TY - JOUR
T1 - Size-Dependent Geometrically Nonlinear Free Vibration of First-Order Shear Deformable Piezoelectric-Piezomagnetic Nanobeams Using the Nonlocal Theory
AU - Gholami , Raheb
AU - Ansari , Reza
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 184
EP - 208
PY - 2018
DA - 2018/10
SN - 10
DO - http://doi.org/10.4208/aamm.2015.m1298
UR - https://global-sci.org/intro/article_detail/aamm/10507.html
KW - Piezoelectric-piezomagnetic nanobeams, geometrically nonlinear free vibration, nonlocal elasticity theory, size effect, magneto-electro-thermal loading.
AB - <p style="text-align: justify;">This article investigates the geometrically nonlinear free vibration of
piezoelectric-piezomagnetic nanobeams subjected to magneto-electro-thermal loading
taking into account size effect using the nonlocal elasticity theory. To this end, the size-dependent
nonlinear governing equations of motion and corresponding boundary
conditions are derived according to the nonlocal elasticity theory and the first-order
shear deformation theory with von Kármán-type of kinematic nonlinearity. The effects
of size-dependence, shear deformations, rotary inertia, piezoelectric-piezomagnetic
coupling, thermal environment and geometrical nonlinearity are taken into account.
The generalized differential quadrature (GDQ) method in conjunction with the
numerical Galerkin method, periodic time differential operators and pseudo arc-length
continuation method is utilized to compute the nonlinear frequency response
of piezoelectric-piezomagnetic nanobeams. The influences of various parameters
such as non-dimensional nonlocal parameter, temperature change, initial applied
electric voltage, initial applied magnetic potential, length-to-thickness ratio and different
boundary conditions on the geometrically nonlinear free vibration characteristics
of piezoelectric-piezomagnetic nanobeams are demonstrated by numerical examples.
It is illustrated that the hardening spring effect increases with increasing the
non-dimensional nonlocal parameter, positive initial applied voltage, negative initial
applied magnetic potential, temperature rise and decreases with increasing the negative
initial applied voltage, positive initial applied magnetic potential and length-to-thickness
ratio.</p>