Vibration behavior of a thick double-curved sandwich panel with auxetic core and carbon nanotube reinforced composite based on TSDDCT and NSGT

One of the advantages of sandwich structures is the high strength ratio to weight; thus, they are used in various industries such as automobile manufacturing, shipping, airplanes, spacecraft, rockets, railways, and bridges. The present study investigates the vibration behavior of a thick double-curved sandwich panel with an auxetic core and carbon nanotube reinforced composite in face sheet layers based on nonlocal strain gradient theory. In this research, the nano-structural dependence of nonlocal vibration behavior for the double-curved sandwich panel is to investigate the existence of a limit for the scale parameter. The displacement field of the double-curved sandwich panel is considered based on the third-order shear deformation double-curved theory. The displacement fields for four cases such as first and third shear deformation theories for double-curved or flat plate states are formulated. Thus, the governing equations of motion using Hamilton's principle are obtained. Various effects including the nonlocal parameter, strain gradient parameter, aspect ratio, thickness ratio, the radius of curvature, different angles of the auxetic core, four-type geometric of structure, four-type displacement field, and different distributions of CNTs on the dimensionless natural frequencies of the thick double-curved sandwich panel are illustrated. The dimensionless natural frequency increases much more for the positive angle compared to the negative angle. It is shown that the effects of external physical parameters and internal characteristic parameters on vibration behaviors of a double-curved sandwich panel are independent. In this article, the thick double-curved sandwich panel includes four cases, such as cylindrical, spherical, elliptical, and flat plate shapes, so it is used in turbine blades and airplane wings.