The aim of the current paper is the probabilistic dynamic stability analysis of graphene-reinforced functionally graded porous cylindrical shells under dynamic axial loads. For this purpose, various sources of uncertainty including the material and geometrical properties of the cylinder and loading are considered. By combining a Lagrangian solution method and a semi-analytical method, some formulations are developed for determining the dynamic buckling loads of the cylindrical shells. In order to model the fluid–reservoir interaction, a semi-analytical boundary solution is used. The functionally graded porous shells reinforced with graphene platelets (FGP-GPL) are modeled with three porosity distributions and three GPL dispersions in the shell thickness based on the Halpin–Tsai formulation. The kinetic equilibrium equations of the shells are derived based on Sanders’ nonlinear theory and the higher order shear theory. Moreover, in order to solve the nonlinear dynamic equations of motion, the Newton–Raphson and the Newmark methods are combined. Finally, the results are presented in terms of the probabilistic density functions (PDFs) and cumulative density functions (CDFs) of the buckling loads. In addition, a parametric study is conducted for the effects of the different material and physical conditions on the probabilistic dynamic buckling loads of the composite cylinders. As a result, in the probabilistic dynamic stability analysis of the composite shells, the distributions of the different buckling loads may have overlaps with each other. This phenomenon indicates that in probabilistic cases, the first buckling mode of a structure is not necessarily always the dominant failure mode.

The probabilistic dynamic stability analysis of fluid-filled porous cylindrical shells reinforced with graphene platelets

Low-velocity impact response of axially moving functionally graded graphene platelet reinforced metal foam plates

In this paper, nonlinear resonance behavior of graphene platelets reinforced metal foams (GPLRMFs) plates under axial motion with initial geometric imperfections is investigated. Material properties, graphene platelets (GPLs) and foams of the plate are assumed to be symmetric with respect to the thickness direction. The Euler-Lagrange principle is employed to derive the equations of motion. Then, the Galerkin principle is applied to discrete nonlinear equations of motion, thus the nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, the single degree of freedom of Duffing equation is obtained by reducing the dimension of the five nonlinear ordinary differential equations and determined by the perturbation method. Numerical results are presented to investigate the effects of the GPLs pattern, the foams distribution, the foams coefficient, the weight fraction of GPLs, the temperature change, axial moving velocity, and the external load on the resonance problem of the GPLRMFs plates under axial motion with geometric imperfections. It can be found that axial moving velocity and initial geometric imperfection have significant impacts on the resonance phenomena. 

Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections

The theoretical modeling of a functionally graded (FG) graphene nanoplatelet (GPL)-reinforced assembled beam–plate structure resting on elastic supports is presented for the first time, and its free vibration analysis is performed. Herein, the assembled structure is modeled according to the Kirchhoff plate theory and the Rayleigh beam theory. The graphene nanoplatelets (GPLs) gradiently distribute in the beam’s radial direction and in the plate’s thickness direction, respectively. By adopting the rule of mixture and the Halpin–Tsai model, the effective material properties can be obtained. By employing the Lagrange’s equation and considering the effects of Coriolis force and centrifugal force, the coupled governing equations of the assembled structure are determined. Furthermore, the assumed modes method and substructure modal synthesis method are applied to obtain the frequencies of the assembled beam–plate structure. A comprehensive numerical investigation is carried out to discuss the influence of the structural and material parameters on the vibration behavior of the beam–plate structure.

Modeling and vibration analysis of a spinning assembled beam–plate structure reinforced by graphene nanoplatelets

Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection

An efficient method is developed to investigate the vibration and stability of moving plates immersed in fluid by applying the Kirchhoff plate theory and finite element method. The fluid is considered as an ideal fluid and is described with Bernoulli’s equation and the linear potential flow theory. Hamilton’s principle is used to acquire the dynamic equations of the immersed moving plate. The mass matrix, stiffness matrix, and gyroscopic inertia matrix are determined by the exact analytical integration. The numerical results show that the fundamental natural frequency of the submersed moving plates gradually decreases to zero with an increase in the axial speed, and consequently, the coupling phenomenon occurs between the first- and second-order modes. It is also found that the natural frequency of the submersed moving plates reduces with an increase in the fluid density or the immersion level. Moreover, the natural frequency will drop obviously if the plate is located near the rigid wall. In addition, the developed method has been verified in comparison with available results for special cases.

An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid

Vibrations of axially traveling plates partially coupled with a viscous, orthogonally flowing liquid

The buckling failure of thin-walled circular shells under local axial compression is common in engineering. This study uses the vector form intrinsic finite element (VFIFE) method to investigate the buckling behavior of thin-walled circular shells under local axial compression by introducing a multilinear hardening model, taking into account geometric and material nonlinearity. A buckling analysis program based on the VFIFE method was developed and verified by comparison with experimental results. The buckling mode and postbuckling behavior of thin-walled circular shells were studied by using the verified program. The results show that the VFIFE method with a multilinear hardening model can accurately calculate the buckling load of local axially compressed thin-walled circular shells, and effectively simulate the buckling development process, which offers great advantages in predicting the postbuckling of structures.

https://www.mdpi.com/2075-4701/13/3/564/pdf?version=1678472847

Han Wu

Papers

An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid

Vibrations of axially traveling plates partially coupled with a viscous, orthogonally flowing liquid

Buckling Analysis of Thin-Walled Circular Shells under Local Axial Compression using Vector Form Intrinsic Finite Element Method