Free Vibration Characteristics of FG-CNTRC Conical–Cylindrical Combined Shells Resting on Elastic Foundations Using the Haar Wavelet Discretization Method

Functionally graded carbon nanotube reinforced composites (FG-CNTRCs) are a novel breed of polymer nanocomposite, in which the nonuniform distribution of the carbon nanotube (CNT) reinforcement is adopted to maximize the macro-mechanical performance of the polymer with a lower content of CNTs. Composite conical–cylindrical combined shells (CCCSs) are widely utilized as loading-bearing components in various engineering applications, and a comprehensive understanding of the vibration characteristics of these shells under different external excitations and boundary conditions is crucial for engineering applications. In this study, the free vibration behaviors of FG-CNTRC CCCSs supported by an elastic foundation are examined using the Haar wavelet discretization method (HWDM). First, by means of the HWDM, the equations of motion of each shell segment, the continuity and boundary conditions are converted into a system of algebraic equations. Subsequently, the natural frequencies and modes of the CCCSs are achieved by calculating the resultant algebraic equations. The convergence and accuracy are evaluated, and the results demonstrate that the proposed method has stable convergence, high efficiency, and excellent accuracy. Furthermore, an exhaustive parametric investigation is conducted to reveal the effects of foundation stiffnesses, boundary conditions, material mechanical properties, and geometric parameters on the vibration characteristics of the FG-CNTRC CCCS.