Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT

In this research, the free vibration analysis of a sandwich plate with a transversely flexible core and functionally graded – carbon nanotubes (FG-CNTs) reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties is presented based on high-order sandwich plate theory (HSAPT). The governing equations of motion are derived using Hamilton's principle. Classical plate theory (CPT) is used for modeling the face sheets and the effective properties of them are defined based on the extended mixture rule. Mechanical properties of the core such as Young's and shear modulli are assumed to be function of temperature. The influences of aspect and side ratios, temperature changes, core-to-face sheet thickness ratio, distribution types and volume fraction of carbon nanotubes are presented. The size-dependent mathematical formulation of the face sheets is developed based on the strain gradient theory (SGT). The results show that with increasing the aspect ratio, the non-dimensional natural frequency increases, however the side ratio has a reverse effect. As the temperature of the system increasing, the non-dimensional natural frequency decreases while by applying the magnetic field, the frequency parameter increases. Also it is concluded that the sandwich plate with X distribution type of carbon nanotubes in the face sheets, has higher frequency compared with the other types. Finally it is observed that by considering the size effect and introducing the material length scale parameters, the frequency of the sandwich plate increases. Employing FG-CNTs in face sheets, magnetic field, and size dependent effect leads to increase stiffness of nanostructures, thus the use of this sandwich plate has a prominent role in modern engineering applications.