A new shell study for dynamical characteristics of nanocomposite shells with various complex profiles – Sinusoidal and cosine shells

Abstract

The paper builds the novel models of the shells with the profile changes according to the sinusoidal and cosine functions that are temporarily named the sinusoidal and cosine shells. Two types I and II are corresponding to the sine and cosine shells that are investigated three cycles for each type. The used materials for the types of the shells are the graphene nanoplatelet reinforced polymer that is estimated through the Halpin-Tsai micromechanical model. Based on the classical shell theory and the Von Karman geometrical nonlinearity assumption, the governing equations for the materials and structural models are built and then, the fundamental frequencies and nonlinear dynamical behaviors of the shells are found out. In addition, the obtained results include the numerical and graphical presents and are validated with the Finite Element Analysis (FEA) to confirm the reliability of the analytical approach. The effects of the environment, geometrics and materials are scrutinized through the charts, 2D and 3D graphical results. The attained results are considered to contribute to the important applications in science and industry.