Size-Dependent Geometrically Nonlinear Free Vibration of First-Order Shear Deformable Piezoelectric-Piezomagnetic Nanobeams Using the Nonlocal Theory

Abstract

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 sizedependent 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 arclength 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-tothickness ratio.

Vibration Behavior of a Sandwich Porous Elliptical Micro-Shell with a Magneto-Rheological Core Based on the Modified Couple Stress Theory

“…Gholami and Ansari [43] investigated the geometrical, nonlinear free vibration behavior of piezoelectric and piezomagnetic nanobeams subjected to magneto-electro-thermal loading, versus the effect, based on the nonlocal elasticity theory. The size-dependent nonlinear governing equations of motion and the corresponding boundary conditions were derived based on the nonlocal elasticity and first-order shear deformation theories with von Karman-type of kinematic nonlinearity.…”