Hygro-thermo-magnetically induced vibration of FG-CNTRC small-scale plate incorporating nonlocality and strain gradient size dependency

Abstract

Free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) small-scale rectangular plates resting on Kerr foundation and subjected to complex environments and in-plane axial loads are analyzed. Based on the higher-order shear deformation theory (HSDT) and using nonlocal strain gradient theory, governing equations of plate are extracted. Utilizing the generalized differential quadrature method (GDQM), the governing equations of motion are solved numerically. To validate the present work, a comparative study is accomplished between the present results and the reported ones in the literature. Effect of size-dependent parameter, the CNT volume fraction, pattern of CNT distribution, humid and thermal environments, magnetic fields, structure aspect ratios, boundary conditions, and foundation types, on the natural frequencies of the structure are studied. Acquired outcomes represent that considering the impacts of the strain gradient parameter and the magnetic field in modeling improve the system vibrational behavior. While imposing the nonlocal term and hygro-thermal effects similar to the in-plane loads have destabilizing influences on the system and make the structure more vulnerable to static instability. Meanwhile, it is deduced that when the Scale Factor <1 (Scale Factor >1), the softening (hardening) impact of the nonlocal (strain gradient) parameter is prominent on the FG-CNTRC small-scale plate.