• Computers and Concrete
• /
• 제30권6호
• /
• pp.433-443
• /
• 2022

In the current paper, the nonlinear resonance response of functionally graded graphene platelet reinforced (FG-GPLRC) beams by considering different boundary conditions is investigated using the Euler-Bernoulli beam theory. Four different graphene platelets (GPLs) distributions including UD and FG-O, FG-X, and FG-A are considered and the effective material parameters are calculated by Halpin-Tsai model. The nonlinear vibration equations are derived by Euler-Lagrange principle. Then the perturbation method is used to discretize the motion equations, and the loadings and displacement are all expanded, so as to obtain the first to third order perturbation equations, and then the asymptotic solution of the equations can be obtained. Then the nonlinear amplitude-frequency response is obtained with the help of the modified Lindstedt-Poincare method (Chen and Cheung 1996). Finally, the influences of the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions on the resonance problems are comprehensively studied. Results show that the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions have a significant effect on the nonlinear resonance response of FG-GPLRC beams.

• Structural Engineering and Mechanics
• /
• 제88권4호
• /
• pp.355-368
• /
• 2023

Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.

• Steel and Composite Structures
• /
• 제50권2호
• /
• pp.149-158
• /
• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• Geomechanics and Engineering
• /
• 제35권1호
• /
• pp.81-93
• /
• 2023

Due to the unclear mechanism of the influence of temperature on the resonance problem of doubly curved shells, this article aims to explore this issue. When the ambient temperature rises, the composite structure will expand. If the thermal effects are considered, the resonance response will become more complex. In the design of structure, thermal effect is inevitable. Therefore, it is of significance to study the resonant behavior of doubly curved shell structures in thermal environment. In view of this, this paper extends the previous work (She and Ding 2023) to the case of the nonlinear principal resonance behavior of graphene platelet reinforced metal foams (GPLRMFs) doubly curved shells in thermal environment. The effect of uniform temperature field is taken into consideration in the constitutive equation, and the nonlinear motion control equation considering temperature effect is derived. The modified Lindstedt Poincare (MLP) method is used to obtain the resonance response of doubly curved shells. Finally, we study the effects of temperature changes, shell types, material parameters, initial geometric imperfection and prestress on the forced vibration behaviors. It can be found that, as the temperature goes up, the resonance position can be advanced.