Journal of Engineering Science
JF - International Journal of Engineering Science
SN - 0020-7225
ER -