Vibrational characteristics of fastening of a spherical shell with a coupled conical-conical shells strengthened with nanocomposite sandwiches contained agglomerated CNT face layers and GNP core under spring boundary conditions

Abstract

The following paper is prepared to compute the Natural Frequency Parameters (NFPs) linked to the Fastened Spherical-Conical-Conical Shell (FSCCS) structures composted of Nanocomposite Sandwich (NS) materials under the effects of springs as Boundary Conditions (BCs). To explain, the NS material implemented here is made of three layers covering Top Face Layer (TFL), Bottom Face Layer (BFL), and Core Layer (CL). In addition, the TFL and BFL are composed of Carbon Nano Tube (CNT) nano-fillers with agglomeration characteristics, while the CL benefits from Graphene Nano Platelet (GNP) nano-materials. For more information, the mechanical values related to the Agglomerated Carbon Nano-Tube Nanocomposite (ACNTN) material composer the TFL and BFL (ACNTN-TFL and ACNTN-BFL) are carried out by the Eshelby-Mori-Tanaka Approach (EMTA). At the same time, the Halpin-Tsai Approach (HTA) is used to extract these values for GNP-CL. To add more, four different sandwich models are implemented by considering the compatibility between layers. Moreover, the First Order Shear Deformation Theory (FOSDT) and Donnell's Shell Theory (DST) are exploited to obtain the primary relationships of the FSCCS segments. Hamilton's strategy is also operated to derive the Governing Differential Equations (GDEs) of the FSCCS's components. Further, the well-systematized computational meshless method tagged the Generalized Differential Quadrature (GDQ) program is carried out to discrete the GDEs coupled with the structure's segments. Furthermore, the calculation of the eigenvalues is implemented to compute the NFPs of the FSCCS structure. After that, to credit the submitted program, the outputs related to the FSCCS calculated by the present framework are analogized with the responses linked to the FE-based commercial software. In the last, multiple examples are styled and computed to point to the influences of the different material, geometric, and BCs forms on the NFPs of the NS-FSCCS structures, including 12 different geometry types related to the NS-FSCCS.